In this paper, we consider a predator-prey model, where we assumed that the model to be an infected predator-free equilibrium one. The model includes a distributed delay to describe the time between the predator’s capture of the prey and its conversion to biomass for predators. When the delay is absent, the model exhibits asymptotic convergence to an equilibrium. Therefore, any nonequilibrium dynamics in the model when the delay is included can be attributed to the delay’s inclusion. We assume that the delay is distributed and model the delay using integrodifferential equations. We established the well-posedness and basic properties of solutions of the model with nonspecified delay. Then, we analyzed the local and global dynamics as the mean delay varies.

中文翻译：

---

具有分布时滞的捕食者－食饵模型的分析

在本文中，我们考虑了一个捕食者－猎物模型，在该模型中，我们假设该模型是一个无感染的捕食者平衡模型。该模型包括一个分布式延迟，用于描述捕食者捕获猎物与捕食者将其转化为生物量之间的时间。当不存在延迟时，模型表现出渐近收敛到平衡状态。因此，当包含延迟时，模型中的任何非平衡动力学都可以归因于延迟的包含。我们假设延迟是分布式的，并使用积分微分方程对延迟进行建模。我们建立了具有不确定延迟的模型解的适定性和基本性质。然后，我们分析了平均延迟变化时的局部和全局动态。