To study the effect of environmental noise on the spread of the disease, a stochastic Susceptible, Infective, Removed and Susceptible (SIRS) model with two viruses is introduced in this paper. Sufficient conditions for global existence of positive solution and stochastically asymptotic stability of disease-free equilibrium in the model are given. Then, it is shown that the positive solution is stochastically ultimately bounded and the moment average in time of the positive solution is bounded. Our results mean that the environmental noise suppresses the growth rate of the individuals and drives the disease to extinction under certain conditions. Finally, numerical simulations are given to illustrate our main results.

中文翻译：

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具有两种病毒的随机SIRS模型的动态行为

为了研究环境噪声对疾病传播的影响，本文引入了带有两种病毒的随机易感性，传染性，去除性和易感性（SIRS）模型。给出了模型中无病平衡的正解的整体存在性和随机渐近稳定性的充分条件。然后，表明正解最终随机地有界，并且正解的时间平均矩有界。我们的结果意味着环境噪声会抑制个体的生长速度，并在特定条件下使疾病灭绝。最后，通过数值模拟来说明我们的主要结果。