Fractional modeling and numerical investigations of COVID-19 epidemic model with non-singular fractional derivatives: a case study

• Published in: Scientific reports Vol. 15; no. 1; pp. 13256 - 19
• Main Authors: Batool, Humera, Khan, Ilyas, Li, Weiyu, Junaid, Muhammad, Zhang, Jin, Nawaz, Asif, Tian, Lixin
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 17.04.2025; Nature Publishing Group; Nature Portfolio
• Subjects: 631/114; 692/699; Boundary value problems; Calculus; Case studies; Computer Simulation; COVID-19; COVID-19 - epidemiology; COVID-19 - virology; COVID-19 vaccines; Disease; Epidemic models; Epidemics; Epidemiological Models; Epidemiology; Humanities and Social Sciences; Humans; Immunization; Mathematical models; Mathematics; Medical research; Mittag-Leffler function; multidisciplinary; Numerical simulations; Optimization techniques; Pandemics; Quarantine; Respiratory system; SARS-CoV-2; Science; Science (multidisciplinary); Simulation; Stability analysis; Toufik-Atangana scheme; Toufik-Atangana scheme; Numerical simulations; Stability analysis; Mittag-Leffler function
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-025-93095-1

This paper focuses on the pivotal challenge of representing fractional dynamics in the context of computational biology, presenting an innovative approach. We utilize a non-singular kernel-type derivative to reformulate a fractional-order epidemic model. Our research focuses on several key aspects. First, we determine the reproductive number, represented as , which is crucial for predicting and understanding the dynamics of the disease being studied. To assess the stability of the system, we employ the Routh-Hurwitz stability criteria. Additionally, we employ the Lasale invariant principle to gain insights into the dynamical behavior of the equilibria. In order to validate our model’s accuracy, we conduct data fitting exercises and subsequently perform numerical experiments to corroborate our theoretical findings. Furthermore, we leverage the Banach and Leary Schauder alternative theorem to establish the existence of solutions with unique characteristics, enhancing the robustness of our approach. To facilitate practical implementation, we utilize the Toufit-Atangana scheme for numerical simulations of the proposed fractional model. Our findings show that the model performs well across the entire density spectrum. Specifically, we note that stability decreases with higher scheme orders but improves with lower fractional-order derivatives.