Sensitivity Analysis and Dynamical Behavior of an Atangana-Baleanu-Caputo Fractional SEIRV Model: A Case Study of the 2004-2005 H3N2 Influenza Season

Abstract This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.