Mathematical Model for Describing the Transmission of Animal African Trypanosomiasis in Cattle
Conrad Akello
Department of Pure and Applied Mathematics, Maseno University, Box 333, Maseno, Kenya.
David Ambogo *
Department of Pure and Applied Mathematics, Maseno University, Box 333, Maseno, Kenya.
Richard Opiyo
Department of Pure and Applied Mathematics, Maseno University, Box 333, Maseno, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we have formulated a mathematical model for the transmission dynamics of African Animal Trypanosomiasis (AAT) by incorporating spraying of the tsetse y population(vector) and treating the cattle population (host) as control strategies. It has been shown that the disease free equilibrium point is globally asymptotically stable and the endemic equilibrium point is locally asymptotically stable. We have also shown that treatment of the host population reduces significantly infection by AAT as compared to spraying of the vector population.
Keywords: AAT, local stability, global stability, numerical simulation, reproduction number