This study develops and analyzes an SVIRLQS epidemiological model to investigate the combined effects of vaccination, waning immunity, immune boosting, and secondary infections on disease transmission dynamics. Understanding these mechanisms is important because immunity acquired through vaccination or natural infection may decline over time, influencing long-term disease persistence and the effectiveness of control strategies. The model is studied using both analytical and numerical approaches. The existence and stability properties of the disease-free and endemic equilibria are established using Lyapunov-based techniques, while bifurcation analysis demonstrates the occurrence of a forward bifurcation at the critical threshold \(({\mathcal {R}}_{0}^{v} = 1).\) To ensure practical relevance, the model is fitted to weekly laboratory-confirmed influenza-positive case data reported through the U.S. Centers for Disease Control and Prevention (CDC) influenza surveillance system, covering the period from September 29 to December 7, 2024. Parameter estimation performed using a nonlinear least-squares approach. Unlike previous waning-immunity models, the proposed framework explicitly incorporates vaccination, vaccine-induced immunity waning, vaccine inefficacy, and breakthrough infections, enabling assessment of their combined influence on disease dynamics. Numerical simulations reveal that vaccination substantially reduces disease burden, while immune waning and secondary infections can promote persistence of transmission. Furthermore, parameter-sweep and roll-out timing analyses identify vaccination regimes capable of reducing transmission potential and outbreak burden, demonstrating that earlier vaccine deployment and higher vaccination coverage lead to lower peak and cumulative infections. These findings highlight the importance of timely and sustained vaccination strategies for effective disease control and long-term outbreak mitigation.
