Outbreak-size distributions under fluctuating rates

Jason Hindes, Luis Mier-Y-Teran-Romero, Ira B. Schwartz, Michael Assaf

Research output: Contribution to journalArticlepeer-review


We study the effect of noisy infection (contact) and recovery rates on the distribution of outbreak sizes in the stochastic susceptible-infected-recovered model. The rates are modeled as Ornstein-Uhlenbeck processes with finite correlation time and variance, which we illustrate using outbreak data from the RSV 2019-2020 season in the U.S. In the limit of large populations, we find analytical solutions for the outbreak-size distribution in the long-correlated (adiabatic) and short-correlated (white) noise regimes, and demonstrate that the distribution can be highly skewed with significant probabilities for large fluctuations away from mean-field theory. Furthermore, we assess the relative contributions of demographic and reaction-rate noise on the outbreak variance and show that demographic noise becomes irrelevant in the presence of slowly varying reaction-rate noise but persists for large system sizes if the noise is fast. Finally, we show that the crossover to the white-noise regime typically occurs for correlation times that are on the same order as the characteristic recovery time in the model.

Original languageAmerican English
Article number043264
JournalPhysical Review Research
Issue number4
StatePublished - Oct 2023

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© 2023 authors. Published by the American Physical Society. 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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