On the Dynamical Analysis of a New Model for Measles Infection

Abstract

Epidemiologists and other health workers all over the world have noted that vaccination is an effective means of preventing most childhood diseases. In this study a compartmental mathematical model was formulated with the inclusion of the vaccinated class in a bid to examine the dynamics of measles within a population. This new class allowed us to determine the required vaccination coverage and dosage that will guarantee eradication of measles. The model is expressed as a system of ordinary differential equations. The stability of the equilibrium states was examined with respect to the basic reproductive number ,and found that the disease- free equilibrium state is locally and globally stable when , and the endemic equilibrium state is stable if . It was also noted that the effective reproductive number under vaccination approaches zero as the proportion of successfully vaccinated individual increases. Lastly, the required vaccination dosage and coverage that can lead to measles eradication were studied.