Global stability of a class of fractional partial differential equations describing the dynamics of viral infection with therapy and adaptive immunity

  • Mohammad Eloualy Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick, Hassan II University
  • Abdelaziz El Hassani Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick, Hassan II University
  • Khalid Hattaf Equipe de Recherche en Mod´elisation et Enseignement des Math´ematiques (ERMEM), Centre R´egional des M´etiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco
  • Abdelhafid Bassou Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick, Hassan II University
DOI: https://doi.org/10.19139/soic-2310-5070-3351
Keywords: Viral infection, fractional partial differential equations, anomalous diffusion, Lyapunov functions, global stability

Abstract

In this article, we formulate a mathematical model based on fractional partial differential equations (FPDEs) to describe the spatiotemporal progression of viral infections, incorporating the effects of adaptive immunity and antiviral treatment. The model includes a regional fractional Laplace operator to account for the anomalous diffusion observed within the infected medium. We investigate the existence and uniqueness of equilibria and establish their global stability using Lyapunov functions tailored to the associated reaction systems. Moreover, numerical simulations are presented to illustrate the analytical results.

Author Biographies

Mohammad Eloualy, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick, Hassan II University
PhD Student, Faculty of Sciences Ben M'Sik, Hassan II University of Casablanca, Morocco.
Khalid Hattaf, Equipe de Recherche en Mod´elisation et Enseignement des Math´ematiques (ERMEM), Centre R´egional des M´etiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco
Professor and Researcher, CRMEF, Casablanca, Morocco
Abdelhafid Bassou, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick, Hassan II University
professeur de mathématiques, Université Hassan II
Published
2026-01-08
How to Cite
Eloualy, M., El Hassani, A., Hattaf, K., & Bassou, A. (2026). Global stability of a class of fractional partial differential equations describing the dynamics of viral infection with therapy and adaptive immunity. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3351
Issue
Online First
Section
Research Articles
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