Global Dynamics of an SEIRS Compartmental Measles Model with Interrupted Vaccination

• 作者: Dominic Otoo Elvis K. Donkoh Eric Okyere Justice A. Kessie Williams Kumi
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Global Stability LYAPUNOV Function MATRIX Theoretic Method NEXT Generation MATRIX SEIRS
• 年，卷（期）: yysxyw_2019,（7）
• 页码范围: 588-604
• 页数: 17页
• 分类号: O1

摘要

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.