中文摘要：

本文研究了一类在齐次Dirichlet边界条件下带有传染病的捕食-食饵模型.利用上下解方法得到了正解的先验估计;借助分歧理论,以扩散系数d为分歧参数,构造了发自半平凡解(槇d;θr,0)处的平衡解分支,从而给出了模型平衡态正解的存在性.

英文摘要：

A prey‐predator model with infectious disease subjected to homogeneous Dirichlet boundary condition is studied .By using upper and lower solution method ,a priori estimates of positive solutions is got .By means of the bifurcation theory ,steady‐state solutions bifurcating from the semi trivial solution (d;θr ,0) are given by treating the diffusion coefficient d as the bifurcation parameter ,which implies the existence of steady‐state solutions .