Asian Journal of Pure and Applied Mathematics

Accurately forecasting epidemics continues to pose significant challenges in public health, especially when incorporating evolving policy measures. Although classical Susceptible–Infected–Recovered (SIR) models offer essential baseline understanding, their fixed structure often falls short in representing the nonlinear effects of time-dependent interventions such as lockdowns or vaccination campaigns. This study proposes a new hybrid approach that combines a policy-adjusted SIR model with an enhanced operational model (EOM) to overcome these constraints. The model introduces a time-varying transmission rate, \(\beta\) (t), shaped by the intensity of government actions, and utilizes the EOM to capture residual discrepancies between theoretical model outputs and real-world data. Both analytical and simulation-based results confirm that the enhanced system adheres to Lipschitz continuity, ensuring the uniqueness and stability of solutions. Using Runge-Kutta 4th Order integration and actual policy datasets, the model demonstrates improved predictive performance over traditional SIR and standalone machine learning techniques. Its flexible architecture allows for real-time updates to intervention strategies, providing a reliable and adaptive tool for public health authorities in managing epidemics.