On finite-time stability of some COVID-19 models using fractional discrete calculus

Abstract

This study investigates the finite-time stability of fractional-order (FO) discrete Susceptible–Infected–Recovered (SIR) models for COVID-19, incorporating memory effects to capture real-world epidemic dynamics. We use discrete fractional calculus to analyze the stability of disease-free and pandemic equilibrium points. The theoretical framework introduces essential definitions, finite-time stability (FTS) criteria, and novel fractional-order modeling insights. Numerical simulations validate the theoretical results under various parameters, demonstrating the finite-time convergence to equilibrium states. Results highlight the flexibility of FO models in addressing delayed responses and prolonged effects, offering enhanced predictive accuracy over traditional integer-order approaches. This research contributes to the design of effective public health interventions and advances in mathematical epidemiology.