A new way of investigating the asymptotic behaviour of a stochastic SIS system with multiplicative noise

In this paper, we investigate a nonlinear stochastic SIS epidemic system with multiplicative noise. First, we transform the Itô's integral into an equivalent Stratonovich integral. Then, by using the solution of Langevin equation and Ornstein-Uhlenbeck process, we prove that the system generates a random dynamical system which has a tempered compact random absorbing set, implying the condition for the extinction of the disease. Finally, the discussion and numerical simulation are given to demonstrate the obtained result.