The health of our respiratory systems is directly affected by the atmosphere. Nowadays, eruption of respiratory disease and malfunctioning of lung due to the presence of harmful particles in the air is one of the most sever challenge. In this chapter, association between air pollution-related respiratory diseases, namely dyspnea, cough, and asthma, is analysed by constructing a mathematical model. Local and global stability of the equilibrium points is proved. Optimal control theory is applied in the model to optimize stability of the model. Applied optimal control theory contains four control variables, among which first control helps to reduce number of individuals who are exposed to air pollutants and the remaining three controls help to reduce the spread and exacerbation of asthma. The positive impact of controls on the model and intensity of asthma under the influence of dyspnea and cough is observed graphically by simulating the model.
TopIntroduction
Rapid growth in population and industrialization have resulted in increasing demand for energy which effects the levels of atmospheric particulate matter. Epidemiological studies have proved that exposure to air pollutants lead to respiratory symptoms and decrease in lung functionality (Gehring U. et al., 2013; Usemann J. et. al., 2019). Toxic and hazardous pollutants from the air penetrates deep into the lungs in inhalation, that can increase one’s risk of cardiovascular and respiratory diseases including cardiac arrests, lung cancer, chronic obstructive pulmonary diseases and respiratory infections (Ciencewicki J., & Jaspers I., 2007, Ko F. W., & Hui D. S., 2012). Air pollution is more significant environmental health risk factor in Asia, as its mortality rate is higher (Abas N. et. al., 2019, Wang Q. et. al., 2019). As a result of increased pollutants in the environment, World Health Organization has estimated that globally more than seven million premature death are occurring mainly due to cardiac arrest, respiratory infections, stroke, lung cancer, chronic obstructive pulmonary disease, chronic bronchitis and asthma (WHO, 2019).
Respiratory defence mechanisms are altered by specific allergens present in polluted environment which trigger asthma exacerbation and enhance rate of hospitalization for asthma (Tatum A. J., & Shapiro G. G., 2005). A recent estimations states that, globally 339 million people are suffering from asthma (Global Asthma Network, 2018). Moreover, its prevalence continues to rise in children as pollutants have damaging effect on their lung function (Brokamp C. et. al., 2019; Fielding S. et. al., 2019; Soto-Martínez et. al., 2019). There is a widespread concern that prevalence of asthma is still rising in developed countries, but the economic and humanitarian effects of asthma are on rise in developing countries, where the prevalence is also rising. Therefore the initial prevention strategies to tackle the asthma epidemic are sought after. Asthma is characterized by production of excess amount of gluey secretions inside the airways which fallouts in inflammation of the respiratory tubes (Groneberg D. A. et. al., 2002). As a result of it, early threatening common sigh seen in asthma patients are tightness in chest, coughing, dyspnea and wheezing. Also, presence of dyspnea and cough enduringly can accelerate asthma exacerbation or generate more harmful diseases.
Dyspnea is normally correlated with the situations in which the neural central control system, the sensory input systems, the muscular effect systems or respiratory system are stop functioning as it should be. In medical term, these situations are characterized by shortness of breath or air hunger (Simon P. M. et. al., 1990; Wasserman K., & Casaburi R., 1988). It is a serious health concern, as interval of shortness of air can differ from minor and momentary to serious and long lasting. Causes of dyspnea depends upon several factors including low blood pressure, asthma, cardiac arrests, stress, anxiety and exposure to air pollutants etc. Dyspnea can reduce life span for patient by inviting other chronic obstructive pulmonary diseases, like cardiac arrest, asthma, etc.