Optimal control and dynamical transmission of asthma due to smoking populations: Incorporating medical and public health measures

Abstract

Smoking has numerous impacts on the human body, including damage to the lungs. Throughout global history, respiratory diseases have presented serious health challenges, with asthma emerging as one of the most prevalent chronic disorders worldwide for health risk control. Addressing the growing impact of asthma requires comprehensive modeling techniques to better understand its spread and to support effective disease management. This study presents a deterministic mathematical model that investigates the dynamics of asthma disease influenced by active smoking. To capture the transmission and progression of the disease, a smoking-induced asthma model is formulated in which the total population is divided into six compartments. Fundamental properties of the model, including positivity, boundedness, invariant regions, and equilibrium points, are rigorously analyzed to ensure biological feasibility. The basic reproductive number $\left(R_0\right)$ is derived and investigated to determine its role in disease persistence or eradication, while sensitivity analysis identifies the most influential factors governing asthma spread. This investigation further explores local stability of the smoking-induced asthma model, with special focus on a small number of observations. To obtain numerical solutions, the well-established Non-standard finite difference (NSFD) scheme is employed to illustrate the systems behavior and validate analytical findings. Additionally, to achieve the fundamental goal of this research, an optimal control approach is introduced by incorporating two control factors: awareness campaigns through social media and treatment protocols aimed at reducing the abundance of infected individuals. Simulations demonstrate the predictive effect of smoking on asthma prevalence and highlight the dynamics under different parameter variations. The findings emphasize that smoking significantly accelerates asthma transmission and severity, underscoring the importance of medical services and public health interventions. This work provides valuable insights into asthma dynamics and establishes a mathematical foundation for developing future strategies to reduce the disease burden.