Fractional order modeling of hepatitis C transmission dynamics with physics-informed neural network solutions

Vetrivel Muthupandi; Arul Joseph Gnanaprakasam; Salah Boulaaras

doi:10.1186/s12879-026-12792-y

Fractional order modeling of hepatitis C transmission dynamics with physics-informed neural network solutions

BMC Infect Dis. 2026 Feb 24;26(1):457. doi: 10.1186/s12879-026-12792-y.

Authors

Vetrivel Muthupandi¹, Arul Joseph Gnanaprakasam², Salah Boulaaras³

Affiliations

¹ Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Chengalpattu District, Tamil Nadu, 603203, India.
² Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Chengalpattu District, Tamil Nadu, 603203, India. aruljoseph.alex@gmail.com.
³ Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia. s.boularas@qu.edu.sa.

Abstract

This study develops a fractional-order mathematical model for Hepatitis C Virus (HCV) transmission using a six-compartment framework and the Caputo–Fabrizio derivative. The operator’s exponential kernel captures essential short-term memory effects in acute infection and treatment response, a key advancement over classical integer-order models. We establish the model’s well-posedness through rigorous positivity, boundedness, existence-uniqueness, and stability analyses. The basic reproduction number formula image confirms epidemic potential, with sensitivity analysis identifying acute transmission (β₂) as the dominant driver, accounting for over 51% of new infections—a critical public health insight. Fractional-order simulations demonstrate that increased memory effects (lower fractional order) delay and flatten outbreak waves, underscoring the importance of sustained interventions. A novel Physics-Informed Neural Network (PINN) is implemented to solve the coupled fractional system. The PINN achieves high predictive accuracy ( formula image , low RMSE) for Susceptible, Exposed, Acute, and Quit Treatment compartments, though performance is moderate for the Chronic stage (, reflecting its more complex, heterogeneous dynamics. The PINN’s success offers a mesh-free, computationally efficient alternative to traditional numerical schemes for complex epidemiological systems. This work’s primary contribution is the first integration of a Caputo–Fabrizio HCV model with a PINN solver, creating a hybrid mechanistic-data-driven framework. The results provide actionable strategies: prioritizing acute-phase control and implementing long-term, memory-aware public health measures. The model serves as a validated tool for optimizing HCV elimination strategies, particularly in resource-limited settings, while highlighting directions for future refinement, including integration with real-world clinical data.

Keywords: Caputo-Fabrizio; Existence and uniqueness using fixed point theory; Machine learning; Newton interpolation in numerical scheme; Physics informed neural network; Prediction; Time series; Ulam-Hyers stability.