关键词: Nonlocal diffusion, nonlocal infection, the basic reproduction number, compactness

Abstract: Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world. It is caused by various species of the genus Aphthovirus of the family Picornavirus, and it always brings a large number of infections and heavy financial losses. The disease has become a major public health concern. In this paper, we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment, which couples virus-to-animals and animals-to-animals transmission pathways, and investigate the dynamics of the disperal. The basic reproduction number $\mathcal R_0$ is defined as the spectral radius of the next generation operator $\mathcal R(x)$ by a renewal equation. The relationship between $\mathcal R_0$ and a principal eigenvalue of an operator $\mathcal L_0$ is built. Moreover, the proposed system exhibits threshold dynamics in terms of $\mathcal R_0,$ in the sense that $\mathcal R_0$ determines whether or not foot-and-mouth disease invades the hosts. Through numerical simulations, we have found that increasing animals' movements is an effective control measure for preventing prevalence of the disease.

Key words: Nonlocal diffusion, nonlocal infection, the basic reproduction number, compactness