Analysing Disease Spread on Complex Networks Using Forman–Ricci Curvature

Infectious-disease dynamics depend on heterogeneous contact structure, which classical homogeneous-mixing models such as SIR/SEIR cannot capture. We develop a curvature-informed network SIR framework that embeds Forman–Ricci curvature (FRC), a discrete topological descriptor of fragility and robustness, into per-edge transmission. We compute FRC on undirected and directed Erdős–Rényi, Watts–Strogatz, Barabási–Albert, and Power–Law Cluster networks, and relate curvature to degree, clustering, and betweenness to identify structurally influential nodes and bridge edges. Using curvature-adjusted transmission, we simulate epidemics across topologies and infection rates, then validate predictively with a controlled “hidden-truth” benchmark: posterior-calibrated FRC models are compared with advanced centrality-weighted baselines (EdgeBetweenness, Degree, Eigenvector) under identical fit/holdout splits. On heterogeneous graphs (Barabási–Albert/Power–Law Cluster), FRC improves holdout Root Mean Squared Error (RMSE), peak-time accuracy, and final-size proximity. A compact sensitivity analysis over baseline transmission and clustering, with Partial Rank Correlation Coefficient (PRCC), shows these gains are robust across parameter regimes. Intervention ablations (cases averted vs. budget) further show that vaccinating high-curvature nodes and protecting extreme negative-curvature bridges can outperform EdgeBetweenness targeting at practical budgets. Directed networks exhibit sharper peaks and faster resolution, with strongly negative out-curvature marking putative exporters. In general, FRC provides a principled geometric signal that enhances network epidemic models and yields concrete, topology-aware guidance for targeted vaccination and community-bridge control.