Abstract
In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic reproduction number R0S which can be regarded as a threshold to use in identifying the stochastic extinction and persistence: if R0S<1, the disease dies out exponentially with probability one; while if R0S>1, there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease.
•A regime-switching SIRS epidemic model with a ratio-dependent incidence rate is studied.•A stochastic reproduction number R0S is proposed to be regarded as a threshold.•If R0S<1, the disease dies out exponentially with probability one.•If R0S<1, there is a unique ergodic stationary distribution of the system.