Desirable Dog-Rabies Control Methods in an Urban setting in Africa -a Mathematical Model

Rabies is a fatal, zoonotic, viral disease that causes an acute inflammation of the brain in humans and other mammals. It is transmitted through contact with bodily fluids of infected mammals, usually via bites or scratches. In this paper, we formulate a deterministic model which measures the effects of different rabies control methods (mass-culling and vaccination of dogs) for urban areas near wildlife, using the Arusha region in Tanzania as an example. Values for various parameters were deduced from five years’ worth of survey data on Arusha’s dog population. Data included vaccination coverage, dog bites and rabies deaths recorded by a local non-governmental organization and the Ministry of Agriculture, Livestock Development and Fisheries of the United Republic of Tanzania. The basic reproduction number R0 and effective reproduction number Re were computed and found to be 1.9 and 1.2 respectively. These imply that the disease is endemic in Arusha. The numerical simulation of the reproduction number shows that vaccination is the most appropriate control method for rabies transmission in urban areas near wildlife reservoirs. The disease free equilibrium ε0 is also computed. If the effective reproduction number Re is computed and found to be less than 1, it implies that it is globally asymptotically stable in the feasible region Φ. If Re > 1 it is implied that there is one equilibrium point which is endemic and it is locally asymptotically stable.