MATHEMATICAL MODEL OF RABIES; IN THE CASE OF NORTH SHEWA, ETHIOPIA

Abstract

The purpose of this study was to develop a mathematical model for the spread of rabies in human and dog population using ordinary differential equation. The underline model is called SEIR model which categorizes a given population into four classes for both human and dog population; namely Susceptible, exposed, infective, and recovered. The feasible region and positivity of the solution set of the model stated by using the theorems. The basic reproduction number was computed by using the next generation matrix method. The disease free equilibrium point and endemic equilibrium point of the model was computed by making the right hand side of the ordinary differential equation equal to zero. Routh –Hurwitz criterion were used to prove the stability theorems of disease free equilibrium point and endemic equilibrium points. The sensitivity analysis of the parameter was computed. For a specified set of values of parameters as deduced from the data provided by North Shewa Health Bearaua the basic reproduction number ℛ0 work out to be 1.0566, which indicates the disease will be endemic. The Sensitivity index of the parameter removing rate, natural death rate, treatment rate and induced death rate are negative, which implies that the parameters are used to control the disease. But contact rate, infection rate and recruitment rate have positive Sensitivity index, which implies that the parameter are expand the disease. Finally, from numerical simulation, increasing the removing rate and treatment rate are used to control the diseases but, increasing contact rate and infectious rate are expand the disease. In order to eradicate rabies from North Shewa the government should teach the community to remove the infected dog before transmitting the virus and enforcement of laws on dog owners to ensure regular treatment of their dogs