Global stability of a two-stage epidemic model with generalized non-linear incidence

A multi-stage model of disease transmission, which incorporates a generalized non-linear 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 R0 (known as the basic reproductive number) is less than unity. On the other hand, the unique endemic equilibrium is globally asymptotically stable for R0>1.