the dynamics behavior of a stochastic SIRS epidemic model with jumps is studied. By using the Lyapunov function method
we show that the model has unique global positive solution with the positive initial value. Then
the asymptotic behavior of solutions around the disease-free equilibrium and endemic equilibrium of the deterministic model is investigated.
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references
Mena-lorca J,Hethcote H W,Dynamic models of infectious diseases as regulations of population sizes[J].Math Biol,1992,30:693-716.
Beretta E,Kolmanovskii V,Shaikhet L,Stability of epidemic model with time delays influenced by stochastic perturbations[J].Math Comp Simul,1998,45:269-277.
Yang Q,Jiang D,Shi N,Ji C,The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with staturated incidence[J].Math Anal Appl,2012,388:248-271.
Mao X,Marion G,Renshaw E,Environmental noise suppresses explosion in population dynamics[J].Stoch Proc Appl,2002,97:95-110.
Bao J,Yuan C,Stochastic population dynamics driven by L′evy noise[J].Math Anal Appl,2012,391:363-375.
Bao J,Mao X,Competitive Lotka-Volterra population dynamics with jumps[J].Nonlinear Anal,2011,74:6601-6616.
Zhang X,Wang K,Stochastic SIR model with jumps[J].Appl Math Letter,2013,26:867-874.
Zhou X,Wang K,Numerical simulations and modeling for stochastic biological systems with jumps[J].Comm Nonl Sci Numer Simul,2014,19:1557-1568.