Dynamics of foot-and-mouth disease spread model for cattle with carrier, vaccination, and environmental transmission

Abstract

In this article, we discuss the dynamics of Foot-and-Mouth Disease (FMD) spread model by considering direct infections from infected and carrier population, indirect infections from patogen population in environment, and the intervention such as vaccination, culling, and environment sanitation. The proposed model contains six subpopulations: susceptible (S), vaccinated (V), exposed (E), infected (I), carrier (I_C), and patogen (P). For the dynamics of proposed model, we first show the non-negativity and boundedness of solutions. The equilibrium point, basic reproduction number, local and global stability of equilibrium points are also investigated analytically. The proposed model has disease-free equilibrium point always exists and endemic equilibrium point exists when R₀ > 1. The disease-free equilibrium point is locally asymptotically stable when R₀ < 1 and fulfills the RouthHurwitz criterion, and globally asymptotically stable when R₀ < 1. While the endemic equilibrium point is locally asymptotically stable when Lienard-Chipart criterion is satisfied, and globally asymptotically stable when R₀ > 1 and one of the following conditions (i) If c = 0 and ϕ = 0, or (ii) If N ≤ Π/µ, is satisfied. Numerical simulations are performed to verify the analytical result. The simulation results demonstrate the local and global stability of equilibrium point.