摘要：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 $\mathcal{R}^{s}>0$ and β ( i ) > α ( i ) , i ∈ S $\beta(i)>\alpha(i), i\in\mathbb{S}$ , then 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
