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Stability analysis of some epidemic models with vertical transmission and different incidences

B. Singh, S. Jain, R. Khandelwal, S. Porwal and G. Ujjainkar

Korobeinikov and Wake [9] introduced a family of Lyapunov functions for three-compartmental epidemiological models which appear to be useful for more sophisticated models. In this paper we have reinvestigated the models of Korobeinikov and Wake [9] with different incidences. The basic reproduction number 0 Â is identified and local stability of the equilibrium states is discussed. The Global stability of the equilibrium states is proved by constructing a Lyapunov function. Some numerical simulations are given to illustrate the analytical results.