A Numerical Audit of Delay Effects in SIR Epidemic Models: Revisiting the Stability Paradigm

This work revisits the delay-based SIR epidemic model originally proposed by Ezekiel et al. (2022) by performing a numerical and graphical comparison of ordi nary differential equations (ODEs) and delay differential equations (DDEs). While the original model studied the stability behavior through analytical methods, it failed to investigate or visualize the dynamical variations brought by delay. We simulate the system using MATLAB tools (‘ode45‘ for ODEs and ‘dde23‘ for DDEs), and analyze the model behavior across different values of time-delay τ. Our results show critical behavioral shifts, including oscillations and instability, not captured in the original pa per. A tabular comparison of peak values highlights the delay sensitivity and further establishes the necessity of incorporating delay in epidemic modeling.This study also lays the foundation for future research in fractional-order epidemic modeling.