(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
The ongoing COVID-19 pandemic, caused by the highly contagious coronavirus, poses significant challenges to public health worldwide. Effective control measures are essential to mitigate the spread of the virus and protect vulnerable populations. This study aims to develop novel mathematical models using fractional derivatives to analyze the dynamics of the COVID-19 outbreak. By employing modified mathematical procedures, we explore the impact of quarantine and isolation as control measures on the disease’s transmission dynamics. We investigate a system representing COVID-19 through three different arbitrary-order derivative operators: the Atangana-Baleanu derivative with the generalized Mittag-Leffler function, the Caputo derivative with a power law, and the Caputo-Fabrizio derivative with exponential decay. Using fixed-point theory, we assess the existence and uniqueness of solutions for the arbitrary-order system. Our analysis includes numerical simulations that reveal how varying the fractional order influences the behavior of the epidemic. The results demonstrate that increasing the fractional order generally slows the disease’s progression, reflecting the memory effect inherent in fractional derivatives. Specifically, higher values of the fractional order correspond to a more gradual spread, reducing the peak number of infections and extending the outbreak’s duration. The work highlights the critical importance of using fractional order models to capture the complex dynamics of disease spread and emphasizes that the implementation of quarantine and isolation for treatment significantly decreases the cumulative number of new cases and the overall transmission rate of COVID-19. This research underscores the effectiveness of utilizing fractional-order models to better understand and control the complex dynamics of disease transmission.