Global threshold dynamics of aninfection age-structured SIR epidemic model with diffusion under the Dirichlet boundary condition

摘要

In this paper, we are concerned with the global asymptotic behavior of an infection age-structured SIR epidemic model with diffusion in a general n-dimensional bounded spatial domain under the homogeneous Dirichlet boundary condition. By using the method of characteristics, we reformulate the model into a system of a reaction-diffusion equation and a Volterra integral equation. We define the basic reproduction number R-0 by the spectral radius of a compact positive linear operator and show that if R-0 < 1, then the disease-free steady state is globally attractive, whereas if R-0 > 1, then a positive endemic steady state exists and the system is uniformly persistent. By numerical simulation for the 2-dimensional case, we show that R-0 depends on the shape of the spatial domain. This result is in contrast with the case of the homogeneous Neumann boundary condition, in which R-0 is independent of the spatial domain. (C) 2020 The Author(s). Published by Elsevier Inc.