Wang Yan Mei, Liu Gui Rong
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China.
Math Biosci Eng. 2019 Jun 29;16(5):6047-6070. doi: 10.3934/mbe.2019303.
In this paper, we investigate the dynamics of a stochastic SIRS epidemic model with non-linear incidence rate and transfer from infectious to susceptible. Firstly, the existence and uniqueness of global positive solution of the model with any positive initial value are proved. Next, sufficient conditions for extinction and persistence of the disease are established. It is found that a large noise intensity has the effect of suppressing the epidemic. At last, some numerical simulations are introduced to demonstrate the theoretical results. Our results generalize and improve the existing results.
在本文中，我们研究了一个具有非线性发病率以及从感染类向易感类转移的随机SIRS传染病模型的动力学。首先，证明了该模型对于任意正初始值全局正解的存在性和唯一性。其次，建立了疾病灭绝和持续存在的充分条件。发现大的噪声强度具有抑制疫情的作用。最后，引入了一些数值模拟来验证理论结果。我们的结果推广并改进了现有结果。
