The Population Dynamics of Nematode Infections of Ruminants: Periodic Perturbations as a Model for Management

Abstract

We propose and analyse a model for the dynamics of directly transmitted nematode infections of ruminants which allows for the long-term effects of the annual removal of hosts. The model is a simple continuous-time formulation which captures the principal features of parasite transmission and the acquisition of immunity to infection by the host. Analysis of the simplest version of the model, which assumes a constant host population through time, indicates that its equilibrium is locally stable for feasible biological parameters. The regular removal of hosts involved in most management strategies is modelled in terms of periodic perturbations. The analysis indicates that the periodic removal of parasitized hosts corresponds effectively to a reduction in the basic reproductive rate of infection. We also demonstrate that the system exhibits a dramatic peak in parasite numbers during each grazing season at its dynamic equilibrium. This phenomenon (which is characteristically observed in real systems) is discussed in terms of the balance between acquired immunity and periodic perturbations of the parasite population.

epidemic models, nematodes, ruminants, periodic perturbations, basic reproductive rate