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Melesse, D.Y. and Gumel, A.B. (2010) Global Asymptotic Properties of an SEIRS Model with Multiple Infectious Stages. Journal of Mathematical Analysis and Applications, 366, 202-217.
https://doi.org/10.1016/j.jmaa.2009.12.041

has been cited by the following article:

• TITLE: Global Dynamics of an SEIRS Compartmental Measles Model with Interrupted Vaccination

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

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

  JOURNAL NAME: Applied Mathematics, Vol.10 No.7, July 24, 2019

  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, 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.