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    Artificial Neural Network (ANN)-Based Analysis and Optimal Control of Smoking Dynamics with Global Sensitivity Assessment
    (2026-06-01)
    Omrane, Ines Ben
    ;
    Ullah, Naeem
    ;
    Alhamzi, Ghaliah
    ;
    Jeelani, Mohammadi Begum
    The main objective of this study is to investigate smoking dynamics, identify the most influential factors governing smoking behavior, and develop effective intervention strategies through the integration of fractional-order modeling, sensitivity analysis, optimal control theory, and artificial neural networks (ANNs). A nonlinear fractional-order compartmental model is formulated by dividing the population into potential smokers, light smokers, heavy smokers, and quit smokers. The smoking reproduction number is derived to characterize the transmission and persistence of smoking behavior within the population. To determine the impact of model parameters on smoking dynamics, both normalized forward sensitivity analysis and global sensitivity analysis based on Latin Hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC) are performed. The obtained results identify the most sensitive transmission and progression parameters and demonstrate their important role in shaping smoking prevalence within the community. Furthermore, the classical integer-order model is compared with the fractional-order formulation, where the fractional model provides a more realistic description due to its ability to incorporate memory and hereditary effects associated with smoking behavior. An optimal control framework involving awareness and treatment strategies is further introduced to investigate effective smoking reduction policies. The numerical results demonstrate that awareness campaigns reduce smoking initiation, while treatment interventions increase smoking cessation, and the combined implementation of both strategies produces the most significant reduction in smoking prevalence. The consistency between the sensitivity analysis and optimal control results further supports the reliability of the proposed framework. Numerical simulations are carried out to analyze the qualitative and quantitative behavior of the system under different epidemiological scenarios. In addition, an ANN-based computational framework is employed as an efficient numerical tool to accurately approximate the complex dynamics of the proposed fractional-order smoking model with very low prediction error. Overall, the present study provides a comprehensive mathematical and computational framework for understanding, analyzing, and controlling smoking behavior within a population.
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    FRACTIONAL-ORDER SENSITIVITY ANALYSIS OF LEPTOSPIROSIS TREATMENT DYNAMICS IN THE PRESENCE OF AN ENVIRONMENTAL BACTERIAL RESERVOIR WITH ARTIFICIAL NEURAL NETWORK SUPPORT
    (2026-01-01)
    Irshad, Ateeq Ur Rehman
    ;
    Ullah, Naeem
    ;
    Hassaballa, Abaker A.
    ;
    Jeelani, Mdi Begum
    ;
    Fatima, Nahid
    In this study, we develop and analyze a deterministic fractional-order human–animal–environment transmission model using the Caputo fractional-order derivative (CFOD) to investigate leptospirosis transmission dynamics, explicitly incorporating treatment for infected humans in the human population. The model accounts for indirect transmission through an environmental bacterial reservoir and shedding from infected animals. The qualitative features of the suggested model, such as positivity, boundedness, existence and uniqueness of solution, equilibrium points, and biological well-posedness of the solutions, are thoroughly demonstrated. The model captures nonlocal and memory-dependent characteristics that cannot be described by classical integer-order derivatives. The next-generation matrix (NGM) approach is used to determine the basic reproduction number (ℛ<inf>0</inf><sup>FV</sup>). The stability properties of the pathogen-extinction steady state and sustained-transmission steady state are investigated. In particular, Lyapunov function techniques are used to check the global stability of the PESS and STSS under suitable conditions, while Ulam–Hyers stability is established to examine the stability of the model solutions under small perturbations. To better understand the influence of model parameters, normalized forward sensitivity analysis is performed, showing that transmission, treatment, and recovery-related parameters exert the strongest influence on disease burden. Numerical simulations are used to verify theoretical results and investigate the effects of key epidemiological parameters on disease transmission. Finally, an artificial neural network (ANN) is employed only as a supplementary computational tool to reproduce the numerically obtained solution trajectories and to provide a consistency check of the computed results. The findings offer a valuable perspective on the dynamics of leptospirosis transmission and could inform disease control and intervention efforts.