Quasi-Periodic SEIR Modeling of COVID-19 incidence under vaccination dynamics

This work investigates the use of time-varying parameters in SEIR epidemic models to describe the temporal evolution of COVID-19 incidence data. Three models are considered: the classical SEIR model with constant parameters, a SEIR model incorporating a quasi-periodic effective progression rate, and an extended SEIR model that additionally includes a periodic vaccination function. The proposed approach is motivated by the observation that epidemic dynamics are influenced by multiple temporal factors acting at different scales, including behavioral changes, public health interventions, environmental variability, and vaccination campaigns. Model parameters were estimated from COVID-19 incidence data corresponding to the third epidemic wave in Jalisco, Mexico, using a differential evolution optimization algorithm. The results show that introducing temporal variability in the effective progression rate improves the agreement between the model and the reported data. Furthermore, the inclusion of a vaccination mechanism yields a substantial reduction in the fitting error. The proposed framework demonstrates that quasi-periodic and periodic parameterizations provide a flexible and effective approach for capturing complex epidemic dynamics and improving the description of observed incidence patterns.