On finite-time stability of some COVID-19 models using fractional discrete calculus
Shaher Momani, Iqbal M. Batiha, Issam Bendib, Abeer A. Al-Nana, Adel Ouannas, Mohamed Dalah
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. • Innovative Fractional-Order SIR Model : This study introduces a fractional-order discrete SIR model, leveraging fractional calculus to capture memory effects and complex dynamics in epidemic transmission, which are often overlooked in traditional models. • Stability Analysis and Key Parameters : The model examines finite-time stability conditions for both disease-free and endemic equilibrium states, identifying critical parameters that help ensure stability within the COVID-19 transmission model. • Validation and Public Health Insights : Numerical simulations confirm the model’s capacity to replicate pandemic progression under various scenarios, underlining the potential of fractional-order discrete models to enhance public health strategies and responses.