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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 \(\mathcal{R}^{s}<0\), then the disease becomes extinct exponentially; whereas if \(\mathcal{R}^{s}>0\) and \(\beta(i)>\alpha(i), i\in\mathbb{S}\), then the densities of the distributions of the solution can converge in \(L^{1}\) to an invariant density.

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