During past decades, the study of the interaction between predator and prey species has become one of the most exciting topics in computational biology and mathematical ecology. In this paper, we aim to investigate the stability of a diseased model of susceptible, infected prey and predators around an internal steady state. To this end, the fractional derivatives based on the Mittag-Leffler kernels in the Liouville-Caputo concept has been taken into consideration. The existence and uniqueness of the acquired solutions to the model are also studied in this paper. In order to investigate the effects of the fractional-order along with other existing parameters in the model, several possible scenarios have been examined. As it is seen in the proposed graphical simulations, the employed fractional operator is capable of capturing all anticipated theoretical features of the model. The numerical technique employed in this contribution is precise and efficient and can be easily adopted to investigate many fractional-order models in biology. It is found that new proposed operators of fractional-order can describe the real-world phenomena even better than integer-order differential equations because of their memory-related properties.

中文翻译：

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使用非奇异分数阶导数研究捕食者系统中传染病传播的新模型

在过去的几十年里，捕食者和猎物之间相互作用的研究已成为计算生物学和数学生态学中最令人兴奋的课题之一。在本文中，我们旨在研究易感、受感染的猎物和捕食者患病模型围绕内部稳态的稳定性。为此，考虑了 Liouville-Caputo 概念中基于 Mittag-Leffler 核的分数阶导数。本文还研究了模型求得解的存在唯一性。为了研究分数阶以及模型中其他现有参数的影响，已经检查了几种可能的情况。正如在提议的图形模拟中看到的那样，所使用的分数运算符能够捕获模型的所有预期理论特征。该贡献中采用的数值技术精确高效，可轻松用于研究生物学中的许多分数阶模型。研究发现，新提出的分数阶算子由于其与记忆相关的特性，比整数阶微分方程更能描述现实世界的现象。