摘要：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 $\mathcal{R}^{s}>0$ and β ( i ) > α ( i ) ( ε ( i ) + γ ( i ) ) $\beta(i)>\alpha(i)(\varepsilon(i)+\gamma(i))$ , i ∈ S $i\in\mathbb{S}$ , the densities of the distributions of the solution can converge in L 1 $L^)$ to an invariant density.
关键词：Stationary distribution ; Markov semigroups ; Asymptotic stability
