Numerical Analysis of a New COVID-19 Control Model Incorporating Three Different Fractional Operators (Journal of Nonlinear Modeling and Analysis, 2025)
The ongoing COVID-19 pandemic, caused by the highly contagiouscoronavirus, poses significant challenges to public health worldwide. Effectivecontrol measures are essential to mitigate the spread of the virus and protect vulnerable populations. This study aims to develop novel mathematicalmodels using fractional derivatives to analyze the dynamics of the COVID-19outbreak. 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 threedifferent arbitrary-order derivative operators: the Atangana-Baleanu derivative with the generalized Mittag-Leffler function, the Caputo derivative with apower law, and the Caputo-Fabrizio derivative with exponential decay. Usingfixed-point theory, we assess the existence and uniqueness of solutions for thearbitrary-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 slowsthe disease’s progression, reflecting the memory effect inherent in fractionalderivatives. Specifically, higher values of the fractional order correspond to amore gradual spread, reducing the peak number of infections and extendingthe outbreak’s duration. The work highlights the critical importance of usingfractional order models to capture the complex dynamics of disease spread andemphasizes that the implementation of quarantine and isolation for treatmentsignificantly decreases the cumulative number of new cases and the overalltransmission rate of COVID-19. This research underscores the effectiveness ofutilizing fractional-order models to better understand and control the complexdynamics of disease transmission.