Memory Effect on COVID-19 Vaccination Dynamics: Fractional-Order Modeling Approach

Accurate estimates of vaccine effectiveness are essential for designing effective COVID-19 vaccination strategies. Memory effects play a critical role in both the development and waning of vaccine-induced immunity. In this study, we develop a fractional-order COVID-19 transmission model using Caputo fractional derivatives to capture the memory-dependent dynamics of immunity acquired through vaccination. The model is calibrated to COVID-19 case data from the United States spanning September 2020 to March 2021 and demonstrates excellent agreement with the observed epidemic trends, highlighting the importance of memory effects in disease transmission under vaccination programs. We derive the basic reproduction number (R0) and establish threshold conditions for the stability of the disease-free equilibrium. The existence and properties of the endemic equilibrium are also investigated. Numerical simulations are conducted to illustrate the influence of fractional-order memory effects on epidemic control through vaccination. Sensitivity analysis reveals that the transmission rate, vaccination rate, immunity waning rate, disease progression rate, and recovery rate are key determinants of COVID-19 transmission dynamics and control. The proposed fractional-order framework provides valuable insights into the impact of vaccine-induced immunity and offers a useful tool for informing public health strategies aimed at mitigating and controlling COVID-19 outbreaks.