Dynamical Analysis of Transmission Model of the Cattle Foot-and-Mouth Disease (CSIAM Transactions on Applied Mathematics, 2020)
The epidemic of foot-and-mouth disease (FMD) in cattle remains particular concern in many countries or areas. The epidemic can spread by direct contactwith the carrier and symptomatic animals, as well as indirect contact with the contaminated environment. The outbreak of FMD indicates that the infection initially spreadsthrough the farm before spreading between farms. In this paper, considering the cattlepopulation, we establish a dynamical model of FMD with two patches: within-farmand outside-farm, and give the formulae of the basic reproduction number $R$0. Byconstructing the Lyapunov function, we prove the disease-free equilibrium is globallyasymptotically stable when $R$01. By numerical simulations, we confirm the global stability of equilibria. In addition, by carrying out the sensitivity analysis of the basic reproduction number on someparameters, we reach the conclusion that vaccination, quarantining or removing of thecarrier and disinfection are the useful control measures for FMD at the large-scale cattle farm.