DYNAMICS OF AN SIRS EPIDEMIC MODEL WITH PERIODIC INFECTION RATE ON A SCALE-FREE NETWORK

Influenced by seasonal changes, the infection rate of many infectious diseases fluctuates in cycles. In this paper, we propose and investigate an SIRS model on a scale-free network. To model seasonality, we assume that the infection rate is periodic. The existence and positivity of solutions of the proposed model are proved and the basic reproduction number R-0 is defined. The global stability of steady states is determined by rigorous mathematical analysis. When R-0 < 1, the disease-free equilibrium E-0 is globally asymptotically stable. When R-0 > 1, the system has a unique positive periodic solution E*, and E* is globally asymptotically stable. Numerical simulations are performed to support our theoretic results, and the effects of various parameters on the amplitude and mean of infected individuals are studied. The sensitivity of parameters of the basic reproduction number R-0 is solved by the Sobol global sensitivity analysis method, and the results show that, the effects of the parameters beta(0) and alpha on R(0 )are remarkable.