Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis

Abstract

In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number 0 R and the effective reproduction number e R works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease - free equilibrium 0 e is computed. When the effective reproduction number 1 e R < it is proved to be globally asymptotically stable in the feasible region F . When 1 e R > there exists one endemic equilibrium point which is locally asymptotically stable.