Dynamics Study On A Class Of SIRS Epidemic Model With Vaccination

During the disease explosion,vaccination is the effective measures to prevent and control the disease spreading.In addition,information intervention and environment noise can also effect the spread of disease.Thus,this paper takes the influence of information intervention and environment noise into the epidemic model with vaccination to study the dynamics of the disease.The details are as follows:(?)The asymptotic behavior of an SIRS epidemic model containing information intervention and vaccination has been studied.Our results indicated that the basic reproduction number R0 is the threshold of disease persistence and extinction.If Ro<1,the system has an disease free equilibrium which is globally asymptotically stable,while if R0>1 the endemic equilibrium exists which is globally asymptotically stable.At last,some numerical examples are given to illustrate our results.(?)Population systems inevitably suffer sudden environmental changes which lead to the uncer-tainty of parameters(such as birth date,death date and so on).To describe the uncertainty of the system,we present a stochastic SIRS epidemic model with vaccination under regime switching.Firstly,we obtain sufficient criteria of extinction of disease and existence of an er-godic stationary distribution.Meanwhile,the threshold which guarantees the existence and the uniqueness of ergodic stationary distribution for stochastic model is obtained.Numerical sim-ulations are given to verify our analytical results,which illustrate that Markov switching has significant effect to the epidemic model.