Fractional Modeling and Dynamic Analysis of COVID-19 Transmission with Computational Simulations

Mohamed. M. Alarady, Mohamed A. Barakat () and Mohamed M. Darwish
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Mohamed. M. Alarady: Department of Computer Science, University College of Alwajh, University of Tabuk, Al Wajh 48721, Saudi Arabia
Mohamed A. Barakat: Department of Computer Science, University College of Alwajh, University of Tabuk, Al Wajh 48721, Saudi Arabia
Mohamed M. Darwish: Department of Computer Science, University College of Alwajh, University of Tabuk, Al Wajh 48721, Saudi Arabia

Mathematics, 2025, vol. 13, issue 22, 1-19

Abstract: Most existing fractional models of COVID-19 describe only the infection process without explicitly accounting for the role of vaccination. In this study, a refined Caputo fractional model is proposed that incorporates a vaccinated class to better understand how immunization influences disease progression. The mathematical formulation guarantees the existence, uniqueness, and positivity of solutions, ensuring that all system trajectories remain biologically valid. The equilibrium points are obtained, and the reproduction number is derived to identify the conditions for disease control. The stability investigation covers local behavior alongside Ulam–Hyers and its extended variants, ensuring the system remains stable under small perturbations. Numerical experiments performed with the Adams–Bashforth–Moulton algorithm illustrate that vaccination reduces infection peaks and shortens the epidemic duration. Overall, the proposed framework enriches fractional epidemiological modeling by providing deeper insight into the combined effects of memory and vaccination in controlling infectious diseases.

Keywords: Caputo fractional model; fractional epidemiology; basic reproduction number; Ulam–Hyers stability; existence and uniqueness; Adams–Bashforth–Moulton method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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