Network-driven vaccination strategies for preventing rebound dynamics in metapopulation epidemic control

A critical question in epidemic control concerns the minimal requirements for a vaccination campaign to effectively halt a contagion process. However, control measures can inadvertently trigger resurgence dynamics, driven by a reservoir of susceptible individuals left unexposed in the controlled wave. This phenomenon, known as the "rebound effect," is often preceded by a temporary drop in cases, usually termed as the "honeymoon period." In this study, we examine the fundamental conditions for rebound dynamics within a metapopulation network framework. By elucidating the mechanisms underlying rebound events, we derive a rigorous mathematical criterion that identifies, based solely on the metapopulation network structure, the specific vaccination strategies likely to precipitate a rebound. Additionally, we propose an alternative vaccination protocol designed to eliminate rebound dynamics entirely. This approach is analytically validated and offers a robust pathway toward sustainable epidemic control.