Modeling the impact of reinfected infectious diseases vaccination using a nonlinear SVEIRD framework: A case study from Alberta, Canada

Mathematical modelling provides a rigorous framework for elucidating the transmission dynamics of infectious diseases and serves as a vital tool for assessing the potential impact and effectiveness of public health interventions. In this study, a nonlinear SVEIRD model is developed and analyzed to examine the effect of vaccination on the spread of COVID-19 across different variant periods, using real-world data from Alberta, Canada. The model incorporates reinfection dynamics, vaccine efficacy, and time-dependent changes in transmission rates. The fundamental reproduction number, denoted by $ R_0 $, is derived. Both the disease-free and endemic equilibrium points are determined, and their stability properties are investigated through local analysis based on the Routh–Hurwitz criteria and global analysis employing Lyapunov functions.Extensive numerical simulations calibrated with empirical data validate the model's accuracy across six pandemic phases, including the pre- and post-vaccination periods. The sensitivity analysis identifies key parameters, such as the infection rate and the recovery rate, that critically influence disease progression. Results indicate that vaccination significantly reduces the basic reproduction number, though its effectiveness varies during periods of variant emergence, such as the Delta variant.This study highlights the potential and limitations of compartmental models in informing short-term health policies. The findings of this study indicate that while vaccination reduces transmission, adaptive strategies including surveillance and healthcare preparedness are vital for long-term epidemic control. The insights derived from this case study can support evidence-based policymaking for current and future public health emergencies.