Fractional modeling of vector-borne disease dynamics using ABC operators and neural networks

Ateq Alsaadi; Ateq Alsaadi

doi:10.3934/math.2025710

AIMS Mathematics

2025, Volume 10, Issue 7: 15841-15866. doi: 10.3934/math.2025710

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Fractional modeling of vector-borne disease dynamics using ABC operators and neural networks

Ateq Alsaadi ^,

Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 25 April 2025 Revised: 09 June 2025 Accepted: 25 June 2025 Published: 14 July 2025
MSC : 34D20, 34K20, 34K60, 92C60, 92D45

This work enhanced the mathematical modeling of vector-borne infections involving vertical transmission and treatment effects within a targeted population by incorporating fractional calculus techniques that account for nonlocal properties and non-singular fading memory behavior. This work investigated a fractional-order mathematical model for poliomyelitis governed by the Mittag-Leffler kernel. By employing fixed point theory, we qualitatively analyzed the model and confirmd the existence and uniqueness of solutions. Additionally, Ulam's type stability is examined through nonlinear analytical methods. To approximate the solution, a fractional Adams-Bashforth numerical scheme is utilized. The model was simulated under various fractional orders and different control scenarios. Results indicate that all compartments exhibit convergence and long-term stability. Notably, lower fractional orders tend to reach stability more rapidly. Furthermore, Artificial Neural Networks were applied, with the dataset partitioned into training, validation, and testing subsets. A comprehensive assessment was carried out for each dataset partition.
- Adams-Bashforth method,
- Mittag-Leffler kernel,
- fixed point theory,
- vector-borne diseases
Citation: Ateq Alsaadi. Fractional modeling of vector-borne disease dynamics using ABC operators and neural networks[J]. AIMS Mathematics, 2025, 10(7): 15841-15866. doi: 10.3934/math.2025710

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Abstract

This work enhanced the mathematical modeling of vector-borne infections involving vertical transmission and treatment effects within a targeted population by incorporating fractional calculus techniques that account for nonlocal properties and non-singular fading memory behavior. This work investigated a fractional-order mathematical model for poliomyelitis governed by the Mittag-Leffler kernel. By employing fixed point theory, we qualitatively analyzed the model and confirmd the existence and uniqueness of solutions. Additionally, Ulam's type stability is examined through nonlinear analytical methods. To approximate the solution, a fractional Adams-Bashforth numerical scheme is utilized. The model was simulated under various fractional orders and different control scenarios. Results indicate that all compartments exhibit convergence and long-term stability. Notably, lower fractional orders tend to reach stability more rapidly. Furthermore, Artificial Neural Networks were applied, with the dataset partitioned into training, validation, and testing subsets. A comprehensive assessment was carried out for each dataset partition.

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