An infection age-space structured SIR epidemic model with Neumann boundary condition. Issue 11 (17th August 2020)

• Record Type: Journal Article
• Authors: Chekroun, Abdennasser; Kuniya, Toshikazu
• Is Part Of: Applicable analysis. Volume 99:Issue 11(2020)
• Page Start: 1972
• Page End: 1985
• Publication Date: 2020-08-17
• Subjects: SIR epidemic model -- infection age -- diffusion -- basic reproduction number -- global attractivity; 35Q92 -- 37N25 -- 92D30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1551997
• Languages: English
• ISSNs: 0003-6811

Abstract

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 .