Stability and control of stochastic infectious disease model under probability dichotomy model

In the report， a stochastic infectious model with probability shunting was constructed， and the effects of the diagnostic rate of isolated individuals （vaccine efficacy） and the fluctuation environment （noise） on disease transmission and control were investigated. The existence and uniqueness of the solution were proved， and the sufficient condition for the extinction and persistence of the disease were validated. If the noise is fixed and the vaccine efficacy increases， becomes bigger and the extinction time demonstrates a negative exponential decay. The numeric results indicated that the noise can accelerate the extinction of the disease and achieve the stochastic optimal control， which not only reduce effectively the number of infected people， but also accelerate the disease extinction.