Dynamical behavior of a stochastic regime-switching epidemic model with logistic growth and saturated incidence rate

This work aims to study the effect of environmental noises like white noise and telegraph noise modeled by Markov switching on the dynamical properties of a modified logistic-growth-type epidemic model. Applying the Khasminskii method via a suitable construction of the Lyapunov function, we prove the existence of a unique solution for the stochastic model with probability one. Then we show the existence of a unique ergodic stationary distribution of the epidemic model which is the stability of stochastic system in the weak sense. It is noteworthy that regime switching can induce state transitions of diseases between extinction and persistence. Further, the pulse control scheme is developed to drive the disease to extinction when χ<0. Several numerical simulations are provided to validate our analytical findings.