Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

Abstract

Consider the heterogeneity (e.g., heterogeneous social behaviour, heterogeneity due to different geography, contrasting contact patterns and different numbers of sexual partners etc.) of host population, in this paper, the authors propose an infection age multi-group SEIR epidemic model. The model system also incorporates the feedback variables, where the infectivity of infected individuals may depend on the infection age. In the direction of mathematical analysis of model, the basic reproduction number R₀ has been computed. The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R₀. More precisely, for R₀ ≤ 1, the disease-free equilibrium is globally asymptotically stable and for R₀ > 1, they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method. By considering a numerical example, they investigate the effects of infection age and feedback on the prevalence of the disease. Their result shows that feedback parameters have different and even opposite effects on different groups. However, by choosing an appropriate value of feedback parameters, the disease could be eradicated or maintained at endemic level. Besides, the infection age of infected individuals may also change the behaviour of the disease, global stable to damped oscillations or damped oscillations to global stable.

Keywords

Multi-group model / Infection age / Feedback / Graph-theoretic approach / Lyapunov function

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