Stochastic SIRS model under regime switching

We propose a new stochastic SIRS model under regime switching in which both white and color environmental noises are taken into account. We show that white noise suppresses explosions in the model and the disease-free equilibrium of the model is stochastically asymptotically stable under certain conditions. Moreover, we show that the model is stochastically ultimately bounded and the moment average in time of the model solution is bounded. An example illustrates the boundedness of the moment average in time of the model solution.