Mathematical models to assess strategies for the control of gastrointestinal roundworms in cattle: 1. Construction

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Abstract

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.

Introduction

Economic losses in the livestock industry due to infestations of gastrointestinal roundworms in cattle and sheep were estimated to be £ 46 million per annum, at a time when £ 20 million was spent annually on anthelmintics to control them (Bain and Urquhart, 1986). Now it is estimated that over £ 33 million is currently spent annually by farmers in Great Britain on anthelmintics to control gastrointestinal roundworms and liver fluke in cattle, sheep and pigs—of which almost £ 20 million goes on endectocides and boluses (National Office of Animal Health, 2004). These values take no account of the labour costs involved in gathering stock and administering the anthelmintics to them.

Earlier surveys of anthelmintic usage by cattle and sheep farmers suggested that farmers did not use anthelmintics at the correct time of year to obtain maximum returns from their investment (Michel et al., 1981). More recent surveys of dairy farms in UK, Germany and The Netherlands indicate how modern prophylactic worming practices have been introduced using slow release and pulsed release boluses, as well as pour-on and injectable long acting wormers (Stafford and Coles, 1999, Schnieder et al., 1999, Borgsteede et al., 1998). It is still important that farmers know the appropriate worming system for their farm, particularly under the severe economic pressures that are affecting livestock farmers. There are many more wormers to choose from, making it even more difficult for farmers to select the appropriate strategy. Infections commonly occur with no obvious signs: the degree of parasitism on a particular farm can vary according to weather, age of stock, pasture conditions, previous grazing history and management. It is not economic or practical for farmers to test wormers for themselves. Field trials carried out on one farm in one year to measure the effect of roundworm control on animal performance do not necessarily represent the effect such control programmes might have in other years on the same farm or at any time on other farms.

One attempted approach to this problem has been the use of mathematical models to simulate the life cycle of particular internal parasites of cattle and sheep to assess the effect of alternative control strategies. For example, mathematical models have been constructed of the life cycle and epidemiology of Ostertagia circumcincta (Paton et al., 1984), O. circumcincta and Trichostrongylus spp in sheep (Paton and Boag, 1987) and used to test the effect of anthelmintic treatment of lambs at different times in the grazing season (Thomas et al., 1986, Callinan et al., 1982).

Smith (1989) evaluated the ability of four such models to represent the parasitic phase of O. circumcincta in sheep, reported from field trials and concluded that ‘discrete time models’, either using Network Analysis (Paton and Gettinby, 1983) or difference equations (Paton et al., 1984) were able to represent pasture contamination in field situations more accurately than continuous time models using differential equations (i.e. those of Callinan et al., 1982, Smith and Galligan, 1988).

Gettinby et al. (1979) modelled Ostertagia ostertagi in cattle, using similar principles to those of Paton for sheep (Paton et al., 1984), to predict the numbers of worm larvae on the pasture and outbreaks of clinical disease as a result of this parasite. Smith et al. (1987b) built a more detailed mathematical model of the population biology of O. ostertagi in cattle using a set of difference and first order differential equations defining ‘rate of change with time of the abundance of individuals’ in various stages of the life cycle. The model was then used to simulate the course of O. ostertagi infection in groups of calves in dissimilar situations, i.e. south east England and Louisiana, USA. This illustrated the potential value of such treatments in their ‘pasture cleaning’ effect giving scope for improvements in animal production (Grenfell and Smith, 1983, Smith and Grenfell, 1985). The limitations of such models in making economic evaluations of worm control strategies was pointed out by Smith and Galligan (1988), and no such model has been constructed that is either applicable at farm level or predicts the effects of control measures on animal performance. Smith (1997) suggested that this might be due to lack of a suitable relationship between parasitism and production.

A mathematical model has now been constructed to simulate the effect of O. ostertagi in growing cattle under a variety of management conditions, in order to make predictions of the effects of pasture conditions and anthelmintic treatment on the liveweight gain of growing cattle. An economic assessment of the effect of worm control measures can then be made for individual farms and used as a basis for advising farmers on the correct use of anthelmintics. It was decided that cattle (whether beef fattening animals or dairy replacements) in their first season at grass be modelled in view of the prime economic importance of internal parasites in this class of stock.

This paper deals with the construction of this model (WORMODEL), concentrating particularly on the novel animal growth model and the interaction with the parasite life cycle model. Subsequent papers will deal with model validation and its use to assess the interactions between animal and pasture management and anthelmintic control strategies through their effect on animal performance and economic returns.

Section snippets

The models

The models were designed to look at the interactions between several parameters that might affect parasite populations and animal growth. These included: anthelmintic treatment (efficacy and duration of action and timing of treatment), pasture conditions, rainfall, temperature, stocking rate and grazing history of the pasture. By comparing the monetary value of the weight gain, or achievement of target weights, to the cost of animal handling and anthelmintic treatment, an economic response

Discussion

The need for a model or adequate field trials to allow an evaluation of the expected return from the use of anthelmintics in farm livestock was highlighted by Smith et al. (1987b), stating that it was a considerable challenge to the modeller or field worker. More recently, Smith (1997) proposed three reasons why such models involving the effect of parasitism on production had not been constructed: (1) there appears to be no linear relationship between parasitism and production loss; (2) it is

Acknowledgements

The author would like to thank Ron Watson of Cauldron Consultants for the extensive programming work required in constructing and testing the computer models.

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