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.
Highlights
Measles, a recurrent virus infection has a short term outbreak but its impact is devastating especially among children under five
Goh-Volterra method is used to establish the stability of the endemic equilibrium. [4] [17] used this matrix theoretic method to study the global dynamics of several specific disease models
[24] used this Lyapunov function involving the Perron eigenvectors to study the global dynamics of several specific disease models while [4] used it to consider a general case for infectious diseases
Summary
A recurrent virus infection has a short term outbreak but its impact is devastating especially among children under five. The authors looked at a case study of the dynamics of measles disease in the case of interrupted vaccination in Sunyani, a thriving metropolis in Ghana, a country where only 57% deliveries are handled by qualified health personnel [2]. The second dose is usually taken when the child is 3 years and 4 months old This can be taken in later years in the management of a disease outbreak. [8] [9] [10] studied the global stability of disease models and inculcated immigration and/or births and death dynamics into the population system. One important measure that determines the dynamics of disease models is the threshold parameter known as basic reproductive number R0 This parameter measures the number of infectives generated by a single infectious individual introduced into the susceptible population. One of the most successful procedures used to construct Lyapunov functions by many researchers is the
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