Author(s)

Dominic Otoo, Justice A. Kessie, Elvis K. Donkoh, Eric Okyere, Williams Kumi

Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana.

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, R₀, using the Next Generation Matrix method. The disease-free equilibrium is globally stable whenever R₀ ≤1 and unstable otherwise. The endemic equilibrium is globally stable when R₀ >1.

Global Stability, Lyapunov Function, Matrix Theoretic Method, Next Generation Matrix, SEIRS

Otoo, D. , Kessie, J. , Donkoh, E. , Okyere, E. and Kumi, W. (2019) Global Dynamics of an SEIRS Compartmental Measles Model with Interrupted Vaccination. Applied Mathematics, 10, 588-604. doi: 10.4236/am.2019.107042.