Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value [Formula: see text] is defined in terms of the basic reproduction number [Formula: see text] for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When [Formula: see text], the cholera infection will extinct within finite periods of time almost surely. When [Formula: see text], the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number [Formula: see text] for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that [Formula: see text], the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.

中文翻译：

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波动环境中霍乱流行模型的动力学

基于我们对霍乱流行的确定性模型，我们提出了一个霍乱流行的随机模型，以结合环境波动，这是一个伊藤随机微分方程的非线性系统。我们对模型的动态行为进行渐近分析。基本随机再生值[公式：见正文]是根据相应确定性模型和噪声强度的基本再生数[公式：见正文]定义的。基本随机再现值决定了随机模型的动态模式。当[公式：见正文]时，霍乱感染几乎肯定会在有限的时间内灭绝。[公式：见正文]时，霍乱感染会持续大部分时间，并且存在一个独特的平稳遍历分布，随机模型的所有解几乎肯定会接近该分布，因为噪声强度是有界的。当对应确定性模型的基本再生数[公式：见正文]大于1，并且噪声强度足够大，使得[公式：见正文]时，霍乱感染被环境噪声抑制。我们进行数值模拟来说明我们的分析，并与相应的确定性模型进行比较。指出了生物学意义。霍乱感染被环境噪音抑制。我们进行数值模拟来说明我们的分析，并与相应的确定性模型进行比较。指出了生物学意义。霍乱感染被环境噪音抑制。我们进行数值模拟来说明我们的分析，并与相应的确定性模型进行比较。指出了生物学意义。