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Application of modelling


The development and application of models in the planning and implementation of reduced and strategic-minimal tick-control strategies in Zimbabwe
Practical experiences in using models for tick control in Malawi
Application of models to screwworm eradication programs
Potential for application of current models for the improvement of helminth control: Advantages, limitations, shortcomings
Initial practical experiences in using epidemiological modelling in Costa Rica
Session discussion


The development and application of models in the planning and implementation of reduced and strategic-minimal tick-control strategies in Zimbabwe

R.A.I. Norval* and S.L. Deem

* Deceased

Department of Infectious Diseases
College of Veterinary Medicine
University of Florida
P.O. Box 110880
Gainesville, Florida 3261 1-0880, USA


Abstract
Introduction
Data used for modelling
Tick-control zones
Modelling tick-control strategies
Planning and implementing control strategies
Effects of alternate dipping strategies on the control of ticks and tick-borne diseases
Discussion
Acknowledgements
References


Abstract

Intensive dipping of cattle for tick control was introduced in Zimbabwe about 80 years ago as a control measure for East Coast fever caused by Theileria parva. The dipping policy was strictly enforced and by the mid-1950s had resulted in the apparent eradication of the more virulent forms of T. parva and the effective control of other tick-borne diseases. However, dipping was disrupted during the pre-independence war in the 1970s and large numbers of susceptible cattle died following exposure to tick-borne diseases. Since independence the costs of dipping have escalated considerably.

The epidemiological implications of and high costs associated with intensive dipping have led to a reevaluation of Zimbabwe's policy on the control of ticks and tick-borne diseases. Recent research on tick population dynamics, production losses caused by ticks, the susceptibility of different cattle breeds to tick infestation and the epidemiology of tick-borne diseases has provided sufficient data to model tick-control strategies. At the same time, the integration of tick distribution data and other variables such as climate and vegetation, by means of geographical information systems (GIS), has allowed tick-control zones to be defined. Most research has been directed towards the two most important tick pests of cattle in Zimbabwe, Rhipicephalus appendiculatus and Amblyomma hebraeum. Cost effective control strategies for R. appendiculatus have been identified and simulated using a tick population model, T3HOST. Also defined has been an economic damage threshold for A. hebraeum.

Specific costed control strategies for exotic taurine and indigenous sanga cattle have been recommended for each tick-control zone. An important potential problem has also been identified using GIS in combination with a climate-matching model, CLIMEX. Namely, large parts of Zimbabwe which are currently free of A. hebraeum are climatically suitable for the survival of this species. As a consequence there is a risk of A. hebraeum (the vector of heartwater caused by Cowdria ruminantium) spreading if dipping frequency is reduced. Notwithstanding this risk the Government of Zimbabwe has begun to implement strategies involving reduced or strategic-minimal dipping. This revised dipping policy has resulted in considerable financial savings and does not appear to have caused any marked increases in production losses caused by ticks or in the incidence of tick-borne diseases. However, the changes in dipping frequency have occurred during a period of extreme drought when tick abundance has been very low, and as a consequence it is too early to assess realistically the impact of the new strategies.

Introduction

Economically important tick-borne diseases of cattle in Zimbabwe include heartwater caused by Cowdria ruminantium, theileriosis (January disease) caused by Theileria parva, anaplasmosis, caused by Anaplasma marginale and babesiosis caused by Babesia bigemina. The control of these diseases has, for the past 80 years, been based primarily on the control of their tick vectors by dipping. Intensive dipping of cattle was made compulsory in 1914 to control East Coast fever (ECF), a virulent form of T. parva infection that had been introduced to southern Africa from eastern Africa in 1901/1902. Although ECF was considered to have been eradicated by 1954, the intensive dipping policy continued to be enforced as a control measure for the other economically important tick-borne diseases (Lawrence and Norval, 1979). Intensive dipping proved extremely effective in the control of Amblyomma hebraeum, the main vector of heartwater, and by the early 1970s the tick had been eradicated from large areas of the country (Norval and Lawrence, 1979). Control of Rhipicephalus appendiculatus, the vector of theileriosis, by means of regular dipping was the only control measure available against January disease (Lawrence and Norval, 1978). Babesiosis, transmitted by Boophilus decoloratus, and anaplasmosis, transmitted by a variety of tick species and biting flies, were also considered to be effectively controlled by intensive dipping (Matson, 1966).

The first major problem with the intensive dipping policy was encountered between 1973 and 1979, when the dipping service in the communal lands (then known as the Tribal Trust Lands) was progressively disrupted by the guerilla war that preceded independence. One million of the approximately three million communal land cattle were estimated to have died as a result of tick-borne diseases during this period (Norval, 1979). The cause of these losses was the exposure of non-immune cattle to tick-borne diseases following the resurgence of tick populations. Immunity to tick-borne diseases in many of the communal land cattle herds had been lost because effective tick control over many decades had interrupted the natural transmission of infection to young animals (Lawrence et al., 1980). The communal land cattle that survived into the 1980s were mostly immune to tick-borne diseases; endemic stability had thus replaced the instability that had existed prior to disruption of dipping (Norval, 1981a; Norval et al., 1983, 1984). The experience of the 1970s thus provided a dramatic and costly illustration of the inherent danger of creating endemic instability by intensive dipping.

When peace returned to Zimbabwe after independence in 1980, there was considerable popular pressure to restore the communal land dipping service because people had associated the cattle losses during the war with lack of dipping. Hence, for political rather than scientific reasons, intensive dipping was resumed in the communal lands in the early 1980s. Fortunately, the level of tick control achieved during those years was not such that endemic stability was disrupted on a wide scale (Norval et al., 1992a). Cost became the principle obstacle to achieving intensive dipping throughout the communal lands. The costs of acaricides, labour, transport and materials for building and maintaining dip tanks increased at a much higher rate than the prices paid for cattle and their products. In the commercial sector the increasing costs were borne by individual farmers but in the communal lands, where dipping was completely subsidized, it was the government that had to make progressively more funds available to maintain the service. By 1988/1989 the total annual expenditure by government on communal land dipping amounted to US$ 9.3 million (Z$ 18.5 million), which constituted 57% of the total budget of the Department of Veterinary Services (excluding expenditure on tsetse and trypanosomiasis control) (Perry et al., 1990a; Norval et al., 1992b)*. Perhaps inevitably, annual increases in the government's communal land dipping budget did not keep pace with cost increases and by 1984 it was clear that intensive dipping (i.e. 45 immersions per annum) could not be sustained.

* Total expenditure was derived from all costs, direct and hidden, associated with dipping. This differs from the 1988/1989 amount of Z$ 9.2 million provided by the Director of Veterinary Services, Dr. S.K. Hargreaves, which only takes direct costs into account (see Figure 1).

Since the epidemiological and economic implications of intensive dipping have become apparent, the Government of Zimbabwe has made a commitment to re-assessing the role of intensive dipping in the control of ticks and tick-borne diseases and has begun to implement revised control strategies. Modelling has played a role in the development and simulation of alternate tick-control strategies. This paper reviews the development and application of models in the planning and implementation of reduced and strategic-minimal tick-control strategies in Zimbabwe.

Data used for modelling

The development of models from which tick-control strategies can be derived is obviously dependent on the existence of relevant data. Such data were not available prior to 1980. The research required to produce the data necessary for modelling was initiated by the Government of Zimbabwe shortly after independence, and has continued until present. Significant inputs to this research have also been made by FAO/DANIDA, USAID, ILRAD and ACIAR.

Tick Population Dynamics

Research has been directed primarily towards the two most important tick pests of cattle in Zimbabwe, the brown ear tick, Rhipicephalus appendiculatus and the southern African bont tick, Amblyomma hebraeum. Studies on the seasonal occurrence of R. appendiculatus in the high rainfall highveld and A. hebraeum in the low rainfall lowveld were carried out by Short and Norval (1981) and Norval et al. (1991), respectively. The development rates, fecundity and survival of R. appendiculatus under field conditions in the highveld, as well as the survival and behaviour of the unfed stages of this species, were studied by Short et al. (1989a, 1989b). The host-finding behaviour of A. hebraeum and the role of the male-produced attraction-aggregation-attachment pheromone (AAAP) in the ecology of this species have been reported by Norval et al. (1989a, 1989b).

Production Losses Caused by Ticks

Although the primary reason for intensive tick control has been the control of tick-borne diseases, a secondary but important reason for tick control has been to prevent production losses in cattle. It was widely believed that without protection from acaricides cattle would be overwhelmed by ticks. A series of field experiments, funded by FAO/DANIDA, was therefore carried out to quantify the production losses caused by R. appendiculatus and A. hebraeum. The aim was to define damage coefficients (loss caused by the successful feeding of a single tick), which could be used in models to estimate the overall losses caused by tick infestations.

No significant production losses were found to be caused by the immature stages of either R. appendiculatus (Norval et al., 1988) or A. hebraeum (Norval et al., 1989c). However, fairly large production losses were caused by the adults of both species. These losses amounted to 4.4 g of live-weight gain (LWG) (Norval et al., 1988) or 7 g of milk (R.A.I. Norval, R.W. Sutherst, J. Kurki, J.D. Kerr and J.D. Gibson, in preparation) per engorged female with R. appendiculatus, and 10 g of LWG (Norval et al., 1989c) or 6 g of milk (R.A.I. Norval, R.W. Sutherst, O.G. Jorgensen and J.D. Kerr, in preparation) per engorged female with A. hebraeum. The relationship between infestation size and screw-worm fly (Chyrsomya bezziana) strikes were recorded for both R. appendiculatus (Norval et al., 1988) and A. hebraeum (Norval et al., 1989c). With both tick species screw-worm became a problem only when cattle were very heavily infested with the adult stage.

Tick Susceptibility of Cattle Breeds

The tick susceptibility of the indigenous (sanga) and exotic (taurine and zebu) breeds of cattle and their crosses that occur in Zimbabwe have been studied by Norval et al. (1989c), Fivaz et al. (1992) and R.A.I. Norval, R.W. Sutherst and J.D. Kerr (in preparation). The three studies yielded consistent findings; namely, that sanga breeds (Mashona and Nkoni) carry much smaller numbers of all tick species than taurine breeds. Exotic zebu cattle (Brahman) also exhibit considerable tick resistance, approaching that of the sanga breeds. Cross-bred cattle are of intermediate resistance. These findings conform with those of similar studies carried out in South Africa (Rechav and Zeederberg, 1986; Spickett et al., 1989; Rechav et al., 1991; Scholtz et al., 1991).

Epidemiology of Tick-Borne Diseases

The distribution and prevalence of babesiosis, anaplasmosis and theileriosis in Zimbabwe were recorded in serological studies carried out in the early 1980s (Norval et al., 1983, 1984, 1985). The three diseases were found to be widely distributed throughout the country. Endemic stability for B. bigemina (herd prevalence rates of antibodies of over 80%) occurred at three-fifths of the localities sampled in communal lands and on one-quarter of the commercial farms sampled. Babesia bovis, which had been introduced to Zimbabwe with Boophilus microplus from Mozambique in the 1970s, disappeared from the country along with B. microplus during the drought years of 1981-1984 (Norval et al., 1983, R.A.I. Norval, R.W. Sutherst, G.F. Maywald and B.D. Perry, submitted for publication). Antibodies to A. marginale occurred commonly in both communal and commercial farming areas, but no clearly defined association was established between detectable antibodies and endemic stability. The theileriosis study results were also difficult to interpret, as disease outbreaks occurred in some areas where antibodies were detected but did not occur in others where prevalence rates were similar or higher. The existence of strains of T. parva of varying virulence and serological cross-reactions between T. parva and the relatively benign T. taurotragi are the likely causes of these anomalous findings (Koch et al., 1988; Koch, 1990). Heartwater was not included in the surveys of the early 1980s because at that time no reliable serological test existed for the detection of antibodies to C. ruminantium. However, Norval (1981b) was able to transmit heartwater using engorged nymphs of A. hebraeum collected from healthy cattle in communal lands, providing indirect evidence of endemic stability. More recently, de Vries et al., (1993) have shown that the occurrence of antibodies to C. ruminantium in cattle in communal lands is closely linked to the presence of Amblyomma ticks.

A second serological survey was carried out in communal lands in 1991 to determine the epidemiological states that currently exist for tick-borne diseases. The sera are at present being screened for antibodies to B. bigemina and A. marginale. The results should show where endemic stability and instability exist, and so provide a guideline as to where immunization against tick-borne diseases should accompany reduced dipping frequency.

Tick Distribution, Climate and Vegetation

Data on the distributions of tick species in Zimbabwe were obtained from a series of papers published between 1981 and 1987 by R.A.I. Norval and others in the Zimbabwe Veterinary Journal and Tropical Animal Health and Production. The data were recorded during a national tick survey, conducted between 1975 and 1985.

Climatic data were obtained from the Department of Meteorological Services of Zimbabwe. Vegetation maps of Zimbabwe were supplied by the National Herbarium, Harare. The amount of vegetation cover in different seasons, agroecological zones and farming systems was derived from the satellite-derived Normalized Difference Vegetation Index (NDVI) (Lessard et al., 1990; Perry et al., 1990b). This spectral vegetation index quantifies the level of photosynthetic activity (i.e. greenness) of vegetation.

Tick-control zones

The intensive dipping policy in Zimbabwe had, since its inception, been applied with equal vigour to both high and low rainfall areas. No allowance was made for the fact that the number of tick species present on cattle, as well as overall tick abundance, decreased from high to low rainfall areas. Norval (1981a) suggested dividing the country into zones based on rainfall, and applying appropriate tick-control strategies in each zone. He defined four zones and recommended control strategies ranging from intensive dipping and immunization to control tick-borne diseases (in the zone receiving highest rainfall) to minimal tick control and the maintenance of endemic stability (in the zone receiving lowest rainfall). Perry et al. (1990a) redefined the tick-control zones for Zimbabwe on the basis of current distribution of tick-borne diseases. However, as noted by Norval et al. (1992a) the distribution of tick-borne diseases, in particular heartwater, are not static and can be expected to change with changes in vector distribution. Geographical models of potential vector distribution are therefore essential in establishing realistic tick-control zones, particularly if changes in tick-control policy or other factors such as altered land use or the translocation of wildlife hosts are likely to cause changes in the distributions of tick species.

The climate-matching model CLIMEX (Sutherst and Maywald, 1985) is being used to determine the climatic suitability of Zimbabwe for R. appendiculatus/R. zambeziensis (B.D. Perry, R.L. Kruska, R.A.I. Norval, D.J. Rogers and U. Ushewokunze-Obatolu, in preparation), B. decoloratus/B. microplus (R.A.I. Norval, R.W. Sutherst, G.F. Maywald and B.D. Perry, submitted for publication) and A. hebraeum/A. variegatum (Norval et al., in press).

The recorded distributions of R. appendiculatus, R. zambeziensis and B. decoloratus match fairly closely their predicted distributions, indicating that these species are unlikely to spread appreciably if management practices change. A limited spread of R. appendiculatus into a predicted unsuitable area did however occur during a period of above average rainfall between 1973 and 1983 (Norval and Perry, 1990), showing that CLIMEX predictions based on long-term climatic averages may be insensitive to short-term changes in climatic suitability. Rhipicephalus appendiculatus may also be absent from overgrazed habitats within areas of predicted climatic suitability, due to the destruction of the microhabitats necessary for its survival (Norval, 1977; Norval et al., 1992a). Theileriosis is therefore absent from many of Zimbabwe's communal lands that are climatically suitable for the vector R. appendiculatus.

Although CLIMEX predicts that the higher rainfall areas of Zimbabwe are suitable for the survival of B. microplus, the species has never become permanently established in the country. Norval et al., (submitted for publication) are of the opinion that the interaction of drought, the restoration of dipping and interspecific competition with B. decoloratus (Norval and Sutherst, 1986), a species which is better adapted to survive in cold and dry conditions, were the factors that contributed to the disappearance of B. microplus from Zimbabwe in the early 1980s.

CIIMEX has been of greatest value in predicting the potential distributions of A. hebraeum and A. variegatum (another vector of heartwater) in Zimbabwe. At present A. hebraeum is confined largely to the dry southern lowveld and A. variegatum to the dry northwest and Zambezi valley. Perhaps surprisingly, these are the parts of the country which the model predicts are the least suitable for the survival of the two species. Predicted climatic suitability for both species increases with increasing rainfall. The apparently anomalous distribution patterns of the species have been investigated by Norval et al., (in press). The authors have found that the current distributions of A. hebraeum and A. variegatum coincide with the distributions of the main wildlife hosts of the adults of the species. It is known that A. hebraeum, and probably A. variegatum, can be eradicated by intensive dipping of cattle if no alternate hosts for the adults are present (Norval and Lawrence, 1979). However, eradication cannot be achieved if dipped (uninfested) cattle share the same pastures as alternate hosts infested with males because attached males emit a pheromone (AAAP) that attracts the unfed nymphal and adult stages to the host on which they are present (Norval et al., 1989a, 1989b). The unfed stages are not attracted to uninfested hosts. The conclusion drawn by the authors is that A. hebraeum and A. variegatum have the potential to spread to the higher rainfall areas of Zimbabwe if intensive dipping is relaxed or if wildlife hosts are introduced to these areas (this is occurring with the increasing popularity of game ranching). In the past five years, A. hebraeum has become established at several foci in the higher rainfall areas but there has been no recorded spread of A. variegatum. Outbreaks of heartwater have been recorded in some of the newly established foci of A. hebraeum.

We believe that the concept of tick-control zones is sound but further research using GIS, which incorporates data on parameters such as the distribution of tick species, climatic suitability, vegetation (type and density), cattle density, distribution and abundance of alternate hosts, acaricide usage and disease prevalence is required to realistically define such zones. The zones defined by Perry et al. (1990a) are currently being used by the Government of Zimbabwe for planning purposes, but their usefulness will obviously diminish if or when heartwater and its vectors become widespread in the higher rainfall areas or if B. microplus and B. bovis are reintroduced.

Modelling tick-control strategies

Floyd et al. (1987) used a tick population dynamics model, T3HOST (Maywald et al., 1980), to design control strategies for R. appendiculatus for the highveld of Zimbabwe. The model was used to simulate strategies based on a three-month period of intensive tick control. The periods of strategic tick control that were predicted to be most effective against R. appendiculatus were those directed against the adult stage (December-February and January-March). Floyd et al. (1987) were also able to predict, using the damage co-efficient for R. appendiculatus, that the most cost-effective strategies are those directed against the adult stage in January, February and March. The authors based their estimations on an average tick-control cost of US$ 0.30 per animal per dipping, the value of beef at US$ 1.2 per kg and a dipping efficiency of 70%; the cattle involved were of the tick-resistant sanga breed. R.B. Floyd, J.R.A. Colborne, R.A.I. Norval and R.W. Sutherst (in preparation) have subsequently used the T3HOST model to simulate control strategies for R. appendiculatus on taurine and sanga cattle in the tick-control zones defined by Norval (1981). Their findings indicate that longer periods of strategic tick control are required to achieve cost-effective control of R. appendiculatus on taurine cattle than on sanga cattle. On taurine cattle, the longest period of strategic tick control is required in the zone receiving the highest rainfall and the shortest period in the zone receiving the lowest rainfall. On sanga cattle, no tick control at all is required in the zone receiving the lowest rainfall.

Rhipicephalus appendiculatus, which has a strictly seasonal pattern of occurrence in Zimbabwe (Short and Norval, 1981), lends itself to control by applying acaricides strategically in a given season to control a particular life-cycle stage. Amblyomma hebraeum, on the other hand, does not have a clearly defined pattern of seasonal occurrence (Norval et al., 1991) and so cannot be controlled efficiently by strategic acaricide application. Meltzer and Norval (1993) have therefore proposed the control of A. hebraeum by threshold acaricide application. The authors have defined an economic damage threshold, using the damage coefficient for A. hebraeum, where the value of the losses caused by an infestation is equal to the cost of applying tick control. Control of A. hebraeum is recommended only when the economic damage threshold is exceeded (i.e. when the value of production losses is greater than the cost of tick control). The threshold is determined by the producer price of beef (or milk) and the cost of tick control (acaricide, labour etc.). For example, when the producer price of beef was Z$ 1.63/kg (US$ 0.33/kg) and the tick-control cost was Z$ 0.29/head/dip (US$ 0.06/head/dip), the threshold was 18 standard female ticks/head/week.

At present there is little overlap between the distributions of R. appendiculatus and A. hebraeum in Zimbabwe, and so it is feasible that strategic tick control can be applied in areas infested with the former and threshold tick control in areas infested with the latter. However, strategies will have to be revised if A. hebraeum becomes widely established in areas infested with R. appendiculatus.

Planning and implementing control strategies

In 1984 the Department of Veterinary Services of Zimbabwe announced that it was abandoning the policy of intensive dipping in the communal lands (Thomson, 1985) and since that time there have been progressive reductions in the frequency of communal land dipping. In an attempt to rationalize the movement away from intensive dipping, Perry et al. (1990a) provided recommendations for alternative tick-control strategies for Zimbabwe's communal lands. These alternative strategies were:

a) Reduced dipping, involving fortnightly dipping in the summer months and monthly dipping for the rest of the year (equivalent to 21 immersions annually).

b) A combination of strategic (weekly dipping during the summer months, equivalent to 12 immersions, supplemented by natural or artificially induced herd immunity to tick-borne diseases) and minimal dipping (equivalent to four acaricide immersions) during the rest of the year.

The T3HOST simulations of the control of R. appendiculatus (described earlier) provided the theoretical basis for reduced and strategic-minimal dipping, which were aimed at achieving effective control of adults of this species during summer. Minimal (or threshold) dipping was aimed at the control of Amblyomma species, in areas that were not infested with R. appendiculatus.

For each control strategy, target populations were identified by zone, and projections of the likely consequences were made. It was assumed that there would be no significant changes in disease risk or on the effects of livestock production by moving from intensive to either of the two alternative strategies. It was also assumed that the alternative strategies would be applied after a transitional period of reduced dipping.

The costs of applying the alternative strategies, compared to intensive dipping, were projected over a 20-year period. Discounted at 14%, reduced dipping was estimated to cost 45% less than intensive dipping and strategic-minimal dipping 62% less.

The transition from intensive dipping to reduced and strategic-minimal dipping, which had already begun in 1985 out of economic necessity, has now for all practical purpose been completed. In presenting the results of a 1989 survey, conducted to determine the frequency of communal land dipping, Barrett (1991) reported the following information. 'Most dips operated for between 17 to 25 times annually. Weighted according to number of cattle presented at each dip, the average dip operated for 20.7 occasions in 1989. The average turnout at dipping days was 82 percent of the cattle census, so that for the overall herd the average number of dip treatments in 1989 was 17.0.' Since 1989 the dipping frequency has declined even further due to economic constraints and a prolonged drought, which has reduced the availability of water for dipping in many areas (S.K. Hargreaves, personal communication).

The report by Norval et al. (1992a) that Amblyomma ticks and heartwater are likely to spread into communal lands in the higher rainfall areas if dipping frequency is reduced, has been a cause of considerable concern to the Department of Veterinary Services. However, a decision has been made to continue to implement reduced and strategic-minimal dipping (S.K. Hargreaves, personal communication). The spread of Amblyomma ticks is being monitored and appropriate control measures are being applied where and when heartwater becomes a problem.

Research is being conducted in Zimbabwe by the University of Florida/USAID/SADCC/Heartwater Research Project on the development of a pheromone-based control system which is specific for Amblyomma ticks, as well as improved heartwater vaccines (Norval et al., 1992c). Progress in either or both of these areas will obviously be of considerable value in dealing with Amblyomma and heartwater problems in the future.

Effects of alternate dipping strategies on the control of ticks and tick-borne diseases

The reduced dipping frequency in the communal lands has not resulted in any obvious decline in cattle productivity due to increased tick infestation or in any increases in the reported incidence of tick-borne diseases (S.K. Hargreaves, personal communication). There has also been no apparent increase in the incidence of tick-associated screw-worm fly strikes. However, it should be noted that the reductions in dipping frequency have occurred to a large extent during a period of prolonged drought (1988-1992), which has caused tick populations to decline to extremely low levels.

Discussion

The transition from intensive dipping to reduced and strategic-minimal dipping in Zimbabwe appears to have been successful in that it has not been accompanied by obvious declines in cattle productivity due to tick infestation, increased frequency of screw-worm fly strikes or increased losses from tick-borne diseases. During the transition period, cattle numbers in the communal lands actually increased by 19.5% from 3.4 million in 1984/1985 to 4.2 million in 1990/1991 (Figure 1). However, as stated earlier, the transition has occurred during a period when tick challenge has been low due to a succession of droughts. Measurement of the overall success of the alternative tick-control strategies, in terms of cattle productivity and tick-borne disease incidence, must obviously be deferred until after several years of normal or above average rainfall to ensure that a realistic assessment is made. In the meantime, tick infestation levels and losses due to tick-borne diseases should continue to be monitored. If increased losses do occur at any time, it may become necessary to revise and modify the control strategies.

The low incidence of tick-borne diseases in communal land cattle during the transitional period also indicates that the assumption made by Perry et al. (1990a), that the transition from intensive to reduced or strategic-minimal dipping would not significantly alter the tick-borne disease risk, was correct. The endemic stability that existed in the communal lands in the early 1980s was obviously not disrupted on a wide scale by the implementation of intensive dipping between 1980 and 1984.

Figure 1. The changes in cattle populations and expenditure on tick and tick-borne disease control in the communal lands of Zimbabwe over the period 1982/1983 to 1991/1992.

To date, the most tangible benefit of reducing the frequency of dipping in the communal lands has been cost saving. During the transition period dipping costs have increased considerably, and as a consequence annual expenditure by the Department of Veterinary Services on communal land dipping has increased steadily (from Z$ 6.5 million in 1985/1986 to Z$ 15.0 million in 1991/1992) despite the reduced frequency of dipping (Figure 1). Assuming a dip tank attendance of 82% of cattle (as recorded by Barrett in the 1989 survey), the dipping cost per head has increased by 325 % from Z$ 0.04 in 1984/1985 to Z$ 0.13 in 1988/1989. According to the Director of Veterinary Services of Zimbabwe, Dr. S.K. Hargreaves, intensive dipping would have been impossible to sustain through the 1980s because of cost factors alone. This point has been illustrated in Figure 1, where the actual cost of intensive dipping in 1984/1985 (the last year that it was enforced) has been compared to the projected cost of intensive dipping in 1988/1989, when the survey on dipping frequency was carried out (Barrett, 1991). The actual cost in 1984/1985 was Z$ 5.3 million and the projected cost in 1988/1989 was Z$ 20.0 million. When the projected cost of intensive dipping in 1988/1989 is compared with the actual expenditure of Z$ 9.2 million, it can be seen that the saving incurred by the alternative strategies amounts to Z$ 10.8 million (54%). This amount saved by the combination of reduced and strategic-minimal dipping for 1988/1989 compares well with the projected savings published by Perry et al., (1990a). Hence, based on cost saving, the implementation of the alternative tick-control strategies in Zimbabwe's communal lands can be considered to have been extremely successful.

As the alternative tick-control strategies proposed by Perry et al. (1990a) were based on the results of modelling, it can be concluded that modelling has played a useful role in rationalizing tick-control policy in Zimbabwe. Although the implementation of the strategies has been somewhat haphazard and driven as much by economic reality and the availability of water for dipping as by scientific planning, the existence of a framework for change has given the Department of Veterinary Services the confidence to proceed with its policy of reduced dipping. The importance of this last point cannot be over emphasized.

The rationalization of Zimbabwe's communal land tick and tick-borne disease policy is obviously far from complete and an important role for modelling clearly exists in the refinement of the policy. For example, if the precise relationship between vegetation cover and the survival of R. appendiculatus is determined and included in a geographic model; it may be possible to further reduce dipping frequency in many overgrazed communal lands. Modelling will also be a necessity in determining how best to deal with the Amblyomma/heartwater threat to the higher rainfall areas. The question that requires an answer is whether it will be more economical to continue to exclude Amblyomma ticks by means of acaricides or to control heartwater by immunization as it spreads. Another role for modelling will be in the design of appropriate tick and tick-borne disease strategies for Zimbabwe's commercial farms, many of which are stocked with tick-susceptible taurine cattle and still practice intensive dipping.

Acknowledgements

We wish to thank the Director of Veterinary Services of Zimbabwe, Dr. S.K. Hargreaves, for invaluable assistance in preparing this paper and for making available cattle census data and annual expenditure by the Department of Veterinary Services on communal land dipping. Sharon Deem is a Howard Hughes Medical Institute Predoctoral Fellow. This study was supported in part by Cooperative Agreement No. AFR-0435A-00-9084-00 with the US Agency for International Development to the University of Florida.

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LESSARD, P., L'EPLATTENIER, R., NORVAL, R.A.I., KUNDERT, K., DOLAN, T.T., CROZE, H., WALKER, J.B., IRVIN, A.D. and PERRY, B.D. 1990. Geographical information systems for studying the epidemiology of cattle diseases caused by Theileria parva. Veterinary Record 126: 255-262.

MATSON, B.A. 1966. Epizootiology and control of the tick-borne diseases of cattle in Rhodesia. Rhodesia Agricultural Journal 63: 118-122.

MAYWALD, G.F., DALLWITZ, M.J. and SUTHERST, R.W. 1980. A systems approach to cattle tick control. In: Proceedings of 4th Biennial Conference, Simulation. Brisbane: Society of Australia, pp. 132-139.

MELTZER, M.I. and NORVAL, R.A.I. 1993. Evaluating the economic damage threshold for bont tick (Amblyomma hebraeum) control in Zimbabwe. Experimental and Applied Acarology 17: 171-185.

NORVAL, R.A.I. 1977. Tick problems in relation to land utilization in Rhodesia. Rhodesia Veterinary Journal 8: 33-38.

NORVAL, R.A.I. 1979. Tick infestations and tick-borne diseases in Zimbabwe-Rhodesia. Journal of the South African Veterinary Association 50: 289-292.

NORVAL, R.A.I. 1981a. A reassessment of the role of dipping in the control of tick-borne diseases in Zimbabwe. In: Whitehead, G.B. and Gibson, J.D., eds. Tick Biology and Control: Proceedings of an International Conference Held in Grahamstown, 27-29 January, 1981. Grahamstown: Tick Research Unit, Rhodes University, pp. 87-90.

NORVAL, R.A.I. 1981b. Heartwater in Tribal Trust Lands in southern Zimbabwe. Zimbabwe Veterinary Journal 12: 56-57.

NORVAL, R.A.I. and LAWRENCE, J.A. 1979. The control of heartwater in Zimbabwe-Rhodesia. Zimbabwe-Rhodesia Agricultural Journal 76: 161-165.

NORVAL, R.A.I. and PERRY, B.D. 1990. Introduction, spread and subsequent disappearance of the brown ear-tick, Rhipicephalus appendiculatus, from the southern lowveld of Zimbabwe. Experimental and Applied Acarology 9: 103-111.

NORVAL, R.A.I. and SUTHERST, R.W. 1986. Assortative mating between Boophilus decoloratus and Boophilus microplus (Acari: Ixodidae). Journal of Medical Entomology 23: 459-460.

NORVAL, R.A.I. BARRETT, J.C., PERRY, B.D. and MUKHEBI, A.W. 1992b. Economics, epidemiology and ecology: a multi-disciplinary approach to the planning and appraisal of tick and tick-borne disease control in southern Africa. In: Fivaz, B.H., Petney, T.N. and Horak, I.G., eds. Current Topics in Tick and Tick-Borne Disease Research. Berlin: Springer Verlag Press, 35-54.

NORVAL, R.A.I., ANDREW, H.R. and MELTZER, M.I. 1991. Seasonal occurrence of the bont tick (Amblyomma hebraeum) in the southern lowveld of Zimbabwe. Experimental and Applied Acarology 13: 81-96.

NORVAL, R.A.I., ANDREW, H.R. and YUNKER, C.E. 1989a. Pheromone-mediation of host selection in bont ticks (Amblyomma hebraeum Koch). Science 243: 364-365.

NORVAL, R.A.I., BUTLER, J.F. and YUNKER, C.E. 1989b. The use of carbon dioxide and natural or synthetic aggregation-attachment pheromone of the bont tick, Amblyomma hebraeum, to attract and trap unfed adults in the field. Experimental and Applied Acarology 7: 171-180.

NORVAL, R.A.I., FIVAZ, B.H., LAWRENCE, J.A. and DAILLECOURT, T. 1983. Epidemiology of tick-borne diseases of cattle in Zimbabwe. I. Babesiosis. Tropical Animal Health and Production 15: 87-94.

NORVAL, R.A.I., FIVAZ, B.H., LAWRENCE, J.A. and BROWN, A.F. 1985. Epidemiology of tick-borne diseases of cattle in Zimbabwe. III. Theileria parva group. Tropical Animal Health and Production 17: 19-28.

NORVAL, R.A.I., FIVAZ, B.H., LAWRENCE, J.A. and BROWN, A.F. 1984. Epidemiology of tick-borne diseases of cattle in Zimbabwe. II. Anaplasmosis. Tropical Animal Health and Production 16: 63-90.

NORVAL, R.A.I., PERRY, B.D. and HARGREAVES, S.K. 1992a. Tick and tick-borne disease control in Zimbabwe: what might the future hold? Zimbabwe Veterinary Journal 23: 1-15.

NORVAL, R.A.I., SUTHERST, R.W., JORGENSEN, O.G., GIBSON, J.D. and KERR, J.D. 1989c. The effects of the bont tick (Amblyomma hebraeum) on the weight gain of Africander steers. Veterinary Parasitology 33: 329-341.

NORVAL, R.A.I., SUTHERST, R.W., KURKI, J., GIBSON, J.D. and KERR, J.D. 1988. The effects of the brown ear tick Rhipicephalus appendiculatus on the growth of sanga and European breed cattle. Veterinary Parasitology 30: 149-164.

NORVAL. R.A.I., MELTZER, M.I. and BURRIDGE, M.J. 1992c. Distribution, economic importance and control measures for Cowdria ruminantium. In: Dolan, T.T. ed. Recent Developments in the Control of Anaplasmosis, Babesiosis and Cowdriosis: Proceedings of a Workshop Held at ILRAD, Nairobi, Kenya, 13-15 May, 1991. Nairobi: International Laboratory for Research on Animal Diseases, pp. 13-27.

PERRY, B.D., MUKHEBI, A.W., NORVAL, R.A.I. and BARRETT, J.C. 1990a. A preliminary assessment of current and alternative tick and tick-borne disease control strategies in Zimbabwe. Report to the Director of Veterinary Services (Zimbabwe). Nairobi: International Laboratory for Research on Animal Diseases, 41 pp.

PERRY, B.D., LESSARD, P., NORVAL, R.A.I., KUNDERT, K. and KRUSKA, R. 1990b. Climate, vegetation and the distribution of Rhipicephalus appendiculatus in Africa. Parasitology Today 6: 100-104.

RECHAV, Y. and ZEEDERBERG, M.E. 1986. Tick populations on two breeds of cattle under field conditions, with a note on blood components related to host resistance. In: Sauer, J.R. and Hair, J.A., eds. Morphology, Physiology and Behavioral Biology of Ticks. Chichester: Ellis Horwood, pp. 445-456.

RECHAV, Y., KOSTRZEWSKI, M.W. and ELS, D.A. 1991. Resistance of indigenous African cattle to the tick Amblyomma hebraeum. Experimental and Applied Acarology 12: 229-241.

SCHOLTZ, M.M., SPICKETT, A.M., LOMBARD, P.E. and ENSLIN, C.B. 1991. The effect of tick infestation on the productivity of cows of three breeds of cattle. Onderstepoort Journal of Veterinary Research 58: 71-74.

SHORT, N.J. and NORVAL, R.A.I. 1981. The seasonal activity of Rhipicephalus appendiculatus Neumann, 1901 (Acari: Ixodidae) in the highveld of Zimbabwe-Rhodesia. Journal of Parasitology 67: 77-84.

SHORT, N.J., FLOYD, R.B., NORVAL, R.A.I. and SUTHERST, R.W. 1989a. Development rates, fecundity and survival of developmental stages of the ticks Rhipicephalus appendiculatus, Boophilus decoloratus and B. microplus under field conditions in Zimbabwe. Experimental and Applied Acarology 6: 123-141.

SHORT, N.J., FLOYD, R.B., NORVAL, R.A.I. and SUTHERST, R.W. 1989b. Survival and behaviour of unfed stages of the ticks Rhipicephalus appendiculatus, Boophilus decoloratus and B. microplus under field conditions in Zimbabwe. Experimental and Applied Acarology. 6: 215-236.

SPICKETT, A.M., De KLERK, D., ENSLIN, C.B. and SCHOLTZ, M.M. 1989. Resistance of Nguni, Bonsmara and Hereford cattle to ticks in a bushveld region of South Africa. Onderstepoort Journal of Veterinary Research 56: 245-250.

SUTHERST, R.W. and MARYWALD, G.F. 1985. A computerized system for matching climates in ecology. Agriculture, Ecosystems and Environment 13: 281-299.

THOMPSON, J.W. 1985. Theileriosis in Zimbabwe. In: Irvin, A.D. ed. Immunization against Theileriosis in Africa: Proceedings of a Joint Workshop, Nairobi, 1-5 October, 1984. Nairobi: International Laboratory for Research on Animal Diseases, pp. 12-15.

Practical experiences in using models for tick control in Malawi

M.W. Mfitilodze

Bunda College of Agriculture
University of Malawi
P.O. Box 219
Lilongwe, Malawi

The control of ticks and tick-borne diseases in Malawi has for a very long time been governed by legislation which requires all animals within a radius of 8 km from a dip tank to be compulsorily dipped in a suitable acaricide every week throughout the year. This is carried out in over 360 dipping tanks constructed and maintained by the Malawi Government. This is uniform for the whole country where arsenic trioxide has continued to be used. In recent years it has become increasingly difficult to sustain such an intensive dipping program because of high costs of the acaricides. This, coupled with an increased awareness of the effects of chemicals on the environment, has led the Malawi Government to review its current policy in favour of cost-effective methods suitable to the different ecological zones without undue risks to the cattle industry from ticks and tick-borne diseases.

Surveys have shown Amblyomma variegatum, Boophilus microplus and Rhipicephalus appendiculatus to be the major tick species to be targeted for control, but with varying relevance in different ecological zones. After initial testing for agreement, the climate-driven computer model CLIMEX was used to map out favourability distributions for these three species in the different ecological zones throughout the whole country and this allowed potential different approaches for their control to be identified. For R. appendiculatus these approaches have been tested and refined using the computer model T3HOST and are now undergoing validation through field trials before specific recommendations can be made to the government.

Using spreadsheet models, the relative costs of using different acaricides under different dipping regimes were compared. Suitable replacements for arsenic trioxide have been suggested and the dipping regimes for their economic utilization also recommended to the government.

So far the indications are that the most economic approach to tick control in Malawi is not dipping at all in some ecological zones and limited dipping in others for the indigenous cattle and incorporation of immunization with limited dipping for cross-bred cattle kept under the smallholder production system of husbandry. However, the exact dipping regimes to be finally adopted will be determined after the field trials, at which time the government will consider changing its basic legislation on tick control.

Application of models to screwworm eradication programs

E.S. Krafsur

Department of Entomology
Iowa State University
Ames, Iowa 50011, USA

Abstract
Introduction
Knipling's model
References


Abstract

Screwworms (Cochliomyia hominivorax, Diptera: Calliphoridae) were eradicated from the United States with E.F. Knipling's 'demonstrative' model that related the relative mating proportions of wild and sterile insects to population fertility and predicted population trends in subsequent generations. Ad hoc correlations between treatments applied and experimental results obtained on Sanibel Island, Florida, in 1952-1953, Curacao, Netherlands East Indies in 1954, and the Florida mainland in 1957 provided a conceptual guide for the eradication campaigns from 1958 until 1967. Many mathematical models have since been proposed that relate pest insect population density at some future time to density, fertility, net reproduction rates, intrinsic reproduction rates, density dependent survival and frequency dependent matings at the present time. Both deterministic and stochastic formulations have been presented, but none has been adapted for use in screwworm eradication programs. A regression model, based on empirical field data, predicts frequencies of sterile matings in the target native populations given sterile fly release indices and estimates of native fly densities. This model is used in central America to help interpret field trials of new screwworm strains for mass production and release and to monitor the efficiency of sterile fly dispersal operations. Even now there is no model that predicts screwworm abundance from estimates of host animal densities, screwworm age structure, or screwworm fertilities and densities. Analysis of sterile fly release experiments, however, hints that density-dependent sterile mating rates obtain in screwworm flies, similar to those demonstrated in tsetse by Rogers and Randolph (1984).

A practical simulation model developed by Foster and colleagues at CSIRO in Canberra is used to evaluate the effects on natural populations of genetic methods of controlling sheep blowflies, Lucilia cuprina (Diptera: Calliphoridae). There also are simulation models for tephritid fruit fly pest species. In practice, however, action agencies seem usually to rely on experience and overkill to achieve goals; practical criteria, not hypothetical models, are generally used to evaluate the results. Treatments are confounded; cause and effect cannot be scientifically or unambiguously demonstrated. Thus field data about the target populations as they respond to treatments may not be collected, and much useful information is lost.

Introduction

In 1955 when Bushland, Knipling and Lindquist informally planned to attempt screwworm eradication in Florida (Knipling, 1955, 1959; Lindquist, 1955), the application of mathematical modelling to predicting the outcome of intervention was not a standard operating procedure.

But Knipling (1955) used a model that predicted trends in a 'theoretical' population of virgin female insects during generation by generation releases of sterile males. The purpose of the model was to demonstrate the principle that underlay the eradication of screwworm flies, Cochliomyia hominivorax, from Curacao, an island of 440 km² in the Netherlands Antilles (Baumhover et al., 1955), by the sterile insect technique (SIT). Taken with Baumhover and colleagues' accomplishment of eradication, Knipling's model convinced skeptical officials to support the establishment of an eradication program in Florida with results that have often been described (Baumhover, 1966; Knipling, 1959; Bushland, 1971). The mechanism of population suppression by SIT is that wild females mated to released, sterile males become inseminated with sperm bearing dominant lethal mutations and their eggs do not hatch. Sterile flies of both sexes are released in screwworm eradication programs; the irradiated females do not undergo vitellogenesis and it is assumed that they have a negligible role.

In this paper I shall relate how Knipling's model was used during the screwworm eradication campaigns in southwestern USA and Mexico. I shall also refer briefly to some other models that, in my opinion, have some bearing on operations in eradication programs.

Knipling's model

Knipling's (1955) original formulation was drafted to examine theoretical expectations and feasibility of insect control by the release of sterile males.

Given a 'stable' population closed to immigration, of uniform age structure, discrete generations, a constant per capita reproductive rate, and the release of sterile males in such a way as to achieve insemination of virgin, wild females in proportion to their frequencies relative to wild, fertile males, Knipling showed that population suppression accelerated if sterile insect releases were kept constant. A later formulation allowed reproductive success to vary with population size; a fivefold rate of increase per generation was assumed until a population reached an arbitrary, stable level, at which growth ceased. Knipling's formulation (Table 1) takes the form of a spreadsheet and can be used as such with any microcomputer and commercially available spreadsheet program. It is intuitively obvious and simple to use and therefore appealing and useful to personnel in action agencies.

This conceptual model provided the principles upon which the USDA and the Mexico-US Commission planned their eradication operations and interpreted the results. Efforts were made to reduce native populations by chemical and cultural methods. Sterile fly production was maintained at the greatest possible levels. Once a 'barrier zone' on the US-Mexico border had been established, expensive sterile fly packaging and distribution costs were reduced by packing ever greater numbers of flies, cheap to produce, in large containers and distributing them from C-45 and C-47 aircraft flying lanes set 8 or 16 km apart. For example, sterile flies were applied at low average densities and distributed in swaths 16 km apart to areas where screwworms were undetected north of the 'barrier'. Because the threat of screwworm infestation had greatly declined, vigilance was reduced and decreased the probabilities of detection. In short, every effort was made to intensify application of sterile flies to areas of greatest infestation at the expense of areas where detections were scarce and scattered; 'overflooding' was thought to be the key variable, and reliance was placed on mere numbers of sterile flies released. When such overkill tactics failed, as they seemed to do in the continuous epidemic of 1972-1976, the failure was attributed by senior program personnel to factors beyond their control. The epidemic was attributed to weather unusually favourable to screwworm survival, ranching practices that allowed many screwworm cases to go undetected and untreated, and possible genetic changes in the native populations that conferred a degree of assortative mating (Bushland, 1974, 1975). Commentators in the academic community suggested that there was production of factory-adapted flies that did not fly or 'compete' in cooler temperatures in the field (Bush and Neck, 1976).

Table 1. Knipling's model showing expected insect population sizes after releases of sterile male insects. A net per capita reproduction rate of 5x per generation is assumed.

Natural population Nt

No. sterile males released

No. Ratio, S:F

Natural fertile matings

population Nt+1

1,000,000

9,000,000

9:1

100,000

500,000

500,000

9,000,000

18:1

26,316

131,580

131,580

9,000,000

68:1

1,907

9,535

9,535

9,000,000

942:1

10

50

50

9,000,000

180,000:1

» 0

» 0

The early success of SIT generated much practical and theoretical research, including numerous mathematical models. I shall mention only a few here, but first must say that, to my knowledge, none were used in evaluating screwworm eradication operations.

Many population phenomena were ignored in Knipling's model. Naturally, scientists were interested in investigating the effects of immigration, density-dependent population growth, predation, multiple matings, etc. on SIT, but actual experiments to do so are difficult to arrange. Mathematical models, however, allow simulation and many algebraic models have been used to explore these questions.

A deterministic model and a probabilistic model that generalized the properties of Knipling's model were put forth by Costello and Taylor (1975). These workers developed their models to capture Knipling's observation that frequencies of sterile matings increase inexorably as target populations decline, providing that sterile male releases are continued. Costello and Taylor also used the Curacao field data (Baumhover et al., 1955) to develop and test their models. Model variables include an environmental carrying capacity (the 'K' in logistic population growth), net reproduction rate, initial population size, and sterile male numbers. Time is treated as a continuous variable for populations that breed continuously and have overlapping generations. The model predicts the probable mean time (in insect lifespans) to extinction. The interesting properties include a sharp threshold in the numbers of sterile males released, below which extinction will not occur and above which additional steriles have little effect. This 'threshold' between success and failure seems to have occurred in practice in Curacao and the southwestern USA. Also interesting is that reduction of a hypothetical pest population before steriles are released had no effect on time to extinction in the simulations. The stochastic formula itself is opaque, and some of its variables seem not to have been defined explicitly. Moreover, the authors wrote that the algorithm for computer simulation was difficult, so one cannot easily use Costello and Taylor's models. Prout (1978) examined the joint effects of SIT and immigration of fertile females on density-regulated populations with discrete generations. Effects of sterile male and female releases on density-dependent growth in continuous populations have also been simulated (Barclay and Mackauer, 1980).

Barclay (1982) simulated the effects of competitiveness of sterile males on sizes of fertile female populations. Density and frequency-dependent competitiveness were treated also. Horng and Plant (1992) studied the role of lek mating on control of wild populations by SIT, with particular reference to fruit flies. It is noteworthy that few of these studies made reference to field data nor were the models tested against data. What uses, if any, do field workers make of models?

An important model by Ito (1977) was predicated on logistic population growth, multiple matings, and a Poisson distribution of sterile and fertile matings. The model was developed from population data on the melon fly, Dacus cucurbitae (Diptera: Tephritidae), and was used in a very practical way to estimate the numbers of sterile flies to be released to achieve melon fly eradication on Kume Island (near Okinawa). Many more sterile males were required to achieve sterile matings than were suggested by the model. Estimates of fertility among wild females and other ecological estimates showed that sterile matings were less than expected because of mortality among the pupae and teneral adults and because sterile males did not distribute themselves spatially in such a way as to encounter wild females. Thus, Ito's model suggested that sterile fly wastage was great and provided important hints about where the problems occurred. Continuous exchange of views between modellers and field biologists before and during a project can make for much more rapid progress than working in sequence.

The sheep blowfly project at CSIRO has routinely used models to evaluate relative costs and feasibility for successful control or eradication by various genetical methods (e.g. GENCON, Foster et al., 1988). The methods include SIT, the release of strains carrying various pericentric inversions, compound chromosomes, and reciprocal translocations singly or in combination. GENCON has also been used to help interpret the results of field tests of genetical control methods (Foster and Smith, 1991).

In an active eradication program, producing sterile flies, packaging them, distributing them over vast geographical areas, following up case reports of screwworm myiasis, site inspections, and so forth, consumes most energies of an institution. Few resources were allocated to long-term research efforts. There are many possibilities to be considered when eradication progress suddenly stops; enormous pressures ensure that most effort will be devoted to 'quick fixes'. Systematic and thorough investigation often will be the method of last resort. I have already mentioned explanations for the screwworm epidemic of 1972-1976. My participation in the eradication program led me to examine critically the hypotheses favoured by the leadership and other, less appealing, explanations as well. I begin with the somewhat diffuse genetical argument that was put forth and show a working model I developed for the USDA to examine the question. This simple, empirical model says nothing about eradication or failure, but can be (and has been) used to evaluate candidate strains of screwworms for mass release and other questions that arise in day-to-day eradication campaign activities.

Natural selection would greatly favour premating isolating mechanisms between released, sterile screwworms and native flies. Premating isolation has therefore been predicted by commentators and is, even now, continuously searched for by screwworm program entomologists. Screwworm outbreaks in the southwestern USA and northern Mexico indeed have been attributed to assortative mating (Bush and Neck, 1976), speciation (Richardson et al., 1982), and climate (Readshaw, 1985). How can these be demonstrated? There is a substantial body of evidence that has an important bearing on the issue of premating and sexual isolation among screwworms.

This body of evidence is the estimates of sterile mating rates among native females, and data have been collected since 1952 with Baumhover's experiments on Sanibel Island, Florida, to more recent observations in Guatemala in 1986. Reproductive isolation between released and native screwworms should be reflected in sterile mating frequencies whatever the cause of isolation. The procedures used in these field evaluations of SIT include releasing sterile flies over large areas for many weeks. Sterile mating frequencies were estimated by the daily collection of screwworm ovipositions from penned, sentinel sheep. Hatched egg masses signify a mating between wild flies, unhatched egg masses signify matings between released males and native females. Released females do not become gravid and therefore do not oviposit.

Table 2 shows the mean observed sterile mating rates in the field unadjusted for different sterile fly release rates, target population densities or other variables. It would seem that large differences existed among strains. These data might support the idea of 'strain deterioration' (Bushland, 1974, 1975; Knipling, 1979). Are these differences related to their heritable competitiveness? An objective method of comparison would be helpful and an attempt was made to develop one (Krafsur, 1985).

Five continuous variables were recognized in attempting to compare objectively numerous field experiments involving sterile male releases. Of principal interest was the dependent variable, sterile mating frequency, Y. Independent, presumptively explanatory variables included the dose rate X1, the mean number of males released per unit area per week; missile rate X2, which is the mean number of fly cartons per unit area per week; swath width X3 is the mean distance between adjacent flight lanes; and an estimate of native population density X4. The effects of categorical, discrete variables also were investigated. These included regions in which sterile fly releases were performed and the strains of flies released. Five regions were recognized: (1) Curacao, (2) Florida, (3) the Edwards Plateau of Texas, (4) semiarid regions of Texas, Tamaulipas, Sinaloa and Yucatan, Mexico, and (5) the tropical humid regions of Mexico (Veracruz, Chiapas) and Guatemala. Data were available representing the effects of releasing 12 strains of screwworms.

Expectations in sterile mating rates are based on historical experience. The empirical model takes the form:

% sterile matings = constant + effect of region + dose effect + missile effect + swath width effect + native population density effect + error.

Regression and analysis of variance methods were used to evaluate the data and fit the model.

ARCSINE = 48.1 + REGION - 0.02(X1) + 8.8(X2) - 1.1(X3) - 19.2 LOG(X4), R2 = 0.82.

When region is ignored, R2 = 0.71. The 95% confidence limits for Y are ± 13.5.

Table 2. Average percent sterile matings observed and corrected for the effects of sterile fly dose rate, missile rate, and target population densities.

Percent sterile matings
Strain released

Uncorrected

Corrected*

A-81

41.6%

40.2%

APHIS

10.3

41.3

ARICRUZ

55.1

29.1

CH-85

26.2

24.8

DE-9

71.4

43.7

FF8

20.1

23.8

FLORIDA

43.6

46.7

KERRVILLE

46.7

30.9

009

36.7

21.6

TEXMEX

16.9

36.5

V-81

32.0

28.5

VF-84

44.7

47.6

* least square means. F = 1.41, df = 11, P = 0.23.

This provisional model incorporates all variables except strain. The effects of region (P = 0.004) and the continuous variables (P £ 0.0045) were statistically highly significant. All the variables were separately or together significantly associated with sterile mating rates. It seems that sterile mating frequencies increased as the dose rate, distance between flight lanes and target population density decreased. A high missile rate was associated with high sterile mating rates, while a high dose rate was not!

The observed sterile mating rates in different experiments can be adjusted for the effects of the continuous variables and then compared. When this was done, no strong differences were obtained among strains of flies released. It seems that strain effects were small with respect to the continuous variables. (Table 2). For many years there was controversy over strain deterioration, mating types, and geographical races, and much expense was incurred in collecting wild material, constructing new strains, and developing them for mass propagation.

The adjusted regional means were significantly different (Table 3). Ecological studies in Mexico suggest that dispersal of released flies is considerably less in well-forested areas than in open savanna woodlands (Krafsur and Garcia, 1978; Krafsur et al., 1979, 1980). Experience shows that sterile fly releases in tropical humid environments elicit lesser sterile mating rates, and this may become increasingly important as the program continues further into Central America.

The regression equation can be used to provide an assessment of program effectiveness independently of reported screwworm case incidence in domestic animals. The model provides an objective method to evaluate sterile mating frequencies by comparing them with their expectations. And it can be used to optimize sterile fly releases with respect to cost and predicted effectiveness. Like all multiple regression models based on historical observations and unplanned comparisons, predictions from applying the model should be viewed with much caution. The large error in Y testifies how limited this model is. The regression model does not predict trends in target population density. But it is interesting that when sterile mating rates estimated in the field exceed c. 70%, densities of the target screwworm flies become too low to measure (e.g. Baumhover et al., 1955; Krafsur and Garcia, 1978). Rogers and Randolph (1984) observed a likely threshold sterile mating rate in tsetse flies of c. 60-70% when fitting a density-dependent model. Of course, screwworm reproductive biology is very much different than that of tsetse. Rogers and Randolph show how to estimate changes in population density (Nt+1/Nt) given the net rate population increase (l) and an exponent b that describes the strength of density-dependent regulation (Maynard-Smith and Slatkin, 1973). Values of Nt+1/Nt for different fertility rates show that change is very sensitive to b, and only weakly sensitive to l. It is high time that some effort was devoted to understanding how density-dependent mechanisms may work in screwworms.

Table 3. Mean sterile mating rates in geographical regions as observed and as corrected for effects of continuous variables related to sterile fly releases.

Region

Observed

Corrected*

Curacao

43.2%

19.8%

Florida

44.7

43.6

Edwards Plateau

48.4

37.5

Semiarid+

35.8

41.9

Tropical Humid++

27.3

24.5

* Least square means. F = 4.77, df = 4, P = 0.004.
+ << 1100 mm rainfall annually (south Texas, Tamaulipas, Sinaloa, Yucatan).
++ >> 1750 mm rain annually (Veracruz, Chiapas, Guatemala).

The field data afford rough estimates of sterile male competitiveness in the various experiments. Coefficient c expresses competitiveness of released R to wild W males cR: W. Let the probability of sterile mating P = cR/(cR+W). This rearranges to c = PW/(1-P)R. P was estimated by the fraction of ovipositions that did not hatch, R was taken as the sterile male release rate (males km-2), and W was estimated by oviposition densities. Note that R actually is sterilized puparia stuffed in boxes and will therefore overestimate the actual number of flies surviving release. W is much smaller than the numbers of wild males because many females do not live long enough to oviposit, those first doing so on day 7 of adulthood and at three-day intervals thereafter (Krafsur et al., 1979; Thomas and Chen, 1990). Estimates of sterile male competitiveness were made for the 42 data sets. I adopted log10 (100 x c) as the estimator of competitiveness. Note that least squares regression of any function of c on sterile male density (R) is invalid, because c itself incorporates R. Pearson correlation coefficients were instead calculated and the results are set forth in Table 4.

The negative relation between sterile mating rates and dose rates observed in the multiple regression model now becomes even more emphasized (Figure 1). Competitiveness of the released males seemed to vary inversely with their abundance, as suggested in tsetse by Rogers and Randolph (1984). The positive relationship of c with missile rates and negative relationship of c with swath width shows that competitiveness is positively related to the chances of placing sterile flies near breeding sites. This confirms an explicit assumption of Knipling (1955) with regard to SIT feasibility that 'adequate dispersion of the released sterile males must be obtained'. Both experimental (Krafsur and Garcia, 1978; Krafsur et al., 1980) and observational evidence (Krafsur, 1978) and the present data suggest that the effectiveness of SIT is enhanced by maximizing the chances of putting sterile males into actual or potential breeding sites. Sterile male field trails (1952 to 1976, Curacao, Florida, Mexico and Texas) gave no evidence that sterile males disperse very far from their original release sites. Sterile females, on the other hand, move considerable distances, and it has been implicitly assumed that males do also. The overkill release strategy once used by program officials was probably counterproductive and helps to explain the 1972-1976 screwworm outbreaks. Different release methods were adopted in 1977 in Texas and 1979 in New Mexico and Arizona; progress in eradication since has been interrupted only by organizational and political matters.

Table 4. Pearson correlation coefficients between sterile male competitiveness (log[100 x c]) and other variables.

Variable

Sterile close rate

Missile Rate

Swath width

Log population Density

Correlation

-.79

0.34

-0.58

-0.29

Significance

0.0001

0.027

0.0001

0.065

Figure 1. Scatterplot of competitiveness on sterile male density from field observations in Sanibel Island, Florida, in 1952 to Guatemala in 1986.

References

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BUSH, G.L. and NECK, R.W. 1976. Ecological genetics of the screwworm fly, Cochliomyia hominivorax (Diptera: Calliphoridae), and its bearing on the quality control of mass-reared insects. Environmental Entomology 5: 821-826.

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COSTELLO, W.G. and TAYLOR, H.M. 1975. Mathematical models of the sterile male technique of insect control. In: Charnes, A. and Lynn, W.R., eds., Mathematical Analysis of Decision Problems in Ecology. Berlin: Springer Verlag, pp. 318-359.

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HORNG, S. and PLANT, R.E. 1992. Impact of lek mating on the sterile insect technique: a modelling study. Research on Population Ecology 34: 57-76.

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KRAFSUR, E.S., HIGHTOWER, B.G. and LEIRA, L. 1979. A longitudinal study of screwworm populations, Cochliomyia hominivorax (Diptera: Calliphoridae), in northern Veracruz, Mexico. Journal of Medical Entomology 16: 470-81.

KRAFSUR, E.S., HIGHTOWER, B.G. and VARGAS, M. 1980. Responses of screwworm (Diptera: Calliphoridae) populations to sterile male challenge in Veracruz. Journal of Medical Entomology 17: 235-241.

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Potential for application of current models for the improvement of helminth control: Advantages, limitations, shortcomings

G. Smith* and J. Guerrero+

* University of Pennsylvania
School of Veterinary Medicine
Department of Clinical Studies
New Bolton Center
382 West Street Road
Kennett Square, PA 19348, USA

+ MDS AGVET
A Division of Merck & Co., Inc.
Rahway, New Jersey, USA


Abstract
Introduction
Complexity as an obstacle to model building
Model validation
Beta testing
Potential for application of current models
PARABAN
Advantages, limitations, shortcomings
References


Abstract

Mathematical models are simply a means of representing and manipulating something that would not otherwise be accessible. They are aids to thought and, if properly constructed, excellent tools for communicating and explaining ideas. There have been many models for the population biology of the common trichostrongylid infections of cattle and sheep. Almost all of them have been constructed in order to design more effective strategies for parasite control. Very few of them have been widely used. There are a number of reasons for this. For example, most were constructed before the personal computer revolution and so were restricted to mainframe format. There was little need to render the models 'user-friendly' because they were used mainly by the model builder. Such models intimidate and deter those who might plausibly be called upon to interpret the results to producers (e.g. veterinary practitioners, government extension agents and pharmaceutical technical services representatives).

With the advent of battery-driven laptop computers, it has become possible to conceive mathematical models that can be taken directly to the producer. One such model is PARABAN, a model for the population biology of several common trichostrongylid nematode parasites of cattle. Experience in implementing PARABAN in South American countries and elsewhere has revealed that such models can be usefully employed to help explain parasite control strategies to producers. To be successful, the model must have a clear, 'user-friendly' screen display, it should not appear to be 'too technical' and it should present the results using local terminology and in a format that is intelligible and familiar to the user. Considerable care should be taken to allay the fears of users who are not computer literate or who might view the model as a threat to their livelihood. It should be emphasized that the model is merely a tool and that the model results represent our 'best conjecture' about what is likely to happen. Particular attention should be paid to training potential users. The limitations as well as the strengths of the model should be dealt with in detail so that the model results can be presented to the user in an appropriate context without inflated expectation or unwarranted cynicism.

Introduction

'Right Decisions'

A colleague of ours recently remarked that physical scientists do not talk about modelling, they just do it. He meant merely that modelling was such an accepted and integral part of their activity that questions of utility simply do not arise. Such is not the case in the biological sciences. It is a peculiar conceit of many in our field that the systems with which we deal are too complex to be modelled; models and modelling have to be justified on a continual basis unless the thing being modelled seems to fall with the province of the physical scientist (e.g. transmission of nerve impulses). This paper begins with the proposition that modelling is an essential adjunct to any scientific endeavor. A model is merely a way of representing and manipulating something that would not otherwise be accessible. Models are aids to thought, and it is precisely because biological scientists deal with complex systems that they require models.

The particular kinds of models that are dealt with in this paper are guides to future action, devices that assist in the decision-making process. This being the case it is worth defining at the outset what we mean by a 'right decision'. A right decision is not a decision proved correct by subsequent events but rather a decision that was arrived at by using all the relevant information in the most rational manner. Implicit in this definition is the notion that we do not know all there is to know about the system in question but that it is necessary to come to a decision anyway. The model is merely an attempt to ensure that we use what we do know in the most effective manner possible. In a thoughtful and provocative chapter on the role of models in a practical context, Botsford and Jain (1992) recount the argument between Slobodkin and May. May took the view that the 'choice was not between perfect and imperfect advice to managers but between crudely imperfect advice and no advice at all'. Slobodkin replied 'that it was by no means obvious that "crudely imperfect advice" from a supposed expert is more or less valuable than no advice at all'. But this is mere sophistry.

Managers make decisions all the time because they are obliged to. No responsible manager takes a uniformed decision and so what matters is the quality of the information. May accepts that all advice, including that engendered by models, will be imperfect. But models and the activity of modelling, by their very nature, have a better chance of providing good advice if for no reason other than that they expose all the relevant arguments in a form that is amenable to review and criticism. Nevertheless, despite the fact that modellers have faith in the usefulness of their activities, models are frequently greeted with distrust by those they are meant to assist. If models are to be applied effectively, we must dispel this apprehension. This article reviews the problem and draws in particular on our experience of implementing a model for the control of bovine helminthiasis in South America.

Complexity as an obstacle to model building

The question frequently arises whether it is even possible to build a useful model of helminth infections. A cursory examination of the literature reveals systems of bewildering complexity. Laboratory and field reports paint a picture of free-living stages that are exquisitely sensitive to variations in temperature, moisture and partial pressure of oxygen, and of a parasitic phase that still has yet to yield up even a small fraction of its secrets. Surely, the argument goes, we cannot build a useful model in the face of all this complexity. The best way to answer this is to refer to what has been achieved in the absence of a formal mathematical framework. Effective control strategies have been devised and even more effective strategies are emerging all the time even in the absence of mathematical models. This has been possible because most of what we observe in the field can be explained in terms of a relatively small number of population processes. By focussing on these simple conceptual models and ignoring the rest, it has been possible to formulate interventions that work.

Mathematical models are feasible for exactly the same reason, we are dealing with a tractably small number of very influential population processes that are easily represented in mathematical formats. But if the simple conceptual models work, why do we need mathematical formulations? The conceptual models that have led to such significant advances in parasite control as strategic dosing programs like WORMKILL (Dash, 1986) are expressed (often incompletely) as qualitative statements. Confidence in these statements grows as they are tested in field trials and forms the basis for generalizations about strategies that are likely to work in as yet untested contexts. Unfortunately, the qualitative nature of the conceptual models makes them increasingly vulnerable to criticism as the argument shifts to contexts more and more removed from those in which they were originally tested. A good example is how one might implement the prophylactic dosing strategies against bovine nematode infections that have proved so successful in the intensive, seasonal grazing systems of Europe in the extensive, year-round systems of South America. Quantitative models are less vulnerable to this kind of criticism because we can be more certain that we have taken full and objective account of all of the most relevant factors. Our confidence is based on the requirement that model performance be tested at a variety of levels. There are two principal phases to testing model performance. The first occurs during model development (model validation) and the second occurs when the model is first introduced to the users (beta testing).

Model validation

Validating realistic models turns out to be very difficult. The problem we face is the same as that encountered when trying to measure the sensitivity and specificity of a diagnostic test... what do we use as a gold standard? A useful 'rule of thumb' is that the model should generate patterns that an experienced field worker would regard as typical. The merit of this apparently subjective criterion is that the mental models of parasite epidemiology we all carry around with us are uncluttered by the nuances of fine detail. With respect to the models dealt with later in this paper, it is the major patterns and trends we are interested in, not the detail. In part this represents a deliberate compromise between precision and tractability. But, rather more, it represents a growing conviction that there is clear tendency in the literature to over-interpret the ups and downs of field data. The vagaries of chance play a far greater role in the patterns we see than most of us like to admit. Because of this, it is important to use additional criteria in the validation process. There are three main steps.

Construct Validity

The first thing to do is to make sure that the mathematics in the model adequately reflects and encompasses the known biology. One tries to make the model a comprehensive and accurate embodiment of current hypotheses about the way in which the parasites interact with their environment.

Testing Elements of the Model

Having made sure that the basic architecture of the model stands up to scrutiny, we can then examine its constituent elements. The best way to do this is to compare model output with the results of laboratory experiments. However, it is frequently the case that one has used the laboratory data in the first place to estimate the model parameters. This presents a problem because it is clearly not legitimate to use those same data in any subsequent test of model validity. Often suitable independent experiments are simply not available - but when they are, they provide a very exacting test of the model adequacy. Some examples of this can be found in the companion paper (Smith, 1992). Unfortunately, the opportunity to carry out that kind of comparison does not arise very often. Usually, one has to rely on field data, and in this case one cannot test constituents of the model. Instead, one must test the entire model.

Testing the Entire Model Against Field Data

We have already alluded to our reservations concerning the adequacy of field data as a criteria for model performance, nevertheless, a decent fit between field data and model predictions is almost the only test of model validity that wins general acceptance. It is not a very good one though. In the laboratory, we frequently have some idea about the precision and reliability of our measures. Often we can transform our counts into something approaching absolute values and we are able to take sufficient samples to be sure that we have a good estimate of the mean. That is not usually the case in the field. There we deal with relative rather than absolute measures and it is wise to be cautious about accepting the calculated means too uncritically. For example, trichostrongyle worm counts and egg counts typically exhibit highly overdispersed frequency distributions. The number of samples required to estimate the mean values accurately is far more than can be managed given normal constraints.

The problem is further compounded because we do not know quite what it is we are measuring. Studies of bovine helminthiases, for example, often involve faecal egg counts. Indeed, many studies measure no other indicator of parasite abundance. Unfortunately, very few of these distinguish between the various trichostrongyle eggs counted. This presents a problem for the modeller. Natural infections are multispecies assemblages whereas all current models of gastrointestinal infections of ruminants deal with only one parasites species at a time. The pattern of egg counts generated by the model pertains only to that species and not to the assemblage of species that is actually present. We illustrate the difficulty this presents in Figure 1. Some years ago Borgsteede (1984) undertook a study in the Netherlands in which he attempted to differentiate between the relative contribution of each species to the overall 'trichostrongyle type' egg count in infected animals. As Figure 1 shows, Ostertagia peaks quite early in the counts, whereas something like Trichostrongylus peaks much later. The qualitative differences between the curves are relatively unimportant if one species always predominates and the model happens to concern that species. But if the species are there in roughly equal numbers, or if one takes over from the other as the season progresses, a detailed comparison between observed numbers for the mixed species assemblage and predicted numbers for a single species model is impossible. Some examples in which model predictions are compared with independently obtained field data are given later in the paper.

Larvae per gram (LPG) of Ostertagia ostertagi and Trichostrongylus spp. in the feces of calves collected over successive two-week periods. The eggs were incubated and the larvae cultured to the third larval stage for identification.

Figure 1.1 Ostertagia ostertagi

Figure 1.2 Trichostrongylus spp

Beta testing

The software which implements the model is first introduced to the potential users during the beta testing phase. Beta testing has two functions: it reveals previously unrecognized flaws in model performance and it is the first phase of user acceptance.

The model must be exposed to the criticism of other modellers. This is done by means of published papers describing model architecture, conference presentations and by hands-on testing. A favourable appraisal can generate good word-of-mouth recommendations for the model; criticisms can be responded to; and errors and imperfections corrected. The next step is to approach those whose opinions influence the potential users. This includes academics, veterinarians and farming extension agents. Model demonstrations in the context of informal question and answer groups work particularly well but will not succeed unless there has been adequate preparation.

The credibility of the model often depends as much on the credibility of the presenter as it does on its own performance. Finally, the user group must be persuaded of the utility of the model and trained in its operation. Preparatory seminars and discussion groups are an essential first step here. The purpose of these sessions is to acquaint the users with the biological underpinnings of the model, its proper use, and the evidence that it does what it is supposed to do. Only then should the users get their first hands-on experience of model operations. Small, fully supervised training sessions work best. The prime purpose of the initial sessions is not to train the users in the commands which operate the model but rather to instil confidence that the model works. Inadvertent key strokes, hardware problems and the specification of unrealistic or impossible biological scenarios (not unusual amongst inexperienced users) erode model credibility very quickly. Finally, training sessions must include access to clear, written instruction manuals. Help screens are useful, but not easily utilized by those not used to computers.

It is important to request and respond to feedback at each step in the beta testing phase. It is also important to keep each group fully aware of the intended purpose of the model and this involves being very clear about its limitations as well as its strengths. Models are damaged as much by their failure to live up to inflated expectations as they are by poor performance in the face of realistic expectations.

Potential for application of current models

Models are built to some purpose. All the existing models of helminth infections of veterinary importance were constructed with a view to increasing our understanding of the population biology of the parasites, and all of them were designed to assist in some aspect of parasite control (Smith, 1992). Nevertheless, the capabilities and specificity of these models vary enormously, and deliberately so. Most deal with just a single parasite. One (PARABAN) deals with a whole family of parasites. Some models are useful only in establishing general rules for treatment, others are more sensitive to local fluctuations in climate and management and are useful in designing area-specific strategies for parasite control.

The two models we consider here address different, but linked, problems. The first model, which deals with strategies to impede anthelmintic resistance, is typical of models which address important practical issues but which are expressly written to communicate ideas to other specialists. In such cases, there is often no systematic attempt to inform those who might benefit most by the ideas generated and tested in the model. This model will serve as a contrast to the second which was written to assist in the design and communication of control strategies for bovine parasites in extensive as well as intensive grazing systems. From its initial conception, this latter model was intended to inform those who have to make decisions about how often to treat and when. Its development followed that outlined in the opening sections of this paper since it was important that the model gained acceptance at all levels of expertise. In neither of these models is there any pretense that they precisely mimic the course of events on this or that farm, but both were expressly designed to provide a rational basis for deciding between competing strategies and this they do very well.

Anthelmintic Resistance

The evolution of anthelmintic resistance is an important impediment to the economic control of gastrointestinal strongylid nematode parasites of sheep, goats and horses and there is recent evidence that it may become a significant factor in the control of gastrointestinal parasites in cattle (Smith, 1990a). We cannot expect to avoid the problems caused by anthelmintic resistance merely by replacing old drugs with new ones. We must manage anthelmintic resistance using the drugs we already have to hand. There is general agreement that regimes involving infrequent treatments of only that fraction of the host population most at risk will impede the spread of anthelmintic resistance but such a strategy may not achieve the production benefits required in the market place. As an alternative, resistance management programs involving more than one kind of anthelmintic preparation have been suggested, but the literature is replete with conflicting claims about the efficacy of each of the competing strategies. Le Jambre et al. (1978) recommended using a single anthelmintic for as long as it remained effective and then switching to an alternative; Prichard et al. (1980) recommended slow rotation of alternate drugs, a strategy that might be particularly effective if one drug selects against resistance to the other; and Dash (1986) recommended using mixtures of anthelmintics.

There have been several models which address anthelmintic resistance in parasites of veterinary importance (Gettinby et al., 1989; Barnes and Dobson, 1990; Smith, 1990a) but only one (Smith, 1990a), which was specifically designed to distinguish between sequential, rotational and simultaneous drug treatment strategies. The basic model was typical of an extensive family of similar models that have been successfully used to evaluate anthelmintic control strategies against various nematode parasites of man and his domestic animals (Anderson, 1986; Smith et al., 1987). It consisted of two coupled differential equations. The first equation described changes in the abundance of the free-living infective larvae and the second changes in the abundance of the sexually mature parasitic adults. The life cycle was direct and the parasite was assumed to be naturally regulated by a density-dependent constraint on the survival of the sexually mature stages. The model assumed that resistance to any given drug was determined by a single major gene comprising two alleles at a single autosomal locus and that resistance to drugs with different modes of action was determined by loci on different chromosomes. The assumption that resistance is determined by a single major gene is almost certainly a simplification but recent work on mechanisms of resistance suggest that the system may not be as genetically complex as once thought (Pritchard, 1990). Finally, the persistence of mutations conferring resistance, despite their deleterious nature in the absence of treatment, was assumed to be the result of heterozygote advantage operating on the survivorship of the free-living stages.

Extensive simulation studies using this model revealed that sequential and rotational strategies were very poor at impeding the spread of anthelmintic resistance. The simultaneous application of two drugs with different modes of action was always the better strategy (Figure 2). The reason is relatively simple, the simultaneous strategy works because it increases the potency of each individual treatment. Parasites resistant to drug A are killed by the simultaneous application of drug B. Unfortunately, the simultaneous strategy is more expensive than either the sequential or rotational strategies and meets with considerable consumer resistance.

The model just described has been criticized for representing the population biology of the free-living phase of the parasite life cycle in too simplistic a manner. This was a deliberate strategy to ensure the genetic mechanisms remained unobscured. Perhaps a more telling criticism is the lack of attention given to the distribution of parasite genotypes amongst the host population. Indeed, this model explicitly avoided the problem by assuming that the host population consisted of only a single host! The difficulty arises because it is unlikely that the distribution of genotypes will be identical in every host in the population and it becomes increasing difficult to estimate the frequency of the all possible mating combinations and thus the frequency of given genotypes amongst the offspring. None of the models cited above deals with this issue and the consequences of unequal distributions of parasite genotypes remain unresolved.

PARABAN

PARABAN is a model for the common trichostrongylid infections of cattle (Smith, 1990a; G. Smith and J. Guerrero, unpublished data). The principal purpose of PARABAN is to help design and communicate effective parasite control strategies. PARABAN is unique in that it uses the same model framework for each of a whole assemblage of parasites. This model exploits the finding that the population processes that regulate and control parasite abundance in the parasitic phase of the life cycle are essentially identical across all the species of interest (Smith, 1992). Moreover, it also assumed that there are negligible differences in the biology of identical species in different geographical locations. This means that if PARABAN works in the sandhill regions of Nebraska, it should also work in, for example, the Chiahuahuan deserts of Texas, the marshes of Louisiana, the Cerrado region of Brazil, the humid Pampas of Argentina or the meadows of Europe. As a result, the user interface is designed so the user can specify the details of almost all the common intensive and extensive management systems. PARABAN deals with a range of parasites (Ostertagia ostertagi, Cooperia spp., Trichostrongylus spp. and Haemonchus axei). The most studied of these is O. Ostertagi and so in order to illustrate PARABAN's potential and provide the greatest contrast of management types and climate, we present the result of two simulations: one for an intensive replacement heifer system in the Netherlands and one for an extensive cow-calf system in Buenos Aires Province in Argentina. We emphasize that the data used in the comparisons were collected entirely independently of any work on the model and so provide a true independent test of the model's value.

Figure 2. Allelic frequencies of alleles for susceptibility to two drugs following the completion of a sequential, rotational and simultaneous strategy. The same number of doses of each drug was given over the same time period in each case (Smith, 1990a.)

The Netherlands

The first trial dealt with an intensive replacement heifer system in the Netherlands (Eysker, 1986). Since Eysker logarithmically transformed his data before presentation, we have similarly transformed the results of the simulation to make the comparison easier (Figures 3 and 4). Eysker also distinguished O. ostertagi from all the other parasites present so the data shown refer to O. ostertagi alone. The trial involved groups of calves first turned out onto pasture in the spring and set stocked until housing in the autumn. One group of calves was left untreated, the other was treated once three weeks after turnout with ivermectin. Figure 3 compares observed and predicted faecal egg counts in untreated groups in 1982 and 1983. With the exception of the egg counts in 1983, the correspondence between observed and predicted trajectories is fair to excellent. The midsummer rise in pasture larval contamination is particularly clear in both years. It might not be immediately obvious why there is such a good fit for the pasture larval contamination in 1983 given the rather indifferent result we obtained for the egg counts. The reason is simply that the pattern of pasture larval contamination depends far more upon the effect of climate on the development and mortality of the free-living stages than it does on the rate of recruitment of eggs. When Eysker treated the calves early in the grazing season, he hoped to eliminate the early surge in egg output, which he most effectively did. Figure 4 shows that PARABAN predicted the same result.

Figure 3. Observed (·) and predicted (solid line) faecal egg counts and pasture larval counts in two successive years. Calves were turned out in April 1982 and May 1983 and set stocked (0.5 calves/hectare) until the end of October in each case. Data from Eysker (1986).

Argentina

Steffan and Entrocasso (1991) were interested in testing a prophylactic treatment strategy in calves in the Humid Pampas of Argentina. Postmortem analysis of the worm burdens in the control calves revealed that O. ostertagi and Trichostrongylus spp. were equally represented. The principals were treated once at weaning with fenbendazole and then three times with ivermectin 3 weeks, 8 weeks and 13 weeks later. The principals and controls were maintained on separate pastures. Pasture larval counts and faecal egg counts were carried out at regular intervals. The results are presented in Figure 5. The data exhibit the variance typical of such trials and so a fitted fifth order polynomial was used to summarize the general trends and the model results compared with the fitted line. The most obvious feature was that the simulated trajectories are below the fitted lines. This is to be expected though, since the model is concerned only with O. ostertagi whereas the fitted line represents a mixed species infection. More importantly, the simulation and the fitted line follow the same temporal trajectory in both the treated and untreated groups indicating an excellent correspondence with regard to the dynamics of the infection.

It is worth emphasizing here that the same model was used in both simulations, only the climatic parameters and management details were differently specified. There were some discrepancies between observed patterns and the simulations, particularly with regard to the egg counts in the Netherlands study. This is to be expected if for no other reason than that there are limits to the accuracy with which we can specify the climatic and management details prevailing during the actual trial. What is important, and what constitutes the acid test for the model is that PARABAN worked well enough that we should have been able to predict the result of each control strategy in the absence of prior knowledge of the outcome. This is what the model was designed to do.

Advantages, limitations, shortcomings

We have presented two models for helminth parasites which seem to us to typify the potential application for helminth models. One dealt with anthelmintic resistance, probably the most important potential impediment to successful parasite control, and the second dealt with the design of effective parasite control strategies, still a contentious issue in extensive grazing systems. The first was intended to communicate information to other specialists, the second was intended to be used in producer group meetings in a variety of countries to elicit and guide discussion about the efficient use of anthelmintics. The first had only to satisfy the usual criterion of peer review in academic journals whereas the second had to undergo in addition the kind of testing and introduction procedures that are generally associated with commercial software. Our experience shows that the successful application of a model intended to be used by those other than the model builders is critically dependent on procedures that build confidence in the intended user group. The users must be confident that the model does what it is meant to do and confident that they can themselves use it effectively in the absence of supervision. We believe that the principal usefulness of these models is that they are both effective aids to thought. But both models represent a compromise between detail and tractability and this limits what it is reasonable to expect them to do.

Figure 4. Observed (·) and predicted (solid line) faecal egg counts and pasture larval counts in 1983. Principal and control calves were turned out on separate pastures in May and set stocked (0.5 calves/hectare) until the end of October. The principals were treated with ivermectin three weeks after turnout. Data from Eysker (1986).

Figure 5. Observed (·) and predicted (solid line) faecal egg counts and pasture larval counts in calves in Buenos Aires Province, Argentina. The calves were born in August 1989, weaned in March 1990 and maintained at a post-weaning stocking density of 2.7 per hectare. The dashed line is a fifth order polynomial fitted to the observed counts. Note that observed counts include both O. ostertagi and Trichostrongylus spp. whereas the predicted line is for O. ostertagi only. The principals were treated with fenbendazole at weaning and then with ivermectin 3, 8 and 13 weeks later. Data from Steffan and Entrocasso (1991). Figure redrawn from Smith and Guerrero (in press).

The model on anthelmintic resistance was designed to investigate a very specific problem and its uncluttered two-equation format reflects that very singular purpose. PARABAN, on the other hand, is considerably more complex, but here too considerable care was taken to eliminate detail unnecessary to its intended function (Smith and Guerrero, 1993). Although we have used the word prediction when referring to model results, perhaps we can express our purpose more clearly when we say that model results are intended to represent our very best conjecture about what is likely to happen given a particular set of circumstances. Neither model is intended to stand alone. Continuing experience with PARABAN buttresses our early impressions that it is a very good mimic of parasite population biology, but this not withstanding, we resist any attempt to use it uncritically and insist that its proper purpose is to elicit informed discussion about parasite control in a regional context. There is no pretense that PARABAN can accurately mimic the nuances of parasite trajectories on this or that ranch. Indeed, given our current state of knowledge, this would be a recklessly ambitious objective for any model. Nevertheless, PARABAN is able to rank competing strategies in a convincing rank order of efficacy and that, for our present purpose, is sufficient.

References

ANDERSON, R.M. 1986. The population dynamics and epidemiology of intestinal helminth infections. Transactions of the Royal Society for Tropical Medicine and Hygiene 80: 686-696.

BARNES, E.H. and DOBSON, R.J. 1990. Population dynamics of Trichostrongylus colubriformis in sheep: computer model to simulate grazing systems and the evolution of anthelmintic resistance. International Journal for Parasitology 20: 823-831.

BORGSTEEDE, F.H.M. 1984. The epidemiology of gastrointestinal helminth infections in young cattle in the Netherlands. Ph.D. thesis, Utrecht, The Netherlands.

BOTSFORD, L.W. and JAIN, S.K. 1992. Applying the principles of population biology: assessment and recommendations In: Jain, S.K. and Botsford, L.W., eds. Applied Population Biology. The Netherlands. Kluwer Academic Publishers, pp. 263-286.

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STEFFAN, P. and ENTROCASSO C. 1991. 3rd Simposio International de Actualization Parasitaria, Buenos Aires, Argentina [Abstract].

Initial practical experiences in using epidemiological modelling in Costa Rica

E. Perez

Herd Health Section
Dutch Interuniversity Cooperation Program
School of Veterinary Medicine
P.O. Box 86-3000
Costa Rica

Abstract
Introduction
Information system
Model 1. The transmission of Tritrichomonas foetus in Costa Rica: An epidemiological simulation model
Model 2. Early calfhood morbidity and mortality in Costa Rican tropical cloud-forest dairy farms: An economical analysis
Model 3. Sero epidemiological studies on anaplasmosis and babesiosis in Costa Rica: Spatial autocorrelation analysis and ecological risk assessment
Conclusion
References


Abstract

The animal production process includes production factors such as soil, feed, labour and animals. Disease as part of this process reduces potential factor sources and increases costs. To optimize production, the factors involved in the disease presentation have to be elucidated and controlled. Updated and accurate data are necessary, but in developing countries information on disease incidence, prevalence, potential causal factors are rarely available. Different sampling strategies can be used to deal with this lack of information. Cross sectional studies using convenience and random samples can be used to estimate regional or national parameters. Recently decentralized computerized farm monitoring packages have become widespread in developed countries and in some developing countries. This information can be used in epidemiological modelling to determine the consequences of various biological variables and management strategies concerning different aspects of the animal production process. Three different examples of the applications of epidemiological modelling in Costa Rica are given; in the first, convenience sampling was used to gather data on bovine trichomoniasis and a simulation model was developed. The model was validated and different control strategies tested. The second example uses data from a random national survey developed by the Ministry of Agriculture in Costa Rica. Biological and geopolitical areas were assessed as potential factors involved in the occurrence of bovine anaplasmosis and babesiosis, using spatial autocorrelation analysis and risk assessment. Finally, using prospective data a deterministic economical model was designed to evaluate the economical impact of diarrhoea and respiratory disease in commercial dairy calves. A Monte Carlo simulation was applied to the model to determine the range of potential outcomes in an average farm with 25 calves.

Introduction

Changing global trading patterns, such as the free trade between Mexico, USA and Canada, is demanding higher production efficiency and quality of agricultural production in the Central American area. At the same time, there is a demand that farming activities encourage sustainable ecological and socioeconomic development.

This ecological and economical situation is forcing livestock production systems in Costa Rica to intensify in order to allow reforestation of degraded areas and still produce sufficient food for a rapidly increasing population. It is in this context that a joint effort between the production, academic and official sectors is necessary to improve the efficiency of natural, human and capital resources in livestock production systems. I will address in this paper the role of modelling in our project in developing of knowledge, information, resources and tools to optimize the Costa Rican livestock production systems. First, there is a brief description of the development of a farm monitoring system in pilot projects (under the control of the unit). An illustration of modelling as a tool in the farmer's decision-making process and in our research activities is then provided.

Information system

The information system was established in a decentralized, farmer-oriented manner, and comprised a data collection and processing unit using a personal computer and VAMPP software (Noordhuizen, 1984). This provided farmers with a user-friendly recording system and immediate feedback of information to support farm management. Farms were visited on a weekly basis by technicians of the pilot projects, when information from the farmers' daily report was entered in a portable computer and processed, providing the farmer with management action lists. This procedure gave appropriate and timely information to the farmer in terms of quantity, quality and format and provided our unit with validated and standardized data. The feedback stimulated the farmers and farmers' advisors for continuation and correction of incomplete data.

The information was centralized and the resulting databases allowed individual (animal), aggregate (herd) or area (region) analyses, limited by production, health and reproduction criteria and other variables such as breed, body condition, parity, etc. This procedure was very useful for applied epidemiology research to support programs in herd health and generate statistics of the region. Information was also generated for extension, teaching and research. It was in this area where the epidemiological modelling was a useful tool. Modelling was applied to define research objectives and current knowledge of the production systems. It also was a helpful tool to identify significant gaps in knowledge.

User Characteristics

A total of 30 stations (computers with software) were using the system. Sixteen of these were owned by farmers servicing their own farms, six stations were administered by veterinary practitioners and eight stations were operated by farmer organizations, technicians or other farm consultants.

All microcomputers were used to run other specific applications (accounting) or non-farming applications (spreadsheets, word processing, etc.). All non-farmer VAMPP stations gave other services to the farmers such as emergency attention, veterinary visits, extension programs or general services (sale of veterinary drugs, nutritional advice, etc.). Several brands of computers (17 PC-AT compatible and 13 PC-XT compatible) with a wide range of configurations were used. The disk space required for the package was in all cases less than seven megabytes. At 28 stations the animal health and production data was collected through farm visits or mail systems with a frequency of less than 30 days. The reports for the farms were generated with intervals of less than 30 days in 14 stations, while in the remaining stations reports were generated in periods greater than 30 days.

Table 1. Available records from the VAMPP database from 221 farms.

Types of records

Number of records

Individual milk recordings

132,122

Inseminations

52,943

Reproductive examination

42,654

Calvings

32,418

Animal identification

26,024

Drying off

10,120

Services and heats

9,597

Young stock body weights

9,192

Disease events

7,733

Culling

4,681

Body condition scores

2,351

Cows to be kept open

561

Farm Characteristics

Out of 221 farms initially approached, 192 farms were actively using the package. A farm inquiry was conducted at 132 of these farms, resulting in the following information: the information system is most prevalent in specialized dairy farms (87 farms; 66%); 42 farms were recording information from dual purpose cattle and three farms from beef (cow-calf) cattle. Most of the farms (84%) were smaller than 200 hectares. All farms received technical assistance from public or private veterinarians, animal scientists or others.

The Database

The integrity of the database was evaluated and no physical or logical errors were found. The database contained information on 26,024 cows and heifers including 32,418 registered calving dates and history. Examples of other records are shown in Table 1.

Based on the information system integrated with the herd health programs in the pilot projects, modelling has been applied to aid in the decision-making process. Three examples are described in the following pages.

Model 1. The transmission of Tritrichomonas foetus in Costa Rica: An epidemiological simulation model

Introduction

Trichomoniasis, and its association with infertility has been recognized worldwide as a major cause of infertility in naturally bred cattle (Johnson, 1964; Clark et al., 1974; Wilson et al., 1979; BonDurant, 1985). In published surveys, the percentage of infected bulls varied from 7 to 15.8% (Skirrow and BonDurant, 1988; BonDurant et al., 1990). In a recent cross-sectional survey in Costa Rica, the prevalence of Tritrichomonas foetus infection was determined in bulls of two major cattle-producing regions (Perez et al., 1992). Herd prevalence rates of 6.74% (6/89) and 15.87% (10/63) and bull prevalence rates of 3.92% (6/153) and 6.22% (14/225) were detected. Within-herd prevalence ranged from 50 to 100% of bulls (mean = 83.3%; median = 75%) in one region and 12.5 to 100% (mean = 39.39%; median = 29.16%) on the other.

For infected herds, in the Tilaran region, the median herd size was one bull (range 1-2) and for uninfected herds it was three bulls (range 1-14). A median herd size of four bulls (range 1-13) was found in San Carlos both in infected and uninfected herds.

Three risk factors for bull infection were identified using binomial logistic regression for distinguishable data: age (> 4 years), breed (Bos taurus) and whether the bull was in service at sampling. The venereal nature of the disease and the high prevalence indicated that trichomoniasis could have a serious economic impact on cattle production in Costa Rica.

Model Construction

Stella software was used to simulate the transmission and persistence of T. foetus in dual purpose and cow-calf herds. A flow diagram of the typical cow-calf production system in Costa Rica, including a subsystem of bovine trichomoniasis, was constructed (Figure 1). A combination of the Reed-Frost model for the transmission and Anderson and May model for the duration of infection and immunity was used based in the following assumptions:

· The simulation covered 96 weeks.

· There are three groups of susceptible animals (first calving heifers, cows with a calf suckling and open cows), all included into the category of susceptible cows in the model.

· There is no seasonal breeding.

· The annual mortality rate is 10%.

· The annual culling rate is 15%.

· It was assumed that 10% of the herd culling rate was in infectious cows due to infertility, and 5% was in immune cows due to other causes.

· The infection rate was calculated using the Reed-Frost equation.

· An infected cow stayed as a diseased animal during three oestrus cycles (nine weeks) (Abbitt, 1980).

· A cow lost her immune status beginning at the 5th week until the 80th week (Clark et al., 1983). In the model, this was assumed to occur randomly between 5 and 80 weeks.

· Bos taurus bulls are the predominant breed in dual purpose herds, and have a 4.58 times greater odds of being infected with T. foetus (Perez et al., 1992), also the B. taurus bulls accomplished an increased number of matings in the same period of time as compared with B. indicus bulls (Galina and Arthur, 1991).

· The effective mating contacts were assumed to be random, being one to five in B. taurus and one to two in B. indicus.

· Cows are equally susceptible to infection.

· Prevalence of T. foetus infection is consistent with field observations for these herds (Perez et al., 1992).

Figure 1. A flow diagram depicting trichomoniasis in the cow-calf production system of Costa Rica.

Results and discussion

The results of the model in both types of herds (beef, dual purpose) are compatible with the behaviour of the disease under field conditions (Figure 2). Cows without previous experience of infection are highly susceptible to T. foetus infection. The susceptibility to re-infection is related to the time that has elapsed since resolution of their previous infection. The progressive loss of the immunity that follows resolution of infection in cows was demonstrated by the model. This situation leads to difficulty in tracing trichomoniasis in a herd, because the infection is persistent so that the rate of new infections is balanced with the rate of recovery. Using the model, two possible control strategies can be tested: 1, Interrupt the transmission of the disease, 2. Eliminate infection from diseased animals.

Figure 2. The prevalence of trichomoniasis in a herd predicted by the model for a 96-day period.

The first strategy can be achieved through abolishing natural mating. This possibility was not tested in this study. The second strategy, eliminating infectious cows, was not very effective. A variable number of infected cows persisted in the herds. Different prevalences and culling rates were tested and the results indicated that increasing the culling rate of infected cows was not effective. This model suggests that a good method of control of trichomoniasis is reducing the transmission through the control of the bull infection and cull only non-pregnant cows.

Model 2. Early calfhood morbidity and mortality in Costa Rican tropical cloud-forest dairy farms: An economical analysis

INTRODUCTION

Although of primary importance for the farmer and the herd health practitioner, the economic loss associated with calf morbidity and mortality in Costa Rica is unknown. Decision analysis is a technique designed to approach decision-making under conditions of uncertainty. For this reason it is inherently adapted for herd health problems. One form of decision analysis, decision-tree analysis, is suitable for solving sequential problems. The components of a decision tree are alternatives, probability values for the outcomes resulting from various decisions, and the monetary value associated with these outcomes or decisions.

The economic aspects of diarrhoea, respiratory disease and death in calves from birth to the third month of age in dairy farms in a tropical cloud forest environment was evaluated using a decision-tree structure.

MATERIALS AND METHODS

Study Population

Dairy farms

The entire northwestern milkshed of the central plateau (San Jose and surrounding area, Poas Pilot Project) was selected for this study. The farms were selected for study if they had more than 10 milking cows, if female calves were raised on the premises and if the owner was willing to cooperate.

Data Collection

A standardized wall chart was provided for prospective recording of events for the 42 out of the 52 participating farms. Only live female calves seen by the owner, calf keeper or manager were considered and individual information for each calf was recorded during the first 90 days of life, including death and clinical disease events. Data collection started in February 1987 and ended in May 1988. Of the 1116 female calves born during the study, 928 were Holsteins and 188 were Jersey. Of all calves born, 41.2% were born during the dry season and 58.8% during the rainy season. A description of the calf-management variables and its association with morbidity and mortality on the 42 farms has been presented elsewhere (Perez et al., 1992).

The Disease Model

The model contains the probabilities that a calf will have scours, respiratory disease or die in a given age interval. All the assumptions and probabilities were drawn from a previous prospective study (Perez et al., 1992). Any calf can follow one of two routes: survival or death, with the probability of being in one of these states being conditioned on having followed a certain pathway. The decision-tree therefore was formulated to evaluated the different pathways and monetary values associated with them. There were five 'decision' nodes for the scour model and four nodes for the respiratory disease model: breed node (Holstein or Jersey); the disease node (respiratory disease, yes or no and diarrhoea, yes or no); the treatment node; second event of diarrhoea node and the treatment for the second episode of diarrhoea. The diagram was initiated when the calf was born and each branch terminated when the calf died or survived to three months of age. For the calf, each event (disease or no disease, death or no death) was associated with a certain probability and a economic value. The expected monetary value for a given event was calculated as the product of the probability of the event and its associated economic value. Thus the model provides an estimate of the economic return per calf in each of the possible pathways that can be followed. The expected monetary values (or expected monetary loss) of each possible outcome is then the sum of the products of the monetary value (loss) of each outcome and the probability of that outcome occurring. Using the tree, it is possible to determine the 'optimal path' that a calf can have, given the occurrence of a preceding event. This method is referred to as a folding-back procedure. When all possible paths are included it is possible to determine the economic cost associated with them.

Conditional Probabilities

The respective conditional probabilities of first scour presentation and respiratory disease were assessed using a Cox Proportional Hazard method, stratified by breed. Each model used the potential risk factor associated with the outcome as covariate. The conditional probability for second scour presentation was assessed using PROC FREQ in SAS (SAS, 1989) for the calves that suffered a second episode of diarrhoea. The conditional probability of death given first scour was also assessed with the Cox method and the conditional probability of death given two episodes of diarrhoea was assessed with PROC FREQ. The respective probabilities for respiratory disease or death given a respiratory disease were assessed using Cox Proportional Method.

Economic Values

The average price of a female calf at 12 months of age in these farms was estimated to be $850. Input costs were estimated as $85.65 for feed costs (milk for three months plus some roughage and mineral salts) and $33.60 for non-feed cost (labour, bedding, equipment). This resulted in a net value of $730.75 and an average monthly return of $60.7 totalling $182.69 in three months. For purposes of the model the net return of a female calf was considered to be $185. Fixed costs were not considered. The first diarrhoea presentation is a mild form of scours. It is treated by removing the milk and feeding only water and electrolytes with activated charcoal. The cost for the three-day treatment for diarrhoea was calculated at $2.50. Repeated episodes of diarrhoea increased the cost to $5.00.

The cost associated with respiratory disease in these herds was calculated to be $ 10.00, due to intensive antibiotic therapy for five days; some cases are also treated with expectorants and electrolytes. No reduction in weight gain was assumed for either diarrhoea, or respiratory disease unless the animal died.

Application of the Model

A deterministic model was run to evaluate the average or expected return per calf. To model the range of potential outcomes, a stochastic Monte Carlo simulation was used considering an average sized farm with 25 calves.

RESULTS AND DISCUSSION

To perform the economic analysis for the clinical events during the three-month study period, we divided it into sub-periods that represented better the biological reality, using the periods of higher incidence of diarrhoea or respiratory disease for calculation of conditional probabilities. However, to fit any particular problem the nature of these periods can be changed.

The crude incidence rate in the 90-day period for diarrhoea was 36.6%, and mortality was 4.8%. Seasonal differences between morbidity and mortality rates were not statistically significant. Calves were at highest risk of scours during the first two weeks of life. In a previous study in these herds Escherichia coli+K99 and rotavirus were isolated, and both agents are associated with diarrhoea during this age. The highest risk for respiratory disease occurred between the third and sixth week in life in Holsteins and the third to fourth week in Jerseys and in both breeds decreased with increasing age.

The average total expected return in surviving calves ranged from $167.70 in the best scenario of a calf suffering one episode of diarrhoea to the worst scenario of $136.80 with a calf suffering two episodes of diarrhoea. The range of potential loss varied from $17.7 to $48.2 per calf. In the respiratory disease model the losses ranged from $28.5 to $32.2. However, the above figures are deterministic and average expected values. In order to examine the range of potential outcomes it will be necessary to make a stochastic model. Using random probability values, the individual animals can be simulated through the tree and summarized according to the monetary value of the path and the number of times that the path was taken. In the best scenario, a calf without diarrhoea and surviving the study period occurred 12.46 times (51%). The worst scenario (death of the calf) occurred 3.4% of the times with a loss that ranged from $185 to $192.50, depending on the number of episodes of diarrhoea. One case of diarrhoea occurred in 38% of the calves with a given a loss of $2.5. Two episodes of diarrhoea occurred in 7% of the calves with a loss of $7.5. In the respiratory disease model, the best path of surviving without respiratory disease happened 92.6% of the time; the worst scenario of total loss (death) happened 2.7% of the time giving a loss of $195. A calf with one episode and surviving happened the 4.7% of the times.

Management is dynamic and complex and therefore its impact must be constantly evaluated. The herd health practitioner must evaluate his/her recommendations for a preventive protocol in calf health and growth on an economical basis. The use of a suitable model like the one described in this report can make the evaluation of the economic impact of morbidity and mortality rates in the dairy farm much simpler and serve to evaluate the herd health protocol. In this situation, the economic loss due to mortality and to calves suffering two episodes of diarrhoea are the worse scenarios given. Combining the information given by these models with the risk assessment performed by epidemiological studies will give the practitioner the tools for economically optimal husbandry advice to the farmer in raising the young stocks. For example in our case, raising Holstein calves in single pens with wood-slat flooring showed a positive economical impact in these dairies by a reduction of the losses due to calf mortality and treatments. The greatest restriction of these models is if no valid up-to-date data exists. In this case, they will be inaccurate and not reflecting the actual situations of the farms under various management systems.

Due to that reason an accurate on-farm surveillance system in combination with a strong analytical epidemiological interpretation is necessary. Finally the simplicity of the tree structure and the analysis performed here makes it easy to demonstrate to the farmer the attention that is necessary in the calf rearing.

Model 3. Sero epidemiological studies on anaplasmosis and babesiosis in Costa Rica: Spatial autocorrelation analysis and ecological risk assessment

INTRODUCTION

Anaplasmosis, babesiosis and their tick vectors were studied in Costa Rica by the Ministry of Agriculture and Livestock in collaboration with FAO from 1977 to 1980. Different rates of seroconversion against anaplasmosis and babesiosis were determined, and economic annual losses due only to death of adult cattle were calculated to be US$ 64,000 (McCauley and Perez, 1980). Livestock production systems in the country vary according to ecologic life zones, natural sets of landscapes ranging from swamps to ridge tops in which equivalently weighted divisions of the three major climatic factors (heat, precipitation and moisture) are considered (Holdrige, 1967).

Ecological comparison of areas can be useful in the investigation of potential factors involved in the serological status of cattle to tick-borne diseases (Deem et al., 1993). Environmental factors could have a considerable influence over the incidence of diseases in animals (Gettinby and Byrom, 1991). In vector-borne diseases humidity, rainfall and temperature are all factors which can modify the transmission rate.

The aim of this study was to determine the seroprevalence of Anaplasma marginale, Babesia bigemina and B. bovis in Costa Rica and to study some geographical, ecological and management factors which could influence the epidemiology of the infection.

MATERIALS AND METHODS

Study Population

A serum bank, created by the National Brucellosis Control Program during 1991, was used to provide data for this study. It consisted of approximately 4000 sera collected from farms in each of the sevem provinces in Costa Rica which were selected by a stratified random sample design used by the 1982 national livestock survey. The following information was available for each serum sample: herd size, farm size, farm type (dairy, dual purpose, cow-calf) and location of the farm. Each sample was classified by ecological life zone (Holdrige, 1967). A proportional random selection by number of head within an ecological area was obtained, using an expected prevalence of 50%, an error level of 5% and a confidence level of 99.5%. A minimum sample size of 689 sera was calculated. We selected 717 sera to allow for loss, contamination or otherwise unsuitable sera (Table 2).

Table 2. Sampling distribution and seroprevalence (%) of see-sampling by ecological area, Costa Rica 1990-1991.

Ecological zone

No.

Percent

Anaplasma Marginale

Babesia bigemina

Babesia bovis

Tropical dry forest, moist transition

74

10.3

72

51

55

Tropical moist forest

180

25.1

71

56

53

Tropical moist forest, perhumid transition

10

1.4

70

70

20

Tropical moist forest, permontane transition

43

6.0

76

35

44

Tropical wet forest

37

5.2

81

67

62

Tropical wet forest, permontane transition

43

6.0

76

67

51

Permontane moist forest

20

2.8

65

55

90

Permontane moist forest, basal transition

24

3.3

66

37

83

Permontane wet forest

70

9.8

74

53

57

Permontane wet forest, basal transition

191

26.6

68

56

50

Permontane rain forest

2

0.3

100

0

0

Lower montane moist forest

3

0.4

66

0

33

Lower montane wet forest

8

1.1

87

87

87

Lower montane rain forest

9

1.3

77

78

11

Montane wet forest

1

0.1

0

100

0

Montane rain forest

2

0.3

100

100

100

Total or mean

717

100.0

72.4

55.4

54.1

Serological Assay

Sera were stored at -20 °C until tested for antibodies against A. marginale using rapid-card agglutination test as prescribed by the manufacture (Brewer Diagnostic kit, Wescott and Dunning, Inc). The indirect fluorescent antibody test (IFAT) as described by Payne and Scott (1982) was used to detect antibodies to B. bigemina and B. bovis. Results of both serological tests were recorded as either positive or negative.

Statistical Analysis

Descriptive analysis

The units of analysis were either geopolitical area (canton), ecological life zone or the individual animal. Means, standard errors, and medians were calculated using PROC UNIVARIATE in SAS (SAS, 1989). Continuous variables were categorized using quartiles. Crude odds ratios were calculated for risk factors using PROC FREQ in SAS (SAS, 1989), using the first category of each variable as the reference level. For variables with three or more levels, each level of the variable was compared with all other levels together as a reference level.

Spatial analysis

Spatial analysis can test the significance of geographical patterns in disease distribution describing them as either clustered, random or dispersed. In theory a random distribution is one in which the prevalence of an area is in no way influenced by other areas. A cluster distribution will be one in which some pattern in the location of the prevalence exists. A dispersed distribution would be one in which the prevalence is evenly and systematically distributed throughout the study areas. When binary data are available, a second order nearest neighbourhood analysis (Getis and Franklin, 1987) can be executed. With non-binary data such as continuous or ordinal values the method developed by Moran (1950) can be employed. The Moran's index or spatial autocorrelation coefficient tests two possible null hypothesis: (1) normality and (2) randomization. The normality hypothesis assumes a free sampling (sampling with replacement) and is employed when a priori probability is considered, i.e. based on information inferred from a larger area. The randomization hypothesis assumes a non-free sampling (sampling without replacement). No reference is made to outside factors. In this study the spatial autocorrelation index using the Moran's coefficient was employed to test the null hypothesis of randomization (Ebdon, 1985).

Risk assessment

Ordinary logistic regression can be used to model herd rates as binomial proportions. The use of this model requires that herd proportions are independent and binomially distributed. These assumptions can be violated by the presence of unmeasured or unmeasurable covariates such as genetics, climate and management. Thus two herds having identically measured covariates (in our case same herd size or belonging to the same life zone), may have different true rates due to differences in unmeasured covariates. This type of extra-binomial variation can be modelled by logistic regression with random effects (Curtis et al., 1993). A second assumption that can be noted is that of within-herd independence, which is likely to be violated due to lateral transmission and clustering of cases within herds. The logistic regression with random effects can also be used to model this type of data. Logistic regression analysis using a logistic binomial for distinguishable data model was performed using EGRET (SERC, 1990). In the multivariate analysis all subsets of variables (farm size, herd size, type of production system and ecological life zone) were used, the reference level for the variables with three or more classes was chosen using the lower level of each category.

RESULTS AND DISCUSSION

The seroprevalence of anaplasmosis and babesiosis are listed in Table 2. These results indicate that A. marginale, B. bovis and B. bigemina were widespread in the country. Even though these sera were originally selected as part of the brucellosis control program, the stratified random sample obtained by separating the population elements into life zone groups (strata), and then independently selecting a random sample for each strata, allowed us to obtain an unbiased estimator of the population mean and variance making this study representative of the national prevalence by ecological area. The serological tests for anaplasmosis and babesiosis are epidemiologically unrelated with the primary purpose of the sampling (Brucella abortus).

Figure 3. Distribution of sero-reactors to Anaplasma marginale in different geographic areas of Costa Rica, 1990-1991.

Transmission of the diseases studied in this work were principally by the tick Boophilus spp. (Young, 1988; Lawrence and de Vos, 1990). Anaplasmosis can occur in the absence of babesiosis with transmission influenced by other genera of ticks or other insects and mechanical agents (Callow, 1984). Differences between seroprevalences could then be explained by the favourability of certain geographical areas for the ticks and other vectors due to direct effects of the climate and vegetation on the free-living stages of the potential vectors and indirect effects of the climate on the resistance of the cattle. The latter could be the explanation of the results of the spatial analysis where the resulting statistically nonsignificant z value of 0.838 (I = 0.069), P < 0.42 for anaplasmosis, and 0.947 (I = 0.083), P < 0.94 for B. bigemina failed to reject the null hypothesis of randomness, implying a random distribution for seroconversion against A. marginale and B. bigemina. On the other hand the z value of 2.314, P < 0.03 for B. bovis (I = 0.235) indicated a clustered distribution for seroprevalence against B. bovis. Possibly bordering cantons shared similar ecological and management factors favourable to the transmission of B. bovis (Figures 3, 4 and 5).

The results of the spatial analysis were corroborated by the risk assessment using the random effects models. With one exception, no statistically significant association was found between any of the farm characteristics under study or geographical area and the seroprevalence of A. marginale, or B. bigemina. Only medium size farms (76-150 heads) had an increased odds of seropositivity of B. bigemina (OR = 2.56, 95% CI of 1.13, 5.82). These results suggest that Costa Rica is a homogeneous, endemic environment with respect to transmission of these infections (Mahoney and Ross, 1972).

Figure 4. Distribution of sero-reactors to Babesia bigemina in different geographic areas of Costa Rica, 1990-1991.

However for B. bovis two ecological areas, Premontane Moist Forest transition to Basal (PMFB) and Premontane Moist Forest (PMF), were associated with a significant higher seroprevalence. The PMF showed an odds of 11.8 and PMFB an odds of 15.3 respectively agreeing with the spatial analysis of clustered presentation (Figure 5). The Tropical Moist Forest showed a P-value of 0.07 and a protective odds ratio of 0.09. These three ecological life zones covered 24 of the 52 cantons of the country, with areas of high and others of low seroprevalence as shown by the spatial analysis (Figure 5). There are differences of maintenance transmission thresholds between species of Babesia, given by the tick bites per day, infection rates in cattle and inoculation rates from differences in the transovarial transmission rate. Babesia bovis is transmitted to cattle by infected larvae (Rick, 1964), and B. bigemina is transmitted by nymphs and adults (Rick, 1964; Dalgliesh et al., 1978). Inoculation thresholds for B. bovis vary from one geographical location to another depending on the tick activity. On the other hand inoculation thresholds in B. bigemina vary less from one location to another (Haile et al., 1992). These differences in thresholds can create as in our case zones of risk (Smith, 1983) where the cattle would be in danger of suffering the disease. Smaller farms (< 40 ha) showed an increased odds of infection as well as farms with more than 40 head, apparently indicating that farms with larger stocking rate (heads/ha) has an increased odds of seroconversion.

Figure 5. Distribution of sero-reactors to Babesia bovis in different geographic areas of Costa Rica, 1990-1991.

These results suggest two foci of seroconversion in the country for B. bovis. One is located mainly in the province of Guanacaste (dry pacific region) where cow-calf enterprises predominates. The annual precipitation in this region ranges from 1000 to 2000 mm, and the average temperature is 24 °C. The other is located in the lowlands of the provinces of Alajuela, Heredia and Limon (Tropical Moist Forest, low seroconversion area) with an annual precipitation of 2000 to 4000 mm and temperatures higher than 24 °C degrees. In this region, dual-purpose and milk enterprises are common.

Conclusion

It is evident for us that in the stage that we are in now the use of modelling has a direct benefit for research and developmental work. Until now we are testing if our field investigations are appropriate for modelling. We believe that the data recovered in our pilot projects are good enough for a clear understanding of the behaviour of the production systems, allowing a detailed knowledge for the model construction. Our next steps will be:

· To develop and validate models in different components of the productions systems (i.e. young stock rearing, reproduction) to determine economical optimum.

· To generate methodologies that can be used by the farmers or advisers.

· To generate methodologies for the researchers.

· To estimate economical losses and potential causal factors.

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Session discussion

Several speakers stressed the importance of validating models. However, it was stressed that careful assessment should be exercised as a model that fails validation under some circumstances might be a very good model under other circumstances, and may raise important questions on the biological processes involved. Validation starts when models are constructed and includes three steps: a) verification of the code in the program; b) verification of the basic output (does it match the expectations?); c) sub-system evaluation, test subsystems of the model (e.g. it should be possible to reproduce properties which have not been forced by the model). Finally it is important that field data are used for testing the model. It was recommended that statisticians should assist in developing validation methods, as there is no difference in principle between testing hypotheses and testing models. It is also useful to compare different models for the same subject, to see to what extent model behaviour depends on the modelling technique/architecture as opposed to the biological assumptions. Validation must include training of the intended user in order that they can properly assess comparisons.

Concern was expressed about the availability of current models for ticks and tick-borne diseases, and the importance of having access to the structure of existing models before developing new models was stressed. A feeling was expressed that where models cannot be made public, scientific principles are violated. The question was raised as to whether models which are expected to be used in the public domain should be made widely available with full documentation. It was, however, pointed out that some models are commercial products and one cannot always expect complete documentation. However, it is possible to make such models accessible, through the provision of user control over variation in parameter values. The main concern raised was that the user might pervert the model, and misrepresent its intended use.

It was discussed as to whether a general model for tick control was a realistic proposition. Experiences from Zimbabwe were tabled; they indicated that the losses caused by ticks are often due to a single species in a certain area, and that regional and local differences may not be well accommodated in a general model.

For the development of new models, many people considered it important that the modellers work in close collaboration with the field workers, particularly in the stage of study design otherwise contradictions between model behaviour and field observations cannot be dealt with in a timely manner. When existing models are used it is important that the user contact the developer for guidance. Funding agencies should make sure that the modelling component is included in the grant applications.

The question of integration of the various kinds of models on livestock production, parasitic diseases etc. was brought up; several modellers considered that although it is technically feasible, it is a risky business unless there is very close collaboration between the different developers. An option is to rewrite someone else's model and integrate a livestock model with say a disease model. Concern was expressed that unknown interactions could be a limitation but model validation might reveal such unknown interactions.

The cost of and funding for modelling was discussed and a general feeling was expressed by the modellers that few people were aware of the costs involved and users often expected to get the models free of charge. The opinion was expressed that costs could be reduced by making more use of adapting existing models.

The potential benefit of having a list of models and a roster of modellers was discussed. It was felt that a roster of modellers would be useful. It was also proposed that an electronic bulletin board should be established in order to exchange information (e.g. Net-News). Doubt was expressed as to whether this would work in the field but several participants reported successful experiences with e-mail in remote places, and it was considered that the trend to increased use of e-mail would continue.


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