A mathematical model for treatment of bovine brucellosis in cattle population

Brucellosis is an infectious bacterial zoonosis of public health and economic significance. In this paper, a mathematical model describing the propagation of bovine brucellosis within cattle population is formulated. Model analysis is carried out to obtain and establish the stability of the equilibrium points. A threshold parameter referred to as the basic reproduction number $mathcal{R}_{0}$ is calculated and the conditions under which bovine brucellosis can be cleared in the cattle population are established. It is found out that when $mathcal{R}_{0}1$. Using  Lyapunov function and Poincair'{e}-Bendixson  theory, we prove that the disease-free and endemic equilibrium, respectively  are globally asymptotic stable. Numerical simulation reveals that control measures should  aim at reducing the  magnitude of the parameters for contact rate of infectious cattle with the susceptible and recovered cattle, and increasing treatment rate of infected cattle.