| Citation: |
Kottakkaran Sooppy Nisar, Muhammad Farman. COMPREHENSIVE FRAMEWORK FOR EYE INFECTIONS IN COMMUNITY UNDER PREVENTIVE AND TREATMENT WITH FRACTIONAL ORDER STUDY[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2913-2944. doi: 10.11948/20250322
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COMPREHENSIVE FRAMEWORK FOR EYE INFECTIONS IN COMMUNITY UNDER PREVENTIVE AND TREATMENT WITH FRACTIONAL ORDER STUDY
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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 $\mathcal{R}_0$ 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.
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References
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Kottakkaran Sooppy Nisar, Muhammad Farman. COMPREHENSIVE FRAMEWORK FOR EYE INFECTIONS IN COMMUNITY UNDER PREVENTIVE AND TREATMENT WITH FRACTIONAL ORDER STUDY[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2913-2944. doi: 10.11948/20250322
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Figure 1.
Schematic representation of the proposed model.
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Figure 2.
Analysis of reproductive number's variations to different parameters.
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Figure 3.
Impact of parameter variations on
$ \mathcal{R}_0 $ -
Figure 4.
$ S(t) $ -
Figure 5.
$ E(t) $ -
Figure 6.
$ I(t) $ -
Figure 7.
$ T(t) $ -
Figure 8.
$ P(t) $ -
Figure 9.
$ R(t) $ -
Figure 10.
Surface plots of
$ S(t) $ -
Figure 11.
Surface plots of
$ E(t) $ -
Figure 12.
Surface plots of
$ I(t) $ -
Figure 13.
Surface plots of
$ T(t) $ -
Figure 14.
Surface plots of
$ P(t) $ -
Figure 15.
Surface plots of
$ R(t) $