A mathematical model for treatment of bovine brucellosis in cattle population

Document Type: Research Paper

Authors

1 Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda

2 Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda

Abstract

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 $\mathcal{R}_{0}<1,$ the disease can be eliminated in the cattle population or persists  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.

Keywords