A double stochastic SIS network epidemic model with nonlinear contact rate and limited medical resources

This paper explores a double stochastic network epidemic model within the constraints of limited medical resources and nonlinear contact rate. Initially, we investigate the dynamic behavior of this infectious disease model. Subsequently, we explore how the intensity of volatility and the speed of reversion influence the model’s dynamics. Moreover, we present the outcomes of simulations conducted on this double stochastic network model. These simulations shed light on the repercussions of various factors, such as the intensity of volatility, the speed of reversion, the intensity of white noise, the availability of limited medical resources, and the nonlinear contact rate on the dynamics of the epidemic. Lastly, we delve into the impact of the intensity of volatility and the speed of reversion on the spread of infectious diseases through a comprehensive examination of smooth distributions. In conclusion, our findings have unveiled the intrinsic mechanisms governing the dynamic changes in this double stochastic epidemic model. Furthermore, our study places a strong emphasis on the influence of volatility intensity and the speed of the reversion within the mean-reverting Ornstein–Uhlenbeck processes on the propagation of infectious diseases.