title: Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination.
abstract: In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.
authors.affiliation: Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Wang
authors.affiliation: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
authors.forename: Zhidong
authors.identifier: 0000-0002-4285-3277
authors.initials: Z
authors.lastname: Teng
authors.affiliation: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
authors.forename: Tingting
authors.initials: T
authors.lastname: Tang
authors.affiliation: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
authors.forename: Zhiming
authors.identifier: 0000-0002-6570-6325
authors.initials: Z
authors.lastname: Li
mesh_terms: D000465:Algorithms; D003140:Communicable Disease Control; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D011336:Probability; D013269:Stochastic Processes; D018746:Systemic Inflammatory Response Syndrome / Q000453:epidemiology* / Q000517:prevention & control*; D014611:Vaccination / Q000379:methods*