Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model

Kazuo Yamazaki, Xueying Wang

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state.

Original languageEnglish
Pages (from-to)559-579
Number of pages21
JournalMathematical Biosciences and Engineering
Volume14
Issue number2
DOIs
StatePublished - Apr 2017

Keywords

  • Cholera dynamics
  • Persistence
  • Principal eigenvalues
  • Stability
  • asic reproduction number

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