Mathematical modelling for transmission and control of African trypanosomiasis

African trypanosomiasis (Trypanosoma brucei rhodesiense) is one of the major causes of deaths among cattle and people in Sub-Saharan Africa, in particular East Africa. In this study, a mathematical model of the transmission dynamics of Trypanosomiasis model is formulated and analysed with the aim of obtain ing deeper insight or understanding on the transmission dynamics of the disease. The study has considered a problem of interaction of population of humans, an imals (cattle) and vector (tsetse-fly), each population is divided into susceptible and infected classes. Upon the introduction of interventions the classes are expanded to include classes of treated humans, animals and trapped tsetseflies. The main aim of the study is to evaluate the impact of control strategies (treatment and trapping) on the spread of the disease. We derive conditions for the clear ance or persistence of the Trypanosomiasis infection through the determination of the model equilibria and analysis of their stability. Simulations and sensitivity analysis are carried out to illustrate analytical results and determine key factors influencing the behaviour of the disease. The study shows that trapping the fliesand treatment of infected human and cattle may reduce the burden of the disease if <eff < 1. The existence of the phenomena of backward bifurcation however, suggests that the disease may fail to clear even under the conditions that would normally lead to elimination of the disease in the population.