Communications on Pure and Applied Analysis (CPAA)

Dynamics of a host-pathogen system on a bounded spatial domain

Pages: 2535 - 2560, Volume 14, Issue 6, November 2015      doi:10.3934/cpaa.2015.14.2535

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Feng-Bin Wang - Department of Natural Science in the Center for General Education, Chang Gung University, Kwei-Shan, Taoyuan 333, Taiwan (email)
Junping Shi - Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795, United States (email)
Xingfu Zou - Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada (email)

Abstract: We study a host-pathogen system in a bounded spatial habitat where the environment is closed. Extinction and persistence of the disease are investigated by appealing to theories of monotone dynamical systems and uniform persistence. We also carry out a bifurcation analysis for steady state solutions, and the results suggest that a backward bifurcation may occur when the parameters in the system are spatially dependent.

Keywords:  Extinction, persistence, steady states, pathogen, backward bifurcation.
Mathematics Subject Classification:  Primary: 35K57, 92B05; Secondary: 92D25.

Received: November 2014;      Revised: July 2015;      Available Online: September 2015.