Long-time behavior of a regime-switching Susceptible-Infective epidemic model with degenerate diffusion

In this paper, we consider a stochastic SI epidemic model with regime switching. The Markov semigroup theory is employed to obtain the existence of a unique stable stationary distribution. We prove that if R s < 0 , then the disease becomes extinct exponentially; whereas if R s > 0 and β ( i ) > α ( i ) , i ∈ S , then the densities of the distributions of the solution can converge in L 1 to an invariant density.