Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model

Kazuo Yamazaki, Xueying Wang

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRS-B) epidemic PDE model. First, a local well-posedness result relying on the theory of cooperative dynamics systems is obtained. Via a priori estimates making use of the special structure of the system and continuation of local theory argument, we show that in fact this problem is globally well-posed. Secondly, we analyze the local asymptotic stability of the solutions based on the basic reproduction number associated with this model.

Original languageEnglish
Pages (from-to)1297-1316
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number4
DOIs
StatePublished - Jun 2016

Keywords

  • Cholera dynamics
  • Disease threshold dynamics
  • Principal eigenvalues
  • Stability
  • The basic reproduction number
  • Well-posedness

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