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分形分数阶结核病模型:存在性与数值解。

Fractal fractional model for tuberculosis: existence and numerical solutions.

机构信息

Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia.

Department of Medical Research, China Medical University, Taichung, 40402, Taiwan.

出版信息

Sci Rep. 2024 May 28;14(1):12211. doi: 10.1038/s41598-024-62386-4.


DOI:10.1038/s41598-024-62386-4
PMID:38806568
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11637044/
Abstract

This paper deals with the mathematical analysis of Tuberculosis by using fractal fractional operator. Mycobacterium TB is the bacteria that causes tuberculosis. This airborne illness mostly impacts the lungs but may extend to other body organs. When the infected individual coughs, sneezes or speaks, the bacterium gets released into the air and travels from one person to another. Five classes have been formulated to study the dynamics of this disease: susceptible class, infected of DS, infected of MDR, isolated class, and recovered class. To study the suggested fractal fractional model's wellposedness associated with existence results, and boundedness of solutions. Further, the invariant region of the considered model, positive solutions, equilibrium point, and reproduction number. One would typically employ a fractional calculus approach to obtain numerical solutions for the fractional order Tuberculosis model using the Adams-Bashforth-Moulton method. The fractional order derivatives in the model can be approximated using appropriate numerical schemes designed for fractional order differential equations.

摘要

本文使用分形分数阶算子对结核病进行了数学分析。结核分枝杆菌是引起结核病的细菌。这种空气传播的疾病主要影响肺部,但也可能扩展到其他身体器官。当受感染的个体咳嗽、打喷嚏或说话时,细菌会释放到空气中,并从一个人传播到另一个人。已经制定了五类来研究这种疾病的动力学:易感类、DS 感染类、MDR 感染类、隔离类和康复类。为了研究建议的分形分数阶模型的适定性和存在结果,以及解的有界性。此外,还研究了所考虑模型的不变区域、正解、平衡点和繁殖数。通常使用分数阶微积分方法,通过使用 Adams-Bashforth-Moulton 方法,对分数阶结核病模型获得数值解。模型中的分数阶导数可以使用针对分数阶微分方程设计的适当数值方案进行近似。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/6a88cf520310/41598_2024_62386_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/25518d26fcdf/41598_2024_62386_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/b14581f252f2/41598_2024_62386_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/d295935d2436/41598_2024_62386_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/27466b985541/41598_2024_62386_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/565e9a89c670/41598_2024_62386_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/fd88e7af4887/41598_2024_62386_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/185028575b7f/41598_2024_62386_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/7175f4d45f2b/41598_2024_62386_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/c3d990447442/41598_2024_62386_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/6a88cf520310/41598_2024_62386_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/25518d26fcdf/41598_2024_62386_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/b14581f252f2/41598_2024_62386_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/d295935d2436/41598_2024_62386_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/27466b985541/41598_2024_62386_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/565e9a89c670/41598_2024_62386_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/fd88e7af4887/41598_2024_62386_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/185028575b7f/41598_2024_62386_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/7175f4d45f2b/41598_2024_62386_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/c3d990447442/41598_2024_62386_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7bc2/11637044/6a88cf520310/41598_2024_62386_Fig10_HTML.jpg

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Fractal fractional model for tuberculosis: existence and numerical solutions.

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本文引用的文献

[1]
Acoustic Fractional Propagation in Terms of Porous Xerogel and Fractal Parameters.

Gels. 2024-1-22

[2]
Studying the efficacy of isolation as a control strategy and elimination of tuberculosis in India: A mathematical model.

Infect Dis Model. 2023-4-6

[3]
Qualitative Analysis of the Transmission Dynamics of Dengue with the Effect of Memory, Reinfection, and Vaccination.

Comput Math Methods Med. 2022

[4]
Impact of diabetes mellitus on tuberculosis epidemiology in Indonesia: A mathematical modeling analysis.

Tuberculosis (Edinb). 2022-5

[5]
Global Tuberculosis Report 2020 - Reflections on the Global TB burden, treatment and prevention efforts.

Int J Infect Dis. 2021-12

[6]
Mathematical model and tool to explore shorter multi-drug therapy options for active pulmonary tuberculosis.

PLoS Comput Biol. 2020-8-18

[7]
COVID-19 and tuberculosis: A mathematical model based forecasting in Delhi, India.

Indian J Tuberc. 2020-4

[8]
Heterogeneous infectiousness in mathematical models of tuberculosis: A systematic review.

Epidemics. 2020-3

[9]
Updates on the risk factors for latent tuberculosis reactivation and their managements.

Emerg Microbes Infect. 2016-2-3

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