PARASITISM, AND HOST PATCH SELECTION - A MODEL USING AGGREGATION METHODS

There is a growing interest in studying the effects of parasites on th e modification and evolution of hosts' behaviour. In this paper, we de al with a case of parasitism affecting the spatial pattern of host dis tribution. We develop a simple model with two patches, one host and on e parasite. Parasites live in Patch 1, hosts live in the two patches a nd migrate from one patch to the other. We study the case of a migrati on independent of parasite density and the case of a migration depende nt on density. In the two cases, we make the assumption that the choic e of patch is fast, whereas the growth of populations are slow. So we use aggregation methods which are particularly adapted for systems exh ibiting different times scales. The aggregated model obtained in the c ase of a density independent migration is a classical predator-prey mo del. The case of a density dependent migration aggregated model is ver y 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 sys tem. This first application of the aggregation methods to epidemiology is very promising because these methods allow us to deal with more re al assumptions about the behavioural interplay between hosts and paras ites.