一个具有干预策略的肺结核模型的阈值动力学行为(英文)

Threshold Dynamics for a Tuberculosis Model with Intervention Strategies

文献[4]研究了肺结核传播的动力学行为.该文献仅从数值模拟上分析了疾病的传播和不同策略对疾病传播的影响.本文从理论上对疾病传播和不同策略对疾病传播的影响进行了分析.主要结论如下:得到了模型的基本再生数R_0.R_0决定了疾病传播的动力学行为:如果R_0<1,则模型仅有一个无病平衡点且是局部渐近稳定的,若R_0>1则模型存在一个地方病平衡点并且疾病是一致持续的.本文还得到了无病平衡点全局渐近稳定的充分条件.

A recent paper[4]explores the dynamics of the spread of tuberculosis （TB）.The analysis there only numerically analyzes the disease spread and the effects of different invention strategies.In the present paper,the spread dynamics of the disease and the effects of different intervention strategies are analyzed theoretically.The main results of the model are：The basic reproduction number R_0 is calculated.It is shown that this number characterizes the disease transmission dynamics：if R_0 1,there exists only the disease-free equilibrium which is locally asymptotically stable;and if R_0 1 then there is a disease endemic equilibrium and the disease persists.Sufficient condition for the global stability of the disease-free equilibrium is also obtained.