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  • Open Access

Critical-like growth in noncritical transitions: Linearized dynamics and epidemic applications

Joshua Looker1, Kat S. Rock2, and Louise Dyson2,3

  • 1EPSRC and MRC Centre for Doctoral Training in Mathematics for Real-World Systems, University of Warwick, Coventry, England, United Kingdom
  • 2The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, and Mathematics Institute, University of Warwick, Coventry, England, United Kingdom
  • 3School of Life Sciences, University of Warwick, Coventry, England, United Kingdom

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Phys. Rev. E 114, 044205 – Published 9 October, 2026

DOI: https://doi.org/10.1103/2fyp-hjbd

Abstract

In the wake of the SARS-CoV-2 pandemic, there has been heightened interest from applied mathematicians in infectious disease modeling. Modeling efforts often focus on predicting whether diseases are likely to be eliminated or, instead, (re)emerge, especially as a result of control measures. This tipping point between elimination and infection waves has been successfully anticipated in the literature through the use of early warning signals and such signals often rely on the theory of critical slowing down. Recent developments have shown that these signals (increases in fluctuation variance and return time) can emerge from the system geometry in the case of non-normal dynamics rather than a change in asymptotic stability. We show how such dynamical behavior occurs in the fluctuations from the mean field in general stochastic systems. Using the susceptible-infectious-recovered model as an example application, we analyze how critical-like behavior can be exploited to anticipate infection waves in the absence of an equilibrium bifurcation.

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Information

Phys. Rev. E 114, 044205– Published 9 October, 2026
  • Received 22 January 2026
  • Revised 14 August 2026
  • Accepted 10 September 2026
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