Asymptotic properties of switching diffusion epidemic model with varying population size

The purpose of this work is to investigate the asymptotic properties of a stochastic version of the classical SIS epidemic model with standard incidence and varying population size. The stochastic model studied here includes white vector noise and telegraph noise modeled by Markovian switching. We established conditions for extinction both in probability one and in pth moment. We also established the persistence of disease under different conditions on the intensities of noises and the parameters of the model. Furthermore, we showed the existence of a stationary distribution and derive expressions for its mean and variance. The presented results are demonstrated by numerical simulations.