Temporal-spatial analysis of an age-space structured foot-and-mouth disease model with Dirichlet boundary condition.

Foot-and-mouth disease is a highly contagious and economically devastating disease of cloven-hoofed animals. The historic occurrences of foot-and-mouth diseases led to huge economic losses and seriously threatened the livestock food security. In this paper, a novel age-space diffusive foot-and-mouth disease model with a Dirichlet boundary condition, coupling the virus-to-animals and animals-to-animals transmission routes, has been proposed. The basic reproduction number R is defined as the spectral radius of a next generation operator K, which is calculated in an explicit form, and it serves as a vital value determining whether or not the disease persists. The existence of a unique trivial nonconstant steady state and at least one nonconstant endemic steady state of the system is established by a smart Lyapunov functional and the Kronoselskii fixed point theorem. An application to a foot-and-mouth outbreak in China is presented. The findings suggest that increasing the movements and disinfection of the environment for animals apparently reduce the risk of a foot-and-mouth infection.