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Global stability of a two-stage epidemic model with generalized non-linear incidence. (English) Zbl 1005.92031
Summary: A multi-stage model of disease transmission, which incorporates a generalized nonlinear incidence function, is developed and analysed qualitatively. The model exhibits two steady states, namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated) provided a certain threshold \({\mathcal R}_0\) (known as the basic reproductive number) is less than unity. On the other hand, the unique endemic equilibrium is globally asymptotically stable for \({\mathcal R}_0>1\).

MSC:
92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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