Mathematical Modeling of the Impact of Desert Dust on Asthma Dynamics

This study presents a mathematical model to describe the transmission dynamics of asthma, explicitly accounting for the impact of dust waves and airborne particulate matter in the environment, recognized as key triggers of asthma exacerbations. The model incorporates a single endemic equilibrium point, which is shown to be locally asymptotically stable. To mitigate the burden of asthma, we employed the Pontryagin Maximum Principle within an optimal control framework, incorporating three time-dependent intervention strategies: vaccination, treatment, and avoidance of environmental triggers such as dust exposure. The model was numerically solved using the fourth-order Runge–Kutta method in conjunction with a forward–backward sweep algorithm to investigate the effects of various control combinations on the prevalence of asthma. Additionally, a comprehensive cost-effectiveness analysis was conducted to evaluate the economic viability of each strategy. The results indicate that the combined application of vaccination and treatment is the most cost-effective approach among the strategies analyzed, significantly reducing the number of asthma cases at minimal cost. All simulations and numerical experiments were performed to validate the theoretical findings and quantify the effectiveness of the proposed interventions under realistic environmental conditions driven by dust activity. The model highlights the importance of integrated medical and environmental control policies in mitigating asthma outbreaks, particularly in regions frequently exposed to dust storms.