Abstract

MODELING THE IMPACT OF VACCINATION ON MEASLES EPIDEMIOLOGY

A. A. Ayoade1, O. Odetunde2, A. B. Kazeem3

---

Abstract Vaccination plays a key role in preventing and stemming infections. By that, a mathematical model is formulated to demonstrate the impact of vaccination on the eradication of measles disease. The model is designed by dividing the system into compartments leading to corresponding differential equations. The disease free and the endemic equilibrium states of the model are established. We conduct stability analyses for the two equilibria by linearization approach and Bellman and Cooke?s theorem respectively. It was established that the disease free equilibrium state is stable if the eigenvalues of the Jacobian determinant are all negative while the endemic equilibrium state is stable only if J1> 0 . Stability of the equilibrium states of the model implied that the disease is doomed to a rapid failure whenever there is an outbreak due to implementation of vaccination strategy. Keywords: Vaccination, mathematical model, infections, stability analyses, measles, equilibrium states

PDF