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新型冠状病毒肺炎与结核病传播动力学的数学建模及分析

Mathematical modelling and analysis of COVID-19 and tuberculosis transmission dynamics.

作者信息

Singh Ram, Rehman Attiq Ul, Ahmed Tanveer, Ahmad Khalil, Mahajan Shubham, Pandit Amit Kant, Abualigah Laith, Gandomi Amir H

机构信息

Department of Mathematical Sciences, BGSB University, Rajouri, 185234, India.

Department of Mathematics, Al-Falah University, Faridabad, India.

出版信息

Inform Med Unlocked. 2023;38:101235. doi: 10.1016/j.imu.2023.101235. Epub 2023 Mar 31.

Abstract

In this paper, a mathematical model for assessing the impact of COVID-19 on tuberculosis disease is proposed and analysed. There are pieces of evidence that patients with Tuberculosis (TB) have more chances of developing the SARS-CoV-2 infection. The mathematical model is qualitatively and quantitatively analysed by using the theory of stability analysis. The dynamic system shows endemic equilibrium point which is stable when and unstable when . The global stability of the endemic point is analysed by constructing the Lyapunov function. The dynamic stability also exhibits bifurcation behaviour. The optimal control theory is used to find an optimal solution to the problem in the mathematical model. The sensitivity analysis is performed to clarify the effective parameters which affect the reproduction number the most. Numerical simulation is carried out to assess the effect of various biological parameters in the dynamic of both tuberculosis and COVID-19 classes. Our simulation results show that the COVID-19 and TB infections can be mitigated by controlling the transmission rate .

摘要

本文提出并分析了一个用于评估新冠疫情对结核病影响的数学模型。有证据表明,结核病患者感染新冠病毒的几率更高。利用稳定性分析理论对该数学模型进行了定性和定量分析。该动态系统显示出地方病平衡点,当 时是稳定的,当 时是不稳定的。通过构造李雅普诺夫函数分析了地方病平衡点的全局稳定性。动态稳定性还表现出分岔行为。运用最优控制理论在数学模型中找到该问题的最优解。进行敏感性分析以阐明对繁殖数影响最大的有效参数。进行数值模拟以评估各种生物学参数在结核病和新冠两类动态中的作用。我们的模拟结果表明,通过控制传播率 可以减轻新冠和结核病感染。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8ad9/10065048/62929682f55c/gr1_lrg.jpg

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