A class of deterministic predator–prey systems, where the prey population is subject to an infectious disease, is studied. The disease can be transmitted both horizontally and vertically within the host population but cannot be spread between the two trophic levels. Using the mathematical tools of uniform persistence, we derive sufficient conditions for which the interacting populations can coexist. Criteria based on model parameters for which either only the infected prey or healthy prey persists are also provided. It is found through numerical investigations that predation can change competition outcomes between healthy and infected prey populations. Depending on the parameter regimes and initial conditions, predation can either eradicate or promote the disease. As infected prey provides a resource for the predators, disease may promote persistence of the predators. However, infected prey may dominate the predator–prey community if disease is very infectious. In addition, disease in the prey population can mediate a hydra effect in predators and may induce chaotic interactions.

中文翻译：

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确定性捕食者-猎物模型在猎物种群中存在疾病

研究了一类确定性捕食者 - 猎物系统，其中猎物种群受到传染病的影响。该疾病可以在宿主种群内水平和垂直传播，但不能在两个营养级之间传播。使用一致持久性的数学工具，我们推导出相互作用的种群可以共存的充分条件。还提供了基于仅受感染猎物或健康猎物持续存在的模型参数的标准。通过数值调查发现，捕食可以改变健康和受感染的猎物种群之间的竞争结果。根据参数方案和初始条件，捕食可以根除或促进疾病。由于受感染的猎物为掠食者提供了资源，疾病可能会促进捕食者的持续存在。然而，如果疾病具有很强的传染性，受感染的猎物可能会主导捕食者-猎物群落。此外，猎物种群中的疾病可以介导捕食者的水螅效应，并可能导致混乱的相互作用。