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 R0 is derived dependent on birth rate, death rate, recovery rate and transmission rate. The disease-free equilibrium of the model is stable when R0≤1 and unstable when R0>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.