一类肺结核模型的性质研究

Property Analysis of a Tuberculosis Model

本文根据肺结核的传播机理,考虑到感染者的自愈和治愈、以及康复者的复发,对Blower等人建立的肺结核传播模型进行了部分改进;利用定性和稳定性理论和方法,求出了模型的基本再生数,讨论了无病平衡点的稳定性、正平衡点的存在条件及其稳定性,并剖析了相应的生物学意义。

According to the mechanism of pulmonary tuberculosis, this paper takes into account the self-healing,healing of infected people and the recurrence of rehabilitation as well as partly improves the model of tuberculosis transmission established by Blower et al. Based on the theory and method of qualitative and stability, the basic regeneration number of the model is obtained. The stability of the diseased disequilibrium point,the existence condition of the positive equilibrium point and its stability are discussed,and the corresponding biological significance is analyzed.