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

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.