In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

中文翻译：

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基于易感个体和康复个体之间关联的随机流行病动态

在本文中，我们提出了一种基于易感个体和康复个体之间关联的新数学模型。然后，我们用确定性案例研究了该模型的稳定性，得到了疾病灭绝的条件。此外，鉴于白噪声扰动的易感个体和康复个体之间的关联，我们还给出了白噪声对疾病的灭绝和持续存在的充分条件。最后，我们进行了数值模拟，以证明所获得的理论结果的正确性。