Comparative analysis of classical and Caputo models for COVID-19 spread: vaccination and stability assessment

Several epidemiological models use the Caputo fractional-order differential operator without establishing its significance. This study verifies a Caputo operator-based fractional-order epidemiological model of the SAIVR type. COVID-19 kills. Infection weakens the immune system. The fractional Caputo operator describes COVID-19 immunization. Fundamental system characteristics are determined using fractional calculus. Our analysis included the fractional system’s Hyers–Ulam–Rassias stability and stable states. The uniqueness and existence of fractional Caputo system solutions are explored. The least-squares approach determines system parameters. The Caputo fractional-order α value is optimized to $6.757\text{e}-01$ $6.757\text{e}{-}01$ , indicating that the system best fits real-life medical data for infection. Caputo and classical systems were compared for absolute mean errors. The Box-Whisker chart case summaries show the Caputo operator superiority. When $\alpha \to 1$ $\alpha \rightarrow 1$ , the memory traces and hereditary traits are also observed. Finally, the Caputo fractional framework simulates COVID-19 using strong numerical methods.