The application of a simulation model to control strategies in ovine gastro-intestinal parasitism

Mathematical models to assess strategies for the control of gastrointestinal roundworms in cattle

Mathematical models were constructed to simulate the effect of Ostertagia ostertagi infections on the growth of young cattle. The equations are based on System Dynamics using the DYSMAP 2 software package in their construction. A pasture and animal growth model simulates the growth of pasture and the influences of management and climate on it; cattle feed intake and conversion into energy for maintenance and liveweight gain; the effect of the parasite burden on feed intake and utilization of energy. This model was then combined with one of the life cycle of O. ostertagi in order to determine the effect of worm burdens on animal growth rate in a range of farm conditions, such as stocking rate, grazing history of the pasture, and rainfall. By converting the resultant liveweight gain into a monetary value, an economic assessment of alternative worm control strategies can be made. In this paper the construction of the models with equations and assumptions is given in detail.

Stochastic modelling of environmental variation for biological populations

We examine stochastic effects, in particular environmental variability, in population models of biological systems. Some simple models of environmental stochasticity are suggested, and we demonstrate a number of analytic approximations and simulation-based approaches that can usefully be applied to them. Initially, these techniques, including moment-closure approximations and local linearization, are explored in the context of a simple and relatively tractable process. Our presentation seeks to introduce these techniques to a broad-based audience of applied modellers. Therefore, as a test case, we study a natural stochastic formulation of a non-linear deterministic model for nematode infections in ruminants, proposed by Roberts and Grenfell (1991). This system is particularly suitable for our purposes, since it captures the essence of more complicated formulations of parasite demography and herd immunity found in the literature. We explore two modes of behaviour. In the endemic regime the stochastic dynamic fluctuates widely around the non-zero fixed points of the deterministic model. Enhancement of these fluctuations in the presence of environmental stochasticity can lead to extinction events. Using a simple model of environmental fluctuations we show that the magnitude of this system response reflects not only the variance of environmental noise, but also its autocorrelation structure. In the managed regime host-replacement is modelled via periodic perturbation of the population variables. In the absence of environmental variation stochastic effects are negligible, and we examine the system response to a realistic environmental perturbation based on the effect of micro-climatic fluctuations on the contact rate. The resultant stochastic effects and the relevance of analytic approximations based on simple models of environmental stochasticity are discussed.

Worm control practices on sheep farms in Denmark and implications for the development of anthelmintic resistance

A questionnaire survey was undertaken on sheep farms in Denmark to obtain information on sheep management and worm control practices. The questionnaires were inserted in the June and July, 1993 issue of the Danish Sheep Breeders Journal, circulated monthly to approximately 1200 sheep breeders nationwide. A total of 183 (11%) questionnaires were returned. A second questionnaire was posted to 50 of the 183 responding farmers to examine the repeatability of responses to the first questionnaire. The majority (97%) of the 183 farmers used anthelmintics. The mean number of doses per year for lambs (< 12 months old) and adult sheep (> 12 months old) were 1.9 and 2.3, respectively. Only 42% of the farms followed predetermined drenching programmes. Live weights were determined by visual appraisal on 45% and 84% of the farms for lambs and adult sheep, respectively. In calculating anthelmintic doses for groups of lambs and adult sheep, the recommended weights of the heaviest animals were only used on only 18% and 27% of the farms respectively. Benzimidazoles were the most commonly used anthelmintics from 1986 to 1993. Eighty one percent of 94 responding farmers had been using the same class of anthelmintic for 3 or more consecutive years. Information from this study indicated lack of knowledge about worm control strategies, anthelmintic use and the problem of anthelmintic resistance among the majority of Danish sheep farmers. The majority of responses to the questionnaire were repeatable at least to a fair degree except when farmers were asked to recall anthelmintics used in past years.

Parasites, animal production and sustainable development

Ecologically sustainable development is aimed at reducing environmental degradation while enabling economic development with equity between the developed and developing worlds and between generations. Parasite control in livestock can both contribute to, and take advantage of, sustainable agriculture. This will tend towards less intensive, lower input, diversified crop and animal production with less risk of parasite-induced losses and greater opportunities for integrated control including the exploitation of grazing management. Chemotherapy will continue to play a part but the most serious problem is resistance in the target species. Except for a few isolated issues, currently used parasiticides are relatively minor contaminants of the food supply or the environment. Nevertheless, the compounds of the future will need to be narrow-spectrum, non-persistent and rapidly degraded, with convenience in the hands of the user reduced in importance. Environmentally friendly alternatives to chemotherapy, including genetic resistance of hosts, vaccines, and biological control, show considerable promise and must be pursued. Sustainable systems pose optimisation problems and more attention must be given to systems research, models and products to aid decisions. If governments are serious about sustainable development, greater support will be needed for longer-term patient, multi-disciplinary research.

Spatial distribution on pasture of infective larvae of the gastro-intestinal nematode parasites of sheep

The horizontal distributions of infective larvae on pasture grazed by sheep have been investigated. Using Taylor's Power Law it was found that larvae had a more aggregated distribution in September than August, the Law index of aggregation being 1.97 and 1.89 for the 2 months, respectively. However, at each time the degree of aggregation remained fairly constant for a range of spacings between points from 5 to 30 m. These results suggest that Taylor's Power Law could be used as a basis for devising an efficient pasture sampling strategy. More data are required, however, to determine the extent to which aggregation of the larvae varies with time of the year.

Anthelmintic resistance and the control of ovine ostertagiasis: a drug action model for genetic selection

A site-specific genetic prediction model is presented, which examines the influences of different anthelmintic treatment regimens on selecting for drug resistance within a sheep management system. The model exploits the power of modern microcomputers to integrate factors such as parasite strain, geographic location, management practice and genetic fitness to identify effective control regimens which do not lead to resistant Ostertagia circumcincta strains over a 30-year horizon. The potential use of the model as a farm level management-support tool is discussed.

Population biology of the parasitic phase of Ostertagia circumcincta

Four current models for the parasitic phase of the Ostertagia circumcincta life-cycle were evaluated with respect to their ability to represent the outcome of experimental infection studies and the population biology of the parasite in the field. Neither of the two discrete-time models was able to mimic the rise and fall in parasite numbers that characterize trickle infection experiments. When the infection rate is constant, both models predict that parasite numbers will eventually reach an asymptotic equilibrium value. This happens because both models are formulated such that parasite mortality is constant when the infection rate is constant. The two continuous-time models are able to mimic trickle infection experiments because both of them represent parasite mortality as an increasing function of the infection rate and the duration of infection. However, the continuous-time models do not adequately represent the demography of the parasitic phase in the field because neither of them takes any account of the effect of variations in infection rate from host to host on the overall mean parasite death rate.

Gastrointestinal nematode parasites and the stability and productivity of intensive ruminant grazing systems

This paper uses mathematical models, describing the transmission dynamics of directly transmitted gastrointestinal nematode parasites of sheep and cattle, to examine the impact of these parasites on the stability and productivity of ruminant grazing systems. Current models of the ecology of grass growth under grazing, and the epidemiology of trichostrongylid nematode parasites of ruminants, are combined in a formulation that captures the general features of the plant - (ruminant) herbivore - parasite interaction. The simplest case, in which herbivore numbers are constant and not food limited (the norm for many agricultural systems) is considered in detail. The effect of gastrointestinal parasitism in reducing herbivore feeding rates is shown to act as a potential density-dependent constraint on the parasite's infection rate. The process is manifested in the model as a progressive linearization of the relation between herbivore feeding rate and plant density at the parasite equilibrium. This effect acts to stabilize the dynamics of the model grazing system and significantly affects its predictions about the impact of parasite control and the pattern of host productivity. Model predictions are discussed in the light of relevant field observations, and areas for future research are identified.

Mathematical models of the population biology of Ostertagia ostertagi and Teladorsagia circumcincta, and the economic evaluation of disease control strategies

The construction and use of mathematical models of the population biology of Ostertagia ostertagi and Teladorsagia circumcincta is discussed. Simulated field trials implemented by deterministic mathematical models currently share with actual field trials the disadvantage that they convey no information concerning the risk associated with the net return demonstrated by the trial. This has important implications when it is necessary to rank disease control strategies in order of usefulness.

Population biology of Ostertagia ostertagi and anthelmintic strategies against ostertagiasis in calves

Five chemoprophylactic or chemotherapeutic strategies against bovine ostertagiasis are compared using a mathematical model of the population biology of Ostertagia ostertagi. The model offers a means of screening novel strategies prior to their further investigation in the field. Under conditions of climate and management typical of many regions in Northern temperate Europe, the model indicates that all of the tested prophylactic strategies will result in a profound reduction in the intensity of infection in grazing beef calves when compared with an untreated control group or the simple therapeutic protocol. Not all of those strategies which caused diminution in the scale of the midsummer rise in pasture larval contamination resulted in progressively less contaminated pastures in subsequent years. Moreover, the reproductive potential of the parasite is so great that the principal advantage of the 'pasture cleaning' effect that is the consequence of some protocols is not that the pasture may eventually be used to graze untreated calves but that the treated animals are subjected to a progressively smaller parasitic challenge with the concomitant pay-off in production gains.

Forecasting parasitic gastroenteritis in lambs

Incorporating estimated temperature data and assuming non-limiting rainfall, a simulation model was used to compare forecast and actual pasture counts of sheep nematode larvae over a 2-year period. The results indicate that the first possible date of the summer larval rise can be predicted up to 6 weeks in advance of its actual occurrence, enabling control measures to be planned and implemented. Rainfall variation had a marked effect on the degree of disparity between the predicted and actual timing of the rise, indicating the importance of this factor.