中文摘要：

考虑一类捕食者带有传染病并具有Holling-Ⅱ功能性反应函数的生态-流行病模型. 讨论其带有扩散项的在齐次Neumann边界条件下问题. 主要考虑其对应的平衡态问题的正解的存在性. 首先应用最大值原理和Harnack不等式给出其反应扩散问题的正平衡解的先验估计（正的上下界估计） ,然后应用能量方法给出了该问题非常数正平衡解的不存在性,最后应用拓扑度理论研究了该问题非常数正平衡解的存在性.

英文摘要：

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.