In this paper, when the predator breeds only by the prey, the relationship among the two classes of prey (susceptible and infected prey) and the predator is represented by using an epidemic model with nonlinear incidence and the response function depending on the density of the three individuals under homogeneous Dirichlet boundary conditions describing a hostile environment at its boundary. For this model, the coexistence steady state of three interacting species is mainly investigated, and the global stabilities of the extinction of all species and the survival of only healthy prey are discussed. Additionally, the conditions of the non-coexistence of three species are established. Finally, an ecological interpretation is also presented based on the results.

在本文中，当捕食者仅靠猎物繁殖时，使用具有非线性发生率和响应函数的流行病模型来表示两类猎物（易感和受感染的猎物）与捕食者之间的关系。在均匀Dirichlet边界条件下的三个人描述了边界处的敌对环境。对于该模型，主要研究了三个相互作用物种的共存稳态，并讨论了所有物种灭绝的全球稳定性和仅健康猎物的生存。另外，建立了三个物种不共存的条件。最后，基于结果也提出了生态学解释。