Dynamics Of A Stochastic Susceptible-Infectivere-Covered (Sirs) Epidemic Model With Vaccination And Nonlinear Incidence Under Regime Switching And Levy Jumps

In this paper, a stochastic susceptible-infectivere-covered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Levy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Levy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Levy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.