A Valid Transport Related SVEIHR Stochastic Epidemic Model with Coverage and Time Delays

The ability of people to move freely between cities is thought to be a major factor in accelerating the spread of infectious diseases. To investigate this issue, we propose a SEVIHR stochastic epidemic model, which emphasizes the effects of transport related infections and media coverage. At the same time, the time delay caused by the information time difference is considered. Firstly, we study the existence and uniqueness of the global positive solution of the model by means of Lyapunov function and stopping time, and obtain sufficient conditions for the extinction and persistence of the disease. Secondly, in order to control the spread of the disease in time and effectively, appropriate control strategies are formulated according to the stochastic optimal theory. Finally, the extinction and persistence of the disease were simulated by MATLAB.