From digital traces to dynamics: extracting diurnal–weekly activity and modelling multi-peak information diffusion

Abstract Multi-peak information diffusion unfolding over days is common yet mechanistically under-explained. There remains a lack of approaches that treat signals learned from large-scale data as first-order inputs to the dynamics and study the resulting nonlinear interactions with contact processes and endogenous mechanisms. Using 8.7 million timestamped digital traces, we first extract a platform-level diurnal–weekly activity field as an external driver. We build an interpretable, shock-aware dynamical model that couples this data-driven rhythm to finite-area external shocks while keeping exogenous inflow separate from peer-to-peer spread. A principal Floquet multiplier delineates absorbing and active regimes; a uniform-decay criterion guarantees that any finite-area shock relaxes without secondary surges; finite trains of shocks leave the long-term threshold unchanged. Calibrated on three multi-peak social-media events spanning 15 thousand to 136 thousand posts, the framework yields low error while retaining parsimony and interpretability. A phase-optimal launch rule maximises 24 h reach, and global sensitivity analyses expose a stage-wise relay: pulses and activation dominate early, rhythmic contrast shapes the middle stage, and active-lifetime decay with contact governs the tail. The analysis identifies efficient levers for crossing the extinction threshold by lowering contact or shortening active lifetime. Together, these results make long-period, multi-peak diffusion interpretable and actionable.