Global Dynamics of an SEIRS Compartmental Measles Model with Interrupted Vaccination

Abstract

Measles is a reemerging disease that has a devastating impact, especially among children under 5. In this paper, an SEIRS model is developed to investigate a possible outbreak among the population of children under 5 in the Sunyani Municipality. We consider waning immunity or loss of immunity among those who were vaccinated, which leads to secondary attacks among some in the population. Using Routh-Hurwitz criterion, Matrix Theoretic and Goh-Volterra Lyapunov functions, the stability of the model was investigated around the equilibria. We have computed the threshold parameter, 0 R , using the Next Generation Matrix method. The disease-free equilibrium is globally stable whenever 0 1 R ≤ and unstable otherwise. The endemic equilibrium is globally stable when 0 1 R > .