Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease

The epidemic of foot-and-mouth disease (FMD) in cattle remains particular concern in many countries or areas. The epidemic can spread by direct contact with the carrier and symptomatic animals, as well as indirect contact with the contaminated environment. The outbreak of FMD indicates that the infection initially spreads through the farm before spreading between farms. In this paper, considering the cattle population, we establish a dynamical model of FMD with two patches: within-farm and outside-farm, and give the formulae of the basic reproduction number R0. By constructing the Lyapunov function, we prove the disease-free equilibrium is globally asymptotically stable when R0 <1, and that of the unique endemic equilibrium when R0>1. By numerical simulations, we confirm the global stability of equilibria. In addition, by carrying out the sensitivity analysis of the basic reproduction number on some parameters, we reach the conclusion that vaccination, quarantining or removing of the carrier and disinfection are the useful control measures for FMD at the large-scale cattle farm. AMS subject classifications: 34D05,34D20