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

Feng-Bin Wang; Junping Shi; Xingfu Zou

doi:10.3934/cpaa.2015.14.2535

Article Contents

2015, Volume 14, Issue 6: 2535-2560. Doi: 10.3934/cpaa.2015.14.2535

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

1.
Department of Natural Science in the Center for General Education, Chang Gung University, Kwei-Shan, Taoyuan 333
2.
Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795
3.
Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

Received: November 2014

Revised: July 2015

Published: November 2015

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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.

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Mathematics Subject Classification: Primary: 35K57, 92B05; Secondary: 92D25.

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