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Global dynamics of a tuberculosis model with fast and slow progression and age-dependent latency and infection.
Journal of Biological Dynamics ( IF 2.8 ) Pub Date : 2019-11-01 , DOI: 10.1080/17513758.2019.1683628
Rui Xu 1 , Junyuan Yang 1 , Xiaohong Tian 1 , Jiazhe Lin 2
Affiliation  

In this paper, a mathematical model describing tuberculosis transmission with fast and slow progression and age-dependent latency and infection is investigated. It is assumed in the model that infected individuals can develop tuberculosis by either of two pathogenic mechanisms: direct progression or endogenous reactivation. It is shown that the transmission dynamics of the disease is fully determined by the basic reproduction number. By analyzing corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, it is proved that the system is uniformly persistent when the basic reproduction number is greater than unity. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, it is verified that the global dynamics of the system is completely determined by the basic reproduction number.



中文翻译:

具有快速和缓慢进展以及年龄依赖性潜伏期和感染的结核病模型的整体动力学。

在本文中,研究了一种描述结核病传播的快慢模型以及与年龄有关的潜伏期和感染的数学模型。在模型中假设感染的个体可以通过两种致病机制之一发展为结核病:直接进展或内源性激活。结果表明,疾病的传播动力学完全由基本繁殖数决定。通过分析相应的特征方程,建立了模型的无病稳态和地方性稳态的局部稳定性。通过对无穷维系统的持久性理论,证明了当基本再现数大于1时,系统具有一致的持久性。通过构造合适的Lyapunov功能并使用LaSalle'

更新日期:2019-11-01
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