Nonlinear Dynamics

, Volume 68, Issue 3, pp 381–399 | Cite as

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

  • M. Langlais
  • M. LéluEmail author
  • C. Avenet
  • E. Gilot-Fromont
Original Paper


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 R 0 is computed in the quasistationary case; it simplifies when slow–fast dynamics are considered. Numerical experiments illustrate our analysis.


Toxoplasma gondii Predator–prey system Fragmented domain Parasite persistence R0 Slow–fast dynamics 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • M. Langlais
    • 1
  • M. Lélu
    • 2
    Email author
  • C. Avenet
    • 2
  • E. Gilot-Fromont
    • 2
    • 3
  1. 1.Univ. Bordeaux SegalenInstitut de Mathématiques de BordeauxBordeaux CedexFrance
  2. 2.Université de Lyon, Université Lyon 1UMR5558 Laboratoire de Biométrie et Biologie EvolutiveVilleurbanne CedexFrance
  3. 3.Université de Lyon, VetAgro Sup, Campus Vétérinaire de LyonSanté Publique VétérinaireMarcy l’EtoileFrance

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