Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
Lei Wang1, Zhidong Teng2, Tingting Tang2
1Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China.
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.
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