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On a vector-host epidemic model with spatial structure

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Published 15 November 2018 • © 2018 IOP Publishing Ltd & London Mathematical Society
, , Citation Pierre Magal et al 2018 Nonlinearity 31 5589 DOI 10.1088/1361-6544/aae1e0

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yixiang.wu@vanderbilt.edu

Author affiliations

1 Mathematics Department, University of Bordeaux, Bordeaux, France

2 Mathematics Department, Vanderbilt University, Nashville, TN, United States of America

Dates

  1. Received 19 April 2018
  2. Accepted 17 September 2018
  3. Published

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0951-7715/31/12/5589

Abstract

In this paper, we study a reaction–diffusion vector-host epidemic model. We define the basic reproduction number R0 and show that R0 is a threshold parameter: if the disease free equilibrium is globally stable; if R0  >  1 the model has a unique globally stable positive equilibrium. Our proof combines arguments from monotone dynamical system theory, persistence theory, and the theory of asymptotically autonomous semiflows.

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