Analysing Disease Spread on Complex Networks Using Forman-Ricci Curvature

Modelling infectious disease dynamics requires frameworks that capture the heterogeneity of real-world contact structures, which are often inadequately represented by traditional homogeneous-mixing models such as SIR and SEIR. This study introduces a curvature-informed epidemic modelling framework that integrates Forman–Ricci curvature (FRC), a discrete topological descriptor of network fragility and robustness, into network-based SIR dynamics. FRC was computed for both undirected and directed synthetic networks generated from Erdős–Rényi, Watts–Strogatz, Barabási–Albert, and Power–Law Cluster models. Correlations between FRC and classical centrality measures (degree, clustering coefficient, betweenness) were analyzed to assess its ability to identify structurally vulnerable and influential nodes. Curvature-adjusted transmission rates were then incorporated into an SIR model to simulate epidemic trajectories under different network topologies and infection rates. The findings show that FRC distributions vary by topology, with scale-free and clustered networks exhibiting strongly negative curvature around hubs, corresponding to potential super-spreader nodes. Incorporating curvature into epidemic dynamics produced more diverse outbreak trajectories, sharper peaks in directed networks, and improved predictions of peak magnitude and timing compared to the classical SIR framework. These results establish FRC as a powerful geometric tool to enhance epidemic models, offering novel insights for targeted interventions such as hub vaccination or cluster-based containment.