Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation
Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation
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DOI：
10.1016/j.physa.2018.01.014
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发表时间：
2018-05-01
影响因子：
3.3
通讯作者：
Kar, Tapan Kumar
中科院分区：
文献类型：
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作者：
Khajanchi, Subhas;Das, Dhiraj Kumar;Kar, Tapan Kumar
本文提出并分析了结核病传播的数学模型，以研究外源性再感染和内源性再激活的作用。该模型具有两个平衡点：无病平衡点和地方病平衡点。当基本再生数R-0 = 1时，TB模型出现了跨临界分支.我们的研究结果表明，疾病传播率β和外源性再感染率α在改变结核病的质量动态方面起着重要作用。当R-0 < 1时，疾病传播率β引起向后分支的可能性，从而存在多个地方病平衡点，其中一个平衡点稳定，另一个平衡点不稳定。我们的分析表明，R-0 < 1可能不足以完全消除这种疾病。我们还研究了结核病传播模型在接触率β和外源性再感染率α方面的Hopf分支。我们进行了一些数值模拟，以支持我们的分析结果。(C)2018由Elsevier B. V.出版
We propose and analyze a mathematical model for tuberculosis (TB) transmission to study the role of exogenous reinfection and endogenous reactivation. The model exhibits two equilibria: a disease free and an endemic equilibria. We observe that the TB model exhibits transcritical bifurcation when basic reproduction number R-0 = 1. Our results demonstrate that the disease transmission rate beta and exogenous reinfection rate a plays an important role to change the qualitative dynamics of TB. The disease transmission rate beta give rises to the possibility of backward bifurcation for R-0 < 1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R-0 < 1 may not be sufficient to completely eliminate the disease. We also investigate that our TB transmission model undergoes Hopf-bifurcation with respect to the contact rate beta and the exogenous reinfection rate alpha. We conducted some numerical simulations to support our analytical findings. (C) 2018 Published by Elsevier B.V.