Integrating machine learning and artificial neural networks for dynamic analysis of a fractional order smoking-induced lungs cancer model

This study introduces a fractional-order framework for modeling the progression of smoking behavior and its relationship to cancer onset. The population is stratified into seven compartments: susceptible, exposed, chronic carriers, active smokers without intervention, smokers under treatment, cancer-diagnosed and recovered individuals. By employing the Caputo fractional derivative, the model inherently captures memory effects, reflecting cumulative smoking exposure and delayed cancer progression. A rigorous theoretical analysis establishes positivity, boundedness, existence and uniqueness of solutions, ensuring biological realism. The basic reproduction number R₀ is derived using the next-generation matrix and equilibrium and stability analyses identify thresholds for disease persistence or elimination. The system is solved numerically via the Adams–Bashforth–Moulton scheme. Additionally, a surrogate model based on a Levenberg-Marquardt backpropagation neural network is developed to estimate the behavior of each compartment. Machine learning tools, including Support Vector Machines and Random Forest classifiers, are applied to assess the surrogate’s performance. This combination of fractional calculus, dynamical systems theory and neural-network approximation illustrates the feasibility of using hybrid computational strategies for analyzing smoking-cancer interactions.