Basic reproduction ratios for almost periodic reaction-diffusion epidemic models

Abstract

The theory of the basic reproduction ratio R0 and its computation formula for the almost periodic reaction-diffusion epidemic models are established. First, we present some dynamical properties for linear almost periodic reaction-diffusion systems. By using evolution semigroup approach, we show that R0−1 has the same sign as the exponential growth bound of an associated linear system. Then, we also apply the developed theory to an almost periodic reaction-diffusion model of vector-borne disease to obtain a threshold type for the uniform persistence and global extinction of the disease. Finally, we illustrate the above results by numerical simulations and show the relationship between the diffusion rate and R0. We also present that the periodic epidemic models may overestimate or underestimate the basic reproduction ratio.