COMPREHENSIVE FRAMEWORK FOR EYE INFECTIONS IN COMMUNITY UNDER PREVENTIVE AND TREATMENT WITH FRACTIONAL ORDER STUDY
Journal of Applied Analysis and Computation, vol.16, no.6, pp.2913-2944, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 16 Issue: 6
- Publication Date: 2026
- Doi Number: 10.11948/20250322
- Journal Name: Journal of Applied Analysis and Computation
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Page Numbers: pp.2913-2944
- Keywords: Chaos control, eyes infection model, fractal-fractional operator, health care, Infectious Diseases, Newton polynomial, stability analysis
- Karadeniz Technical University Affiliated: No
Abstract
Environmental biopollutants and airborne contaminants contribute to eye infection diseases through prolonged exposure. Despite natural protections, some microorganisms can infect the eyes. This study develops a fractional-order mathematical model analyzing the transmission dynamics of environmentally induced eye infections, incorporating biopollutant exposure and air quality effects. The model uses a generalized fractional derivative to account for memory and hereditary effects from cumulative exposure and delayed immune responses of the ocular system. We verified that a single solution with a positively invariant region exists. The Banach fixed point theorem and Krasnoselskii type are used to investigate the existence and uniqueness of the eye infection model. It highlights local stability while accounting for limiting observations, a critical component of epidemic models. The reproductive number R0 is calculated to evaluate its impact on compartments and community-wide transmission rates. A sensitivity study of the model’s parameters is used to investigate its behavior. We used the linear feedback control technique to stabilize the system and also verified the local and global stability of equilibria. The study conducted numerical replications for a range of outcomes in order to demonstrate the efficacy of fractional coupled differential equations in modeling ocular infections, producing evidence that is compatible with theoretical conclusions. This study advances knowledge of eye infections and the creation of sensible preventative measures.