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Curvature in infectious disease network: A metric for vaccination and control

Sara Najem

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Phys. Rev. E 114, 034312 – Published 24 September, 2026

DOI: https://doi.org/10.1103/c44l-89p7

Abstract

We investigate the geometric structure of evolving infectious-disease networks using a notion of node curvature, which is based on the heat-kernel expansion that naturally extends to edges. Applying this measure to networks reconstructed from infection counts whose degree and strength distributions transition toward a steady power-law, we observe a corresponding transition in curvature. We relate the latter to an underlying hyperbolic space and reveal a phase transition in the network's effective temperature. We further compare our curvature measure with existing definitions in the literature, demonstrating that all capture the transition consistently. Our results suggest that curvature provides a metric for characterizing structural changes in dynamic networks arising from infectious processes and identifies distinct phases where targeted vaccination strategies may be most effective, when used within a multimetric public health decision-making framework.

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Phys. Rev. E 114, 034312– Published 24 September, 2026
  • Received 10 January 2026
  • Accepted 4 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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