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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\u2013weekly 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.<\/jats:p>","DOI":"10.1140\/epjds\/s13688-026-00624-7","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T08:06:26Z","timestamp":1769069186000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["From digital traces to dynamics: extracting diurnal\u2013weekly activity and modelling multi-peak information diffusion"],"prefix":"10.1140","volume":"15","author":[{"given":"Yushi","family":"Sun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"issue":"772","key":"624_CR1","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. 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