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