Host and vector migration on the spread of animal African trypanosomiasis: the effect of seasonal variation

Abstract

In this paper, a two patch-model for animal African trypanosomiasis (AAT) disease transmission that incorporates seasonal variation, livestock, wild animals and tsetse flies is proposed and studied. The main assumption in the formulated model is that seasonal variation is associated with migration of both hosts and vectors from one patch to another. From model analysis, we computed the basic reproduction number in a periodic environment. We noted that the disease can be eliminated in the population whenever the basic reproduction number is less than unity and exist whenever greater than one. We performed the numerical simulation of the model considering two scenarios: symmetrical and asymmetrical movement of hosts and vectors. Overall, we noted that migration of hosts and vectors have influence on the spread of disease in the population. Additionally, we observed that solution profile of all infected species is associated with periodic oscillations caused by the seasonal variations.