A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County
Jane S. Musaili *
Department of Mathematics, Kenyatta University, P.O Box 43844 Nairobi, Kenya.
Isaac Chepkwony
Department of Mathematics, Kenyatta University, P.O Box 43844 Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virus
in dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations done using Matlab indicated that education of the public on administration of both pre and post exposure vaccines to dogs and responsible dog ownership leads to a decrease in the numbers of rabies virus infected dogs which shows that public health education is an ecient means for controlling rabies.
Keywords: Rabies, reproduction number, stability, numerical simulation.