Global stability of endemic equilibrium of an epidemic model with birth and death on complex networks

We study global stability of endemic equilibrium of an epidemic model with birth and death on complex networks. Under some conditions, the local asymptotic stability of the endemic equilibrium was established by Zhang and Jin (2011) for correlated networks, and the global asymptotic stability was obtained by Chen and Sun (2014) for uncorrelated networks. In this work, we remove those conditions, and prove by constructing a Lyapunov function that the endemic equilibrium is globally asymptotically stable. Numerical simulations are also presented to illustrate the feasibility of the result.