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A mathematical model for treatment of bovine brucellosis in cattle population | ||
| Journal of Mathematical Modeling | ||
| مقاله 4، دوره 5، شماره 2، اسفند 2017، صفحه 137-152 اصل مقاله (295.64 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2017.2523 | ||
| نویسندگان | ||
| Julius Tumwiine1؛ Godwin Robert2 | ||
| 1Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda | ||
| 2Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Bovine brucellosis؛ endemic equilibrium؛ global Stability؛ Lyapunov function؛ vertical transmission | ||
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