Lassa Fever (LF) is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa, causing thousands of deaths annually. This study develops a dynamic model of Lassa virus transmission, capturing the progression of the disease through susceptible, exposed, infected, and recovered populations. The focus is on simulating this model using the fractional Caputo derivative, allowing both qualitative and quantitative analyses of boundedness, positivity, and solution uniqueness. Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions, while Lyapunov functions establish the global stability of both disease-free and endemic equilibria. The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method. This approach offers practical advantages in handling additional data points in integral forms, though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods. Graphical simulations validate the proposed numerical approach for different fractional orders ( $\nu$) and illustrate the influence of model parameters on disease dynamics. Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations. Moreover, fractional-order modeling provides more nuanced insights than traditional integer-order models, suggesting potential improvements for medical intervention strategies. The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models, offering a promising direction for future research in epidemiological modeling.

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.