Asymptotic behavior of a regime-switching SIR epidemic model with degenerate diffusion

In this paper, we consider a stochastic SIR epidemic model with regime switching. The Markov semigroup theory will be employed to obtain the existence of a unique stable stationary distribution. We prove that, if $R^s<0$, the disease becomes extinct exponentially; whereas if $R^s>0$ and $\beta \left(i\right)>\alpha \left(i\right)\left(\epsilon \right(i)+\gamma (i\left)\right)$, $i\in S$, the densities of the distributions of the solution can converge in $L^1$ to an invariant density.