Global stability of the steady states of an epidemic model incorporating intervention strategies

Yongli Cai, Yun Kang, Weiming Wang

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment. We prove that the reproduction number R0 can be played an essential role in determining whether the disease will extinct or persist: if R0 < 1, there is a unique disease-free equilibrium which is globally asymptotically stable; and if R0 > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. Furthermore, we study the relation between R0 with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control.

Original languageEnglish (US)
Pages (from-to)1071-1089
Number of pages19
JournalMathematical Biosciences and Engineering
Volume14
Issue number5-6
DOIs
StatePublished - Oct 1 2017

Keywords

  • Basic reproduction number
  • Disease-free equilibrium
  • Endemic
  • Spatial heterogeneity

ASJC Scopus subject areas

  • Medicine(all)
  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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