Clinical and immunological parameters in patients infected with Cutaneous Leishmaniasis: Case control study- investigation of fractal fractional mathematical model in Lebesgue space

Cutaneous Leishmaniasis (CL) is a skin disease that causes plaques, ulcers, and nodules on various body parts. The first aim of this study is to investigate the effect of CL on hematological and immunological markers. A total of 180 individuals (80 cases and 100 controls) examined. All patients received parasitological confirmation by a dermatologist and stained smears, and blood samples had been collected for the analysis of hematological parameters using a Coulter count machine. IL-17 and TGF levels were measured using the ELISA technique. A high rate of CL was observed among males, rural residents, and those in the 35–54 age group, with infection rates of (62.5%), (53.7%), and (37.5%), respectively. Single lesions were observed in (68.8%) of cases, while multiple lesions occurred in (31.2%). Lesions appeared most frequently on the upper extremities (41.2%), lower extremities (31.2%), face (18.8%), and neck (2.5%). Most lesions presented as moist (62.5%), with the remaining (37.5%) classified as dry. Higher concentrations of IL-17 and TGF existed in Cutaneous leishmaniasis patients compared to the control group. Infected subjects exhibited decreased red blood cell counts and hemoglobin concentrations, while white blood cell counts hlshowed an elevation. Various socioeconomic and environmental factors contribute to the spread of Cutaneous leishmaniasis in the region, which helps to understand the disease's epidemiology and reduce its transmission. Implementing programs for managing vector-borne diseases is essential. The second aim is to analyze the fractal-fractional mathematical model that illustrates the eight stages of Cutaneous leishmaniasis using the Caputo–Fabrizio derivative. Our study establishes the existence and uniqueness of solutions to this model through the application of Schauder's and Banach's fixed-point theorems. Additionally, stability analysis utilizing the Ulam–Hyers and Ulam–Hyers–Rassias techniques is performed in L^p-space. An application is presented, along with tables and MATLAB figures, to confirm the theoretical results.