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Global Dynamics of an SEIRS Compartmental Measles Model with Interrupted Vaccination
Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
- 1 Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
- 2 Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
- 3 Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
- 4 Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
- 5 Department of Mathematics & Statistics, University of Energy & Natural Resources, Sunyani, Ghana
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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, R 0 , using the Next Generation Matrix method. The disease-free equilibrium is globally stable whenever R 0 ≤ 1 and unstable otherwise. The endemic equilibrium is globally stable when R 0 >1.
KeywordsGlobal StabilityLyapunov FunctionMatrix Theoretic MethodNext Generation MatrixSEIRS
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