A stochastic epidemic model with infectivity rate in incubation period and homestead–isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.

中文翻译：

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潜伏期传染性和易感者居家隔离的随机流行病模型

为了揭示随机白噪声对长期行为的影响，建立了潜伏期感染率和易感者宅基地隔离的随机流行病模型。获得了对该疾病平均值的灭绝和强持久性的良好理解。此外，我们为模型的独特遍历平稳分布的存在推导出了足够的标准。我们的理论结果表明，适当大的噪声可以使疾病灭绝，而较小的噪声有利于疾病的持续存在和平稳分布。