具有季节传播的两株肺结核传染病模型

A Two-Stain Tuberculosis Model with Seasonality

在已有肺结核传染病模型基础上建立了具有季节性的耐药性与药物敏感性的肺结核传染病模型,分析了此模型基本再生数R0=max{R1,R2},得到了当R0<1时此模型存在唯一的无病平衡点是全局渐进稳定的.最后分析肺结核疾病持续的两种情况:第一种是当R1<1且R2>1时只有耐药性菌株持续;第二种是当R1>1且R2<1时两个菌株都是持续的.

Tuberculosis （TB） transmission has a periodic trend according to statistical data of TB cases showing seasonal fluctuations in poor resource‐settings .A two‐strain TB model incorporating seasonality is developed and the basic reproduction number R0 =max{R1 ,R2}is defined ,for i=1 ,2 denotes drug‐sensi‐tive strain and drug‐resistant strain ,respectively .It is show n that the disease free equilibrium is globally asymptotically stable and the disease always dies out if R0 〈1 ;while the disease is uniformly persistent if R0 〉1 .The drug‐resistant stain has at least one positive periodic solution if R2 〉1 and R1 〈1 ;the two‐strain TB model has at least one positive periodic solution if R1 〉1 and R2 〈1 .