A Fractional-Order Caputo SEICRD Model for Evaluating Non-Pharmaceutical Interventions in COVID-19 Transmission Dynamics in South Africa

Abstract

The COVID-19 pandemic has had a significant impact on South Africa, motivating the development of reliable mathematical models to evaluate intervention strategies. In this paper, a fractional-order SEICRD model based on the Caputo derivative is proposed to describe the transmission dynamics of COVID-19 and to assess the effects of non-pharmaceutical interventions. Memory effects are incorporated through the fractional-order formulation, while a time-dependent infectious communication rate is modeled using the Woods-Saxon function to mathematically represent the continuous shifts in transmission rates resulting from evolving public health policies. The basic reproduction number and the effective reproduction number are derived, and model parameters, including the fractional order, are estimated using reported daily cases, daily recovered cases, and ICU data from May 26, 2020, to March 20, 2021, covering the first and second epidemic waves. Sensitivity analysis is performed to identify the most influential parameters. The fractional-order model fits the observed infected and ICU data at least as well as its integer-order counterpart while parsimoniously capturing memory effects in transmission; a profile analysis indicates that the fractional order itself is only weakly identified, and the model’s adequacy is supported by residual diagnostics and a random hold-out test. Numerical simulations indicate that non-pharmaceutical interventions, such as lockdowns and reduced contact rates, play a crucial role in controlling disease spread. Translating the fitted ICU trajectories into operational terms, the memory-driven dynamics correspond to a saving of roughly 125,000 ICU bed-days relative to the integer-order projection, and initiating contact-reduction measures 7–10 days ahead of a turning point substantially lowers peak ICU demand. The results highlight the importance of early implementation and sustained control measures in mitigating COVID-19 transmission in South Africa.