Ergodicity and extinction in a stochastic susceptible-infected-recovered-susceptible epidemic model with influence of information

ABSTRACTAn epidemic model with stochastic contact transmission coefficient takes into account white noise and the influence of information. Sufficient conditions for the extinction and persistence of the disease are expressed. The existence of a stationary distribution and the ergodic property are proved. The peak of infected population can be decreased by information. The analytical results are showed by simulations and the influence of white noise and information on the dynamics of epidemics are evaluated.