Parasitism and host patch selection: A model using aggregation methods

Abstract

There is a growing interest in studying the effects of parasites on the modification and evolution of hosts' behaviour. In this paper, we deal with a case of parasitism affecting the spatial pattern of host distribution. We develop a simple model with two patches, one host and one parasite. Parasites live in Patch 1, hosts live in the two patches and migrate from one patch to the other. We study the case of a migration independent of parasite density and the case of a migration dependent on density. In the two cases, we make the assumption that the choice of patch is fast, whereas the growth of populations are slow. So we use aggregation methods which are particularly adapted for systems exhibiting different times scales. The aggregated model obtained in the case of a density independent migration is a classical predator-prey model. The case of a density dependent migration aggregated model is very different and a nonstandard one, and exhibits an interesting result. Under certain conditions, parasites always become extinct in the case of a density independent migration, whereas the adaptation of hosts (density dependent migration) allows to stabilize the host-parasite system. This first application of the aggregation methods to epidemiology is very promising because these methods allow us to deal with more real assumptions about the behavioural interplay between hosts and parasites.