  In this paper, a stochastic SEQIR epidemic model with Markovian
regime-switching is proposed and investigated. The governmental policy and
implement efficiency are concerned by a generalized incidence function of the
susceptible class. We have the existence and uniqueness of the globally
positive solution to the stochastic model by using the Lyapunov method. In
addition, we study the dynamical behaviors of the disease, and the sufficient
conditions for the extinction and persistence in mean are obtained. Finally,
numerical simulations are introduced to demonstrate the theoretical results.
