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

Incorporating white and color noises into deterministic SIRS epidemic model, we establish a stochastic regime-switching SIRS model with degenerate diffusion. We prove that if Rs0, the densities of the distributions of the solution can converge in L1 to an invariant density. •We propose a regime-switching SIRS epidemic model with Beddington–DeAngelis incidence.•The diffusion term of stochastic model is degenerate.•We present a sufficient and necessary condition for the existence of stationary distribution.