Global Stability of an Epidemic Model with Latent Stage and Vaccination

摘要

In this paper, an epidemic model with latent stage and vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the partial immunity against infection before gaining the complete immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing the Lyapunov functions, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the unique endemic equilibrium is globally stable when the basic reproduction number is greater than one. When proving the global stability of the endemic equilibrium, the derivative of the given Lyapunov function may be rearranged in the different forms to show its negative definiteness or semi-definiteness.