On the basic reproduction number of reaction-diffusion epidemic models

Abstract

The basic reproduction number R 0 serves as a threshold parameter of many epidemic models for disease extinction or spread. The purpose of this paper is to investigate R 0 for spatial reaction-diffusion partial differential equation epidemic models. We define R 0 as the spectral radius of a product of a local basic reproduction number R and strongly positive compact linear operators with spectral radii one. This definition of R, viewed as a multiplication operator, is motivated by the definition of basic reproduction numbers for ordinary differential equation epidemic models. We investigate the relation of R 0 and R.