A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results.

中文翻译：

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具有随机猎物和Holling II型功能性反应的疾病的随机捕食者-食饵模型的分析

提出了一种具有疾病反应且具有Holling II型功能性反应的疾病的随机捕食者—食饵模型，并对其动力学进行了分析。我们讨论了动力学系统的有界性，并找到了所有可行的平衡解。对于随机系统，我们获得了存在全局唯一解，有界性和一致连续性的条件。我们得出了物种灭绝和永续的条件。此外，我们构造了适当的Lyapunov函数并讨论了平衡点的渐近稳定性。为了说明我们的理论发现，我们进行了数值模拟并给出了结果。