Related Experiment Video
Updated: Jun 23, 2025
A 3D Human Lung Tissue Model for Functional Studies on Mycobacterium tuberculosis Infection
Published on: October 5, 2015
A mathematical fractal-fractional model to control tuberculosis prevalence with sensitivity, stability, and
Muhammad Farman1, Aamir Shehzad2, Kottakkaran Sooppy Nisar3
1Faculty of Arts and Sciences, Department of Mathematics, Near East University, Northern Cyprus, Turkey; Department of Computer Science and Mathematics, Lebanese American University, 1107-2020, Beirut, Lebanon.
Background:
Tuberculosis, a global health concern, was anticipated to grow to 10.6 million new cases by 2021, with an increase in multidrug-resistant tuberculosis. Despite 1.6 million deaths in 2021, present treatments save millions of lives, and tuberculosis may overtake COVID-19 as the greatest cause of mortality. This study provides a six-compartmental deterministic model that employs a fractal-fractional operator with a power law kernel to investigate the impact of vaccination on tuberculosis dynamics in a population.
Methods:
Some important characteristics, such as vaccination and infection rate, are considered. We first show that the suggested model has positive bounded solutions and a positive invariant area. We evaluate the equation for the most important threshold parameter, the basic reproduction number, and investigate the model's equilibria. We perform sensitivity analysis to determine the elements that influence tuberculosis dynamics. Fixed-point concepts show the presence and uniqueness of a solution to the suggested model. We use the two-step Newton polynomial technique to investigate the effect of the fractional operator on the generalized form of the power law kernel.
Results:
The stability analysis of the fractal-fractional model has been confirmed for both Ulam-Hyers and generalized Ulam-Hyers types. Numerical simulations show the effects of different fractional order values on tuberculosis infection dynamics in society. According to numerical simulations, limiting contact with infected patients and enhancing vaccine efficacy can help reduce the tuberculosis burden. The fractal-fractional operator produces better results than the ordinary integer order in the sense of memory effect at diffract fractal and fractional order values.
Conclusion:
According to our findings, fractional modeling offers important insights into the dynamic behavior of tuberculosis disease, facilitating a more thorough comprehension of their epidemiology and possible means of control.
Related Concept Videos
01:18Steps in Outbreak Investigation
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:14Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
01:28Pulmonary Tuberculosis II
Here is a detailed explanation of its pathophysiology:
Transmission: The process begins when a person inhales droplet nuclei containing M. tuberculosis. These are typically released into the air when an individual with pulmonary or...
01:28Pulmonary Tuberculosis V
Latent tuberculosis infection occurs when TB bacteria are present in a person's body, but are not causing illness or symptoms. It is not contagious, and preventive treatment is crucial to avoid the...