Finite-time synchronization in a novel discrete fractional SIR Model for COVID-19

This paper presents a novel discrete fractional Susceptible-Infected-Recovered (SIR) model tailored for analyzing the dynamics of COVID-19 transmission. The model categorizes the population into four groups: susceptible (S), infected (I), recovered (R), and deceased (D), employing fractional calculus to encapsulate the memory effects and non-local interactions inherent in disease spread. A comprehensive mathematical framework is developed, incorporating the fractional sum and Caputo fractional difference operator to characterize the dynamics of the system. The study explores the conditions for finite-time synchronization among interconnected SIR models, leveraging Lyapunov stability theory to derive sufficient conditions for convergence within finite time. Numerical simulations illustrate the model's effectiveness and its sensitivity to key parameters, such as infection and recovery rates. The findings have significant implications for understanding disease dynamics and informing public health strategies, including vaccination optimization and outbreak control. Future research directions are suggested, emphasizing the enhancement of synchronization techniques and the robustness of the model in more complex epidemic scenarios.