A fractional mathematical model for assessing cancer risk due to smoking habits

Anil Chavada; Nimisha Pathak; Sagar R. Khirsariya; Anil Chavada; Nimisha Pathak; Sagar R. Khirsariya

doi:10.3934/mmc.2024020

Mathematical Modelling and Control

2024, Volume 4, Issue 3: 246-259. doi: 10.3934/mmc.2024020

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Research article

A fractional mathematical model for assessing cancer risk due to smoking habits

1.
Department of Applied Mathematics, Faculty of Technology & Engineering, The Maharaja Sayajirao University of Baroda, Vadodara 390001, Gujarat, India
2.
Department of Mathematics, Marwadi University, Rajkot 360003, Gujarat, India

Received: 10 January 2024 Revised: 17 March 2024 Accepted: 07 May 2024 Published: 03 July 2024

This article presents and analyzes a mathematical model for smoking-related cancer that involves fractional-order derivative with seven different compartments. The model uses the ABC fractional derivative to describe the transmission dynamics of cancer caused by the smoking habit. We employed the Adams-Bashforth-Moulton method to find the numerical and graphical results of the model and we achieved a good level of accuracy. The existence and uniqueness of the model solution were established using Banach's fixed-point theory. For stability, we investigated the steady state points and basic reproduction number of the system. Additionally, the model's stability was discussed using the Hyers-Ulam criterion. The two-dimensional (2D) and three-dimensional (3D) simulations were performed for the different compartments and for the various values of the fractional-order parameters.
- smoking-related cancer model,
- Atangana-Baleanu fractional derivative,
- Adams-Bashforth-Moulton method,
- stability analysis
Citation: Anil Chavada, Nimisha Pathak, Sagar R. Khirsariya. A fractional mathematical model for assessing cancer risk due to smoking habits[J]. Mathematical Modelling and Control, 2024, 4(3): 246-259. doi: 10.3934/mmc.2024020

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Abstract

This article presents and analyzes a mathematical model for smoking-related cancer that involves fractional-order derivative with seven different compartments. The model uses the ABC fractional derivative to describe the transmission dynamics of cancer caused by the smoking habit. We employed the Adams-Bashforth-Moulton method to find the numerical and graphical results of the model and we achieved a good level of accuracy. The existence and uniqueness of the model solution were established using Banach's fixed-point theory. For stability, we investigated the steady state points and basic reproduction number of the system. Additionally, the model's stability was discussed using the Hyers-Ulam criterion. The two-dimensional (2D) and three-dimensional (3D) simulations were performed for the different compartments and for the various values of the fractional-order parameters.

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