Infectious diseases affect prey populations, and predators choosing susceptible prey may lead to the extinction of the prey population. We propose a mathematical model of prey–predator interaction with the prey population divided into two classes: susceptible and infected. The susceptible prey subpopulation becomes infected by direct contact with the infected prey subpopulation, and the predator consumes only susceptible prey. An analysis of the model enabled the establishment of thresholds for the spread of disease in the absence and presence of predators. In the absence of predators, we obtain the classic basic reproduction number ℜ₀, and in the presence of predators, we obtain a new threshold ${\Re }_0^P$, which measures the effect of predators in the disease spread. Furthermore, these thresholds establish conditions for the existence and stability of biologically viable equilibrium points. Using numerical simulations, we determined the different biological characteristics of the model and illustrated the analytical results.

中文翻译：

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修正的莱斯利-高尔捕食者-猎物模型，具有替代食物和未感染猎物的选择性捕食

传染病影响猎物种群，捕食者选择易感染的猎物可能导致猎物种群灭绝。我们提出了一个食饵-捕食者相互作用的数学模型，其中食饵种群分为两类：易感性和感染性。易感的猎物亚群通过直接与被感染的猎物亚群接触而被感染，并且捕食者仅消耗易感的猎物。通过对模型的分析，可以确定在没有掠食者存在和存在的情况下疾病传播的阈值。在不存在的天敌，我们得到经典基本再生数ℜ ₀，并且在捕食者的存在，我们得到一个新的阈值${\Re }_0^P$，用于衡量捕食者在疾病传播中的作用。此外，这些阈值为生物学上可行的平衡点的存在和稳定性建立了条件。使用数值模拟，我们确定了模型的不同生物学特性，并说明了分析结果。