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Journal Articles Nonlinear Dynamics Year : 2012

A simplified model system for Toxoplasma gondii spread within a heterogeneous environment

Abstract

This study is dedicated to building and analyzing the spatial spread of Toxoplasma gondii through a heterogeneous predator‐prey system. The spatial domain is made of N patches hosting various population species, some of them being prey, others being predators. Predators offer strong heterogeneities with respect to local sustainable resources yielding variable growth rates, from exponential decay to logistic regulation. T. gondii life cycle goes through several stages, starting in the environment where oocysts are released from cat feces, reaching prey within which asexual reproduction yields cysts and then predators wherein sexual reproduction takes place. The resulting model system is complex to handle. We consider some relevant toy models with three patches, two resident predator species and Lotka‐Volterra functional responses to predation. We provide the existence and local stability of a persistent stationary state for the underlying predator‐prey model systems. The reproduction number R0 is computed in the quasi‐stationary case; it simplifies when slow‐fast dynamics are considered. Numerical experiments illustrate our analysis.

Dates and versions

hal-00992632 , version 1 (19-05-2014)

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Michel Langlais, Maud Lélu, Cecile Avenet, Emmanuelle Gilot-Fromont. A simplified model system for Toxoplasma gondii spread within a heterogeneous environment. Nonlinear Dynamics, 2012, 68 (3), pp.381-399. ⟨10.1007/s11071-011-0255-4⟩. ⟨hal-00992632⟩
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