We study a discrete fractional-order SIR model for COVID-19 incorporating memory effects and delayed responses, which are often missed in the classical integer-order models. Using Caputo-like operators, the model captures complex transmission dynamics influenced by past states. We analyze finite-time stability and demonstrate through simulations the model’s ability to replicate realistic outbreak patterns. To manage the nonlinear and chaotic aspects of COVID-19 spread, we propose feedback control and synchronization strategies that leverage fractional-order memory properties for enhanced stability and coordination across populations. The obtained results demonstrate that the proposed techniques effectively suppress chaotic dynamics and facilitate convergence toward stable epidemic states and highlight the superior performance of discrete fractional-order models compared to traditional integer-order approaches, offering more robust and accurate tools for epidemic forecasting and pandemic control.