Stability of a novel stochastic epidemic model with double epidemic hypothesis

In this paper, a novel SIR disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation. We present the stability conditions of the disease-free equilibrium of the SIR model without stochastic perturbation and with stochastic perturbation. We obtain the deterministic stability threshold β1∗∗ and β2∗∗ of the disease-free equilibrium, under which the disease-free equilibrium is stochastically stable such that the disease will disappear finally leaving all the population susceptible. The results show that double epidemic hypothesis and stochastic perturbation have significant effects on the dynamics behaviors of the model.