Epidemic spreading in hyperbolic geometry

Abstract

Epidemic spreading on complex networks is strongly influenced by the underlying network structure. In this work we simulate stochastic SIR epidemics on networks generated with the S¹H² model and compare the results with non-geometric models, including Erdős–Rényi, Barabási-Albert and Configuration model. Using distance-dependent infection rates from the H² embedding and native S¹H² coordinates, we analyse the epidemic dynamics through the variability of the recovered nodes and the spatio-temporal distribution of infection events. We find that hyperbolic networks exhibit lower epidemic thresholds than non-geometric networks, consistent with a hierarchical radial placement of hubs in the centre of the hyperbolic plane enhancing the epidemic transmissibility. The average hyperbolic distance reached by the infection follows a universal rescaled behaviour largely independent of the network topology. Furthermore, only the hyperbolic model displays an approximately coherent wavefront-like propagation through latent space, whereas non-geometric networks exhibit almost instantaneous spreading with weak distance dependence. These results show that hidden hyperbolic geometry qualitatively amplifies epidemic propagation and shapes the dynamical organisation of the spreading process.