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Modeling and Mathematical Analysis of the Dynamics of Eye Infection (Conjunctivitis) Virus using Fractal-Fractional and Machine Learning Approach |
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PP: 155-171 |
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doi:10.18576/pfda/120110
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Author(s) |
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Mohammed A. El-Shorbagy,
Arifa Samreen,
Mati ur Rahman,
Hossam A. Nabwey,
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Abstract |
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| Mathematical modeling are the key for understanding the diseases transmission within a society. The developed article utilizes the Caputo fractal-fractional operator to examine the dynamics of a mathematical model for viral conjunctivitis infection in the eyes. We presents the existence and uniqueness of the solution for the model under consideration using fixed-point theory. To evaluate the stability of the said system, we uses the Ulam-Hyers (UH) technique. Additionally, we have obtained a numerical solution for the model using fractional Adams-Bashforth iterative methods having predictor and corrector approach. By using the actual numerical values, we examine several options to limit the fractal dimension ξ and the fractional order λ, allowing for an approximation of the model. The application of fractal-fractional calculus has proven effective rule in managing the pandemic and understanding real-world problems. Numerical simulations demonstrate the significance of arbitrary derivative orders, revealing that fractional-fractal orders provide greater insights into the complex dynamics of the proposed conjunctivitis virus model. To illustrate the model dynamics at various fractional orders, several graphical displays are provided. Moreover, a machine learning framework was employed to further assess the effectiveness of the proposed approach in form of neural networking. The obtained results were systematically compared with those generated by the learning model, highlighting both qualitative and quantitative aspects of performance. This comparative analysis revealed that the present method not only provides more accurate and stable solutions having very small small absolute, mean and root mean square errors but also demonstrates improved reliability, thereby confirming its superiority over the machine learning baseline. |
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