Time-delay enhanced SIR model for COVID-19 waves in Mexico: Parameter estimation using evolutionary algorithms

In this work, we analyze the progression of COVID-19 across six distinct epidemic waves in Mexico using a time-delay SIR model, focusing specifically on whether the inclusion of incubation and recovery delays into the classical SIR framework enhances the model's ability to capture the complex dynamics observed in epidemic data. To achieve robust and reliable estimation of both model parameters and time delays despite the inherent uncertainties present in pandemic data, we employ Particle Swarm Optimization (PSO) and Genetic Algorithms (GA). The performance of these optimization methods is assessed by examining their effectiveness in accurately reconstructing parameters across varying data with noise and uncertainties. Our findings indicate that both PSO and GA yield robust parameter and time-delay estimations even under scenarios where data have uncertainties, highlighting the critical role that time delays play in realistically modeling epidemic dynamics. The obtained results provide valuable insights into COVID-19 transmission patterns in Mexico and demonstrate the practical advantages of evolutionary algorithms for epidemic model calibration.