Dynamical behaviors of a stochastic SIRI epidemic model. Issue 16 (10th December 2017) - Lei, Qiao; Yang, Zhichun
Abstract : In this paper, we initially propose a stochastic SIRI epidemic model. The existence, uniqueness, and boundedness of the positive solution of the stochastic system are derived. By using some novel Lyapunov functions and stochastic analysis tools, we mainly investigate asymptotical behaviors of the SIRI model under stochastic perturbations according to the basic reproduction number . That is, when (or ) and some conditions on white noise are satisfied, the solution of stochastic model will oscillate around the disease-free equilibrium (or endemic equilibrium) of the deterministic model and the estimate for the oscillation amplitude is obtained. Furthermore, the existence of a stationary distribution and the ergodicity of solutions are studied for the stochastic system. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained results.