Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary conditions

Fei Ying Yang, Wan Tong Li, Shigui Ruan

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11 Scopus citations


In this paper we study a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the spatial movement of individuals is described by a nonlocal (convolution) diffusion operator, the transmission rate and recovery rate are spatially heterogeneous, and the total population number is constant. We first define the basic reproduction number R 0 and discuss the existence, uniqueness and stability of steady states of the nonlocal dispersal SIS epidemic model in terms of R 0 . Then we consider the impacts of the large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease. The obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease. In particular, our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease.

Original languageEnglish (US)
Pages (from-to)2011-2051
Number of pages41
JournalJournal of Differential Equations
Issue number3
StatePublished - Jul 15 2019


  • Basic reproduction number
  • Disease-free equilibrium
  • Endemic equilibrium
  • Nonlocal dispersal
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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