Analysis of Transmission Dynamics of Anthrax in Animals: A Modeling Approach
George Thiong’o Githire *
Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Kenya.
George Kimathi
Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Kenya.
Mary Wainaina
Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This paper seeks to develop a SIR model with vaccination compartment in the study of anthrax transmission dynamics in animal population. The model employ ordinary differential equations in the formulation of its equation. The model’s steady states solutions are investigated. The disease free equilibrium and endemic equilibrium of the model are analyzed qualitatively. Vaccination rate below a certain critical value causes the anthrax disease to persist. Recruitment and contact rates are the most sensitive parameters that significantly contribute to the basic reproductive ratio.
Keywords: Anthrax, disease, vaccination, SIR model, endemic equilibrium.