MICHEL LANGLAIS
	"DESTOBIO 2000" August 23-27, 2000 West Lafayette, Indiana, USA

"Modeling Host-Microparasite Systems in Heterogeneous Environment"

ABSTRACT: The impact of a parasite on a host population living in a highly heterogeneous domain has been the focus of many research programs. Here we assume that the spatial heterogeneities have a strong impact on the carrying capacities, on the birth and death rates, on the social structures of the host population, as well as on the diffusion or dispersion of individuals. Then the transmission of a parasite in such a heterogeneous system is likely to be enhanced or reduced, depending on local structures, local dynamics and local transmission modes.
A simple question is: how can we understand the global dynamic of the resulting host-parasite system, even in simple situations? As a case study we consider the system made of a cat population and two of its retroviruses, the Feline Immunodeficiency Virus (FIV) and the Feline Leukemia Virus (FeLV). For moderately heterogeneous systems numerical simulations, based on field data collected during the last ten years on five cat populations, suggest that a parasite can take advantage of heterogeneities to invade the whole spatial domain, but can also be globally eradicated. This is consistent with data concerning the prevalence of these two viruses and also with data showing both immune cats and zero prevalence for FeLV in some populations. For highly heterogeneous systems, homogenization techniques devised to understand the behavior of composite materials can be helpful in deriving simple systems with constant coefficients from which the macroscopic dynamics can be described.

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