Fractional-Order Compartmental Models: Stability, Optimal Control, and Neural Network Validation — with a Proposed Extension to Cancer Immunotherapy

Speaker(s)

Zakirullah

Affiliation

School of Mathematical Sciences, University of Electronic Science and Technology of China

Language of the talk

English

Date

May 13, 2026, 2:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/97187479863?pwd=4ERaSaNt4dbYv77P5T9Ru1AawSYnia.1

Information about the event

Tym razem spotkanie online

Seminar

Seminar of Biomathematics and Game Theory Group

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In this talk, I present my recent work on mathematical modelling of infectious disease dynamics using fractional-order compartmental models with Caputo, Caputo–Fabrizio, and Atangana–Baleanu–Caputo operators. The models are analyzed for existence and uniqueness, positivity and boundedness, basic reproduction number R₀, and local and global stability via Lyapunov functions. Optimal control strategies are formulated using Pontryagin’s Maximum Principle and solved via the forward–backward sweep algorithm. For numerical validation, I use two complementary approaches: Physics-Informed Neural Networks (PINNs) for joint parameter identification, and Artificial Neural Networks (ANNs) for cross-validation of fractional solutions across multiple values of the fractional parameter. Results from models for Nipah virus, Chikungunya virus, Herpes Simplex Virus, and HIV will be presented. I conclude by outlining a proposed PhD research direction aimed at extending these mathematical tools to cancer immunotherapy models, building directly on the work of the Warsaw Biomathematics group

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