An infection age-space structured SIR epidemic model with Neumann boundary condition. Issue 11 (17th August 2020) - Chekroun, Abdennasser; Kuniya, Toshikazu
ABSTRACT: In this paper, we are concerned with an SIR epidemic model with infection age and spatial diffusion in the case of Neumann boundary condition. The original model is constructed as a nonlinear age structured system of reaction–diffusion equations. By using the method of characteristics, we reformulate the model into a system of a reaction–diffusion equation and a Volterra integral equation. For the reformulated system, we define the basic reproduction number R 0 by the spectral radius of the next generation operator, and show that if R 0 < 1, then the trivial disease-free steady state is globally attractive, whereas if R 0 > 1, then the disease in the system is persistent. Moreover, under an additional assumption that there exists a finite maximum age of infectiousness, we show the global attractivity of a constant endemic steady state for R 0 > 1 .