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中文摘要：
传染病动力学的研究具有重要的实际意义，越来越受到人们的普遍关注．研究一类具常数接触率的传染病模型，用上下解方法讨论了该模型解的存在性、唯一性，讨论了半正常数稳态解的渐近行为，即无病平衡点及染病平衡点的渐进行为，得到了各自全局稳定的充分条件．
英文摘要：
Researches on epidemic dynamics, which are of great practical significance, are receiving an ever-increasingly attention from people of different walks. In this paper, an epidemic model with constant contact is approached by the upper-and-lower solution method to discuss the asymptotic behaviors of disease-free equilibrium and endemic equilibrium. Sufficient conditions for the system to have a semi-positive globally asymptotically stable solution are obtained.
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