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Séminaire Dynamique des populations

Responsable : Beddredine Ainseba

  • Le 15 mai 2018 à 14:00
  • Salle de Conférences
    Yixiang Wu, Department of Mathematics, Vanderbilt University, USA
    Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates
    In this talk, we consider a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts. We first prove that the solution of the model exists globally and the model system possesses a global attractor. We then identify the basic reproduction number $\mathcal{R}_0$ for the model and prove its threshold role: if $\mathcal{R}_0\le 1$, the disease free equilibrium is globally asymptotically stable; if $\mathcal{R}_0>1$, the solution of the model is uniformly persistent and there exists a positive (pathogen persistent) steady state. Finally, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected hosts approaches zero. Our result suggests that the infected hosts concentrate at certain points which can be characterized as the pathogen's most favoured sites when the mobility of the infected host is limited. This is joint work with Xingfu Zou.

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