Abstract:
A deterministicmodel for the transmission dynamics of a communicable disease is developed and rigorously analysed. Themodel,
consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable diseasefree
equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (R0), is less than
unity; in such a case the endemic equilibrium does not exist. On the other hand, when the reproduction number is greater than
unity, it is shown, using nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle’s invariance principle,
that the unique endemic equilibrium of the model is globally asymptotically stable under certain conditions. Furthermore, the
disease is shown to be uniformly persistent whenever R0 > 1.
