标题： 捕食者-猎物种群中传染病的动力学：随机模型、可持续性与不变测度 显示英文标题

标题： Dynamics of infectious diseases in predator-prey populations: a stochastic model, sustainability, and invariant measure

摘要： 本文介绍了一种针对捕食者-猎物种群传染病的创新模型。我们不仅证明了全局非负解的存在性，还建立了系统衰减和可持续性的基本标准。此外，我们展示了Borel不变测度的存在性，为理解该系统增添了新的维度。为了说明我们的发现的实际意义，我们给出了数值结果。通过我们模型的综合方法，我们旨在为传染病动力学及其对捕食者-猎物种群的影响提供有价值的见解。 显示英文摘要

摘要： This paper introduces an innovative model for infectious diseases in predator-prey populations. We not only prove the existence of global non-negative solutions but also establish essential criteria for the system's decline and sustainability. Furthermore, we demonstrate the presence of a Borel invariant measure, adding a new dimension to our understanding of the system. To illustrate the practical implications of our findings, we present numerical results. With our model's comprehensive approach, we aim to provide valuable insights into the dynamics of infectious diseases and their impact on predator-prey populations.