Global stability analysis of an SIR epidemic model with demographics and time delay on networks

In this paper, a susceptible-infected-recovery (SIR) epidemic model is governed with demographics and time delay on networks. Firstly, the basic reproduction number R 0 is derived dependent on birth rate, death rate, recovery rate and transmission rate. The disease-free equilibrium of the model is stable when R 0 ≤ 1 and unstable when R 0 > 1 . Secondly, based on a Jacobian matrix calculated along with the disease-free equilibrium, we find that the system does not occur Hopf branch under the disease-free equilibrium. Thirdly, the global asymptotic stability of a disease-free equilibrium and a unique endemic equilibrium are proved by structuring two Lyapunov functions. Finally, numerical simulations are performed to illustrate the analysis results.