Analysis of a SIQS epidemic model with non-linear incidence rate and application in GMF information dissemination

A SIQS epidemic model with non-linear incidence rate is proposed. With or without considering the stochastic perturbations, we study two models. The existence and global stability of the equilibriums for deterministic model is obtained by theoretic analysis and the second Lyapunov functional method. For stochastic model, by using the Itôs formula and some famous results, we obtain the conditions for disease's extinction and stationary distribution. At last, the simulations verify the theoretic conclusions gotten and an example for the GMF information dissemination is given in the paper.