A Markovian switching diffusion for an Sirs epidemic model on complex network

The purpose of this research is to deepen our comprehension of a scale-free network stochastic SIRS epidemic model. Our investigation centers on the global dynamics of a scale-free network that undergoes regime switching. We begin by demonstrating that, for every positive starting value, the system has a unique global positive solution. Then, under the right circumstances, we show that the model has some interesting asymptotic properties. These properties include the extinction of the disease and its persistence in the mean. Through rigorous analysis, we explore the circumstances under which these outcomes occur and provide scientific evidence to support our findings.