MATHEMATICAL MODEL FOR TRANSMISSION DYNAMICS AND CONTROL ANALYSIS OF TRYPANOSOMIASIS (SLEEPING SICKNESS)

Abstract

In this thesis a Mathematical model for the transmission dynamics and control of trypanosomiasis commonly called African sleeping sickness was developed and analyzed. Three interacting population of humans, livestock and vector were considered. The West African Sleeping Sickness (Chronic) caused by Trypanosoma BruceiGambiense evolving two stages; hemo-lymphatic and meningo-encephalitic were considered. The threshold value for the effective reproduction number was obtained and the threshold value was used to obtain the conditions for local and global stabilities of the Disease-free and Endemic equilibrium states. The Disease-free equilibrium state is locally asymptotically stable if .The method of Castillo-Chavel was used to establish the global stability of the Disease-free equilibrium. We use the general bifurcation theory based on the approach by Castillo-Chavel and Song to analyze the local stability of the endemic equilibrium point, also considering the global behavior of the endemic equilibrium point, we constructed a suitable Lyapunov function based on the approach by Korobeinikov