On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models

The basic reproduction number R₀ serves as a threshold parameter of many epidemic models for disease extinction or spread. The purpose of this paper is to investigate R₀ for spatial reaction-diffusion partial differential equation epidemic models. We define R₀ 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 R₀ and R.