Mathematical analysis of an SIR network model with imperfect vaccination and varying size of population

Epidemic Spreading is a major global health problem. Modeling epidemic spreading dynamics is important for understanding and controlling epidemic spreading, providing prevention strategies. This paper points out some flaws existing in the susceptible-infected - susceptible (SIS) model proposed by Safan and Rihan, and proposes a modified susceptible-infected-recovered (SIR) model on homogenous networks. It is proved that if the basic reproduction number Rv of the model is less than one, then the infection-free equilibrium of the model is globally asymptotically stable. On the other hand, if Rv of the model is more than one, the endemic equilibrium of the model is globally asymptotically stable. This paper also numerically predicts the effect of vaccination ratio on the size of HBV infected mainland Chinese population.