Mathematical Model For Determining The Influence Of Treatment And Vaccination On Measles

Abstract In this paper work, a mathematical modeling of the influence of treatment and vaccination on measles control was developed using a system of ordinary differential equations. Local stability analysis on the disease-free equilibrium was done using the Jacobian matrix approach. The semi-analytical solutions of the model were obtained using the Differential Transformation method and the solutions were plotted using Maple. The result of the findings shows that the Disease Free Equilibrium State (DFE) of the model is stable if R0˂1. The result of the numerical simulation shows that a reduction in the contact rate with infectious individuals reduces the transmission rate of the disease. The simulation also reveals that at high vaccination rate for the infected individuals, the number of recovered individual’s increases. Hence, the combination of treatment and sanitizer at 75% will curb measles to the barest minimum in less than one year, also effective vaccination will help in preventing those who are susceptible from contacting the disease. Keyword: Mathematical model, Measles, Simulation, Treatment and vaccination.