Asymptotical profiles of an age-structured foot-and-mouth disease with nonlocal diffusion on a spatially heterogeneous environment

Abstract

Spatial heterogeneity deeply affects the habits of animals and transmission behaviors of foot-and-mouth disease. To consider the effects of heterogeneous habits on the evolution of the disease prevalence, an age-structured foot-and-mouth disease (FMD) model with nonlocal diffusion is proposed to describe the long distance movements of cattle. The next generation operator G is derived through establishing an extensively renewal equation and then the basic reproduction number R0 is the spectral radius of G. Moreover, the value of R0 serves as a threshold which distinguishes between the disappearance and an outbreak of FMD. The outbreak of FMD is the presentation of the endemic steady state by using the Krasnoselskii fixed point theorem. Finally, numerical simulations shed light on how the magnitudes of nonlocal diffusions affect the evolution of FMD spread.