Investigating the Link between Ascaris Lumbricoides and Asthma in Human with Analysis of Fractal Fractional Caputo-Fabrizio of a Mathematical Model

Asthma is the most common allergic disorder and represents a significant global public health problem. Strong evidence suggests a link between ascariasis and asthma. This study aims primarily to determine the prevalence of Ascaris lumbricoides infection among various risk factors, to assess blood parameters, levels of immunoglobulin E (IgE) and interleukin-4 (IL-4), and to explore the relationship between ascariasis and asthma in affected individuals. The secondary objective is to examine a fractal-fractional mathematical model that describes the four stages of the life cycle of Ascaris infection, specifically within the framework of the Caputo-Fabrizio derivative. A case-control study was conducted that involved 270 individuals with asthma and 130 healthy controls, all of whom attended general hospitals in Duhok City, Iraq. Pulmonary function tests were performed using a micromedical spirometer. The presence of Ascaris lumbricoides antibodies-Immunoglobulin M (IgM), Immunoglobulin G (IgG), and Immunoglobulin E (IgE)-was detected using ELISA. Blood parameters were analyzed using a Coulter counter. The overall infection rate was (42.5%), with the highest rates observed among asthmatic men (70.0%) and rural residents (51.4%). Higher infection rates were also recorded among low-income individuals (64.3%) and those with frequent contact with the soil (58.6%). In particular, infected individuals exhibited a significant decrease in red blood cell count and hemoglobin concentration, while a marked increase in white blood cell count was recorded. In addition, levels of Immunoglobulin E (IgE) and interleukin-4 were significantly higher in the infected group compared to the controls. Effective disease awareness strategies that incorporate health education and preventive measures are needed. Exposure to Ascaris has been associated with reduced lung function and an increased risk of asthma. More research is required to elucidate the precise mechanisms that link Ascaris infection with asthma. Furthermore, the existence and uniqueness of solutions for the proposed model are investigated using the Krasnosel’skii and Banach fixed-point theorems. The Ulam-Hyers and Ulam-Hyers-Rassias stability types are explained within the framework of nonlinear analysis in Ł^p-space. Finally, an application is presented, including tabulated results and figures generated using MATLAB to illustrate the validity of the theoretical findings.