ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT

A. H. Permatasari, R. H. S. Utomo
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Abstract

A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease. 
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不同治疗效果下肺结核动力学模型分析
研究了一个整合感染前和活动性感染阶段以及两个治疗参数的结核病模型。该模型还考虑了结核病前感染的死亡率。利用基本繁殖比研究了平衡点的局部稳定性和全局稳定性。利用Routh Hurwitz准则分析了未感染平衡点的局部稳定性。给出了地方性平衡的存在性。在得到地方性平衡后,利用Lyapunov函数分析了地方性平衡的全局稳定性。用数值模拟的方法研究了治疗对结核病传播的影响。
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