Fractional-Order Modeling and PINN-Based Analysis of Monkeypox Transmission with Optimal Control

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DOI: https://doi.org/10.28924/2291-8639-24-2026-137
Published: Apr 30, 2026
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Shanmugam Manikandan, Prabakaran Raghavendran, Rithik Sam Abraham, Mana Donganont, Vediyappan Govindan, Fractional-Order Modeling and PINN-Based Analysis of Monkeypox Transmission with Optimal Control, Int. J. Anal. Appl., 24 (2026), 137.

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Shanmugam Manikandan, Prabakaran Raghavendran, Rithik Sam Abraham, Mana Donganont, Vediyappan Govindan

Abstract

Monkeypox, a zoonotic viral disease, is becoming a major health issue worldwide and requires advanced mathematical models to understand its complicated transmission patterns. A new monkeypox transmission model based on Atangana-Baleanu-Caputo (ABC) fractional derivatives, which considers memory and hereditary effects due to the interactions of human and animal populations, is proposed in this study. Fixed-point theory is applied to prove the existence and uniqueness of solutions and also an optimal control problem is posed with the aim of reducing the number of infected people and at the same time lowering the costs of treatment and preventive measures required, the necessary optimality conditions are derived using Pontryagin’s Maximum Principle. A Physics-Informed Neural Network (PINN) framework is used not only to approximate the solution of the ABC-fractional system but also to infer key model parameters directly from the governing dynamics in order to improve the applicability and computational efficiency of the model. Numerical experiments reveal a very close match between the solutions derived from the PINN approach and the results obtained from conventional fractional numerical methods, thus pointing to the considerable impact of fractional-order effects on the dynamics of the epidemic, notably in terms of delayed outbreak peaks and extended infection periods. The combined approach of fractional calculus and AI constitutes a powerful and versatile tool for outbreak prediction, thus facilitating the health authorities to make well-informed decisions.

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