Environmental noise and infectious diseases are important factors affecting the development of the population. This paper develops a mathematical system to investigate the impacts of environmental noise and infectious diseases on predator–prey interactions. The globally unique positive solution is confirmed by using conventional methods. The stochastic uniform boundedness of the solution is obtained under certain conditions. Sufficient conditions for the persistence and extinction are given to measure the level of population size. Asymptotic dynamics of the solutions are carried out by two criteria parameters. The long-term dynamics of the solutions are demonstrated by numerical simulations. The results show that small-intensity environmental perturbations can cause population size to fluctuate around a certain level, while high-intensity environmental perturbations may lead to population extinction.

中文翻译：

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捕食者与猎物相互作用的分析：包含疾病入侵的随机模型

环境噪声和传染病是影响人口发展的重要因素。本文开发了一个数学系统来研究环境噪声和传染病对捕食者与猎物相互作用的影响。通过使用常规方法可以确定全局唯一的正解。在某些条件下获得了溶液的随机均匀有界度。给出了维持和灭绝的充分条件，以衡量种群数量的水平。解的渐近动力学由两个标准参数执行。数值模拟表明了解决方案的长期动态。结果表明，小强度的环境扰动会导致种群规模在一定水平附近波动，