<p>This paper is concerned with a nonlocal (convolution) dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary conditions. We first investigate the influence of dispersal rates on the basic reproduction number. Then, we establish the existence and uniqueness of endemic steady states with the help of an equivalent equation and finally study the asymptotic profiles of the endemic steady states for small and large dispersal rates. Our results demonstrate that restricting the movement of susceptible individuals cannot eradicate the disease and that a varying total population size can enhance disease persistence. In contrast, large dispersal rates drive the disease to extinction.</p>

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Asymptotic Profiles of a Nonlocal Dispersal SIS Epidemic Model with Dirichlet Boundary Conditions

  • Yan-Xia Feng,
  • Wan-Tong Li,
  • Fei-Ying Yang

摘要

This paper is concerned with a nonlocal (convolution) dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary conditions. We first investigate the influence of dispersal rates on the basic reproduction number. Then, we establish the existence and uniqueness of endemic steady states with the help of an equivalent equation and finally study the asymptotic profiles of the endemic steady states for small and large dispersal rates. Our results demonstrate that restricting the movement of susceptible individuals cannot eradicate the disease and that a varying total population size can enhance disease persistence. In contrast, large dispersal rates drive the disease to extinction.