A remark on stochastic stability of a novel hybrid system

A stochastic switching Susceptible-Exposed-Infective-Removed (SEIR) epidemic model with continuous and impulsive control schemes is proposed and investigated, in which a general incidence function is considered. The existence and uniqueness of the global positive solution is achieved. By using the Lyapunov-Razumikhin approach, sufficient conditions are developed which guarantee the hybrid system is stochastically stable. The results of simulating our new SEIR model indicate that the hybrid control schemes could be an effective strategy to eradicate the disease.