Periodic solution of the DS-I-A epidemic model with stochastic perturbations

Abstract

The paper introduces DS-I-A model with periodical coecients. First of all, we show that there is a unique positive solution of the stochastic model. Furthermore we deduce the conditions under which the disease will end
and continue. At last, we draw a conclusion that there exists nontrivial positive periodic solution for the stochastic system by stochastic Lyapunov functions. Simulations are also carried out to conrm our analytical results.