Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 48: Nonlinear Dynamics and Time-Delay Systems

DY 48.1: Vortrag

Donnerstag, 12. März 2026, 09:30–09:45, ZEU/0118

From Case Counts to Contact Networks: Inferring Epidemic Coupling in Space and Time — •Adrian Pelcaru and Dirk Brockmann — Center Synergy of Systems (SynoSys), TUD Dresden University of Technology, Dresden, Germany

Inferring spatio-temporal transmission structure from incidence data alone is a central problem in epidemic modelling, with implications for real-time surveillance and for how we interpret mobility and contact information. We analyse discrete-time renewal SIRS models on a network of metapopulations that incorporate infection-age structure, seasonality, mobility between regions, and time-varying local contact rates. In the analysis, these ingredients are combined into an effective spatio-temporal contact kernel that quantifies how cases in region m at a given infection age contribute to new infections in region n one day ahead. Stacking multi-region incidence histories across lags into a delay-embedded state, the renewal dynamics define a map on this reconstructed space whose local Jacobian is the convolution operator determined by the contact kernel and the susceptibles. Aggregating the kernel over infection age with suitable weights yields a time-dependent effective contact matrix and associated effective distances that summarise how infections propagate between regions. This construction provides a transparent link between mechanistic assumptions about mobility and varying infection rates and the resulting effective couplings in space and time, and identifies a natural operator that can, in principle, be compared to reconstructions from incidence data to detect systematic deviations from mobility-based expectations.

Keywords: Epidemic Modelling; State Space Reconstruction; Delay Embedding; Renewal Equation