Mathematical Analysis of Rabies Transmission Dynamics and Control

Abstract

Rabies is a dangerous disease that kills many people than any other communicable disease and yet it is underrated. This results from the little knowledge on the myriad ways of transmission of the virus. A deterministic model is proposed to study the spread of the rabies virus in both domestic dogs (Canis familiaries) and humans (Homo sapiens). We elaborately studied the spread of the rabies virus from dogs to-dogs, dogs-to-humans and for the first time, humans-to-humans. Sensitivity analysis is performed to determine the influence of various parameters on the transmission of rabies the most. The rabies-free equilibrium and the endemic equilibrium points were determined and the conditions under which the equilibria are stable were also obtained. The stability conditions provide the conditions under which the disease will persist or get to be eradicated. Numerical solutions of the model were obtained using the ode45 routine in MATLAB. The study demonstrated that for rabies to be eradicated, the rate at which dogs are recruited must be decreased, culling of exposed and infected dogs should be increased and mass vaccination of the dog population should be targeted.