Synchronization Control and Stability Analysis for a Variable-Order Fractional SIR Reaction-Diffusion Model

Authors

  • Iqbal H. Jebril Department of Mathematics, Al-Zaytoonah University of Jordan, Amman, 11733, Jordan.

Keywords:

Variable-orderfractionalsystems, Reaction-diffusion epidemic model, Stability analysis, Lyapunov methods, Complete synchronization, Epidemic control

Abstract

This paper investigates the stability and synchronization of a class of variable-order fractional (VFO) epidemic reaction-diffusion systems (RDs). The proposed model extends the classical SIR framework by incorporating spatial diffusion and memory effects through Caputo fractional derivatives of variable order. We establish novel asymptotic stability conditions for the equilibrium points (EPs) of the system with diffusion, using Lyapunov direct methods adapted to VFO systems.  Furthermore, we design a linear control strategy to achieve complete synchronization between drive and response systems, ensuring convergence of the synchronization error in the L^2-norm. Numerical simulations are presented to validate the theoretical analysis, demonstrating the effectiveness of the proposed complete synchronization (CS) approach in spatially distributed epidemic models. The results provide a rigorous mathematical framework for analyzing and controlling epidemic spread in heterogeneous populations, with potential applications in public health planning and intervention strategies.

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Published

2026-03-28

Issue

Special Issue on Mathematical and Computational Methods in Nonlinear Systems: Theory and Applications

Section

Special Issue

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Copyright (c) 2026 Iqbal H. Jebril

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How to Cite

Synchronization Control and Stability Analysis for a Variable-Order Fractional SIR Reaction-Diffusion Model. (2026). Journal of Prime Research in Mathematics, 68-80. https://jprm.sms.edu.pk/index.php/jprm/article/view/325