Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.

中文翻译：

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登革热病毒在蚊子和人类之间传播的随机动力学

考虑到环境白噪声对疾病传播媒介的数量和行为的影响，本文提出了描述登革热在蚊子和人类之间传播的随机微分模型。通过使用李雅普诺夫方法和伊藤公式，我们首先证明了该模型的全局正解的存在性和唯一性。进一步地，利用一系列随机不等式的技术，得到了该随机模型均值消退和持续存在的一些充分条件。此外，我们还讨论了导致这种疾病随机持续存在的独特平稳分布的存在。最后，进行了几个数值模拟来说明这一贡献的主要结果。