Predictive and Global Effect of Active Smoker in Asthma Dynamics with Caputo Fractional Derivative

Smoking is harmful to the lungs and has numerous effects on our bodies. This leads to decreased lung function, which increases the lungs’ susceptibility to asthma triggers. In this paper, we develop a new fractional-order model and investigate the impact of smoking on the progression of asthma by using the Caputo operator to analyze different factors. Using the Banach contraction principle, the existence and uniqueness of solutions are established, and the positivity and boundedness of the model are proved. The model further incorporates different stages of smoking to account for incubation periods and other latent effects, enhancing the accuracy of system dynamics. Within this Fractional operator framework, key analyses are performed, including the identification of equilibrium points, computation of the basic reproduction number, sensitivity analysis, and assessment of local and global stability with the Lyapunov function. Additionally, chaos stability employing linear response regulation is implemented mathematically, and the effect of the compartment shows through simulations. A numerical iterative method employing Newton polynomial interpolation is used to illustrate the effectiveness of the suggested model, and numerical simulations reveal its enhanced efficiency at various fractional orders. The fractional-order framework offers a more realistic representation than classical integer-order models.