位晓艳， 张娟^*

（  华北电力大学数理学院，北京，102206；  ）

摘要： 肺结核病是一种由结核杆菌引起的慢性呼吸道传染病，严重威胁着人类的健康。影响肺结核传播的因素有很多，其中环境因素对其传播有着重要影响。本文根据肺结核病的传播机理，建立了有关环境污染的肺结核病动力学模型。通过对模型进行定性分析，得到了模型的基本再生数，无病平衡点和地方病平衡点存在的充分必要条件，并证明了无病平衡点的稳定性。
关键词： 生物数学；肺结核；基本再生数；平衡点；稳定性

Wei Xiaoyan， Zhang Juan^*

（  Department of Mathematics and Physics,North China Electric Power University,Beijing,102206；  ）

Abstract： Tuberculosis is an infectious disease caused by chronic respiratory tract caused by Mycobacterium tuberculosis, a serious threat to human health. Factors that affect the spread of tuberculosis there are many environmental factors which have an important impact on its spread. Based on the mechanism of transmission of tuberculosis, tuberculosis established a dynamic model of environmental pollution. Through qualitative analysis of the model to obtain basic reproduction number model, necessary and sufficient conditions for disease-free equilibrium and the endemic equilibrium exists, and proved that the disease free equilibrium stability.
Keywords： Biomathematic;Tuberculosiss;Basic reproduction number;Equilibrium;Stability

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