Work

The Fractional SI Reaction–Diffusion Model with Incommensurate Orders: Stability Analysis and Numerical Simulations

Year: 2025

Type: article

Abstract: In this work, we present a fractional-order reaction–diffusion model for the spread of infectious diseases, incorporating incommensurate Caputo derivatives to capture memory effects and heterogeneous temporal behavior across compartments. Focusing on a generalized SI model with nonlinear incidence, we explore the local asymptotic stability of both disease-free and endemic equilibria. The model accommodates spatial diffusion, saturation effects, and varying fractional orders, yielding a more realistic depiction of epidemic propagation. Analytical techniques—ranging from linearization to spectral analysis—are employed to rigorously establish stability conditions. Numerical simulations support the theoretical findings, highlighting the impact of memory and spatial structure on long-term dynamics. This study offers a refined mathematical lens to understand the persistence or eradication of infectious diseases under memory-dependent and spatially heterogeneous environments.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10010003

Authors: Ali Aloui, Amel Hioual, Omar Kahouli, Adel Ouannas, Lilia El Amraoui, Mohamed Ayari

Institutions: University of Ha'il, Larbi Ben M'hidi University of Oum El Bouaghi, Princess Nourah bint Abdulrahman University, Northern Border University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $3,258