Heterogeneity can markedly increase final outbreak size in the SIR model of epidemics

Alexander Leibenzon, Michael Assaf

Research output: Contribution to journalArticlepeer-review


We study the susceptible-infected-recovered (SIR) model of epidemics on positively correlated heterogeneous networks with population variability, and explore the dependence of the final outbreak size on the network heterogeneity strength and basic reproduction number R0 - the ratio between the infection and recovery rates per individual. We reveal a critical value R0c, above which the maximal outbreak size is obtained at zero heterogeneity, but below which the maximum is obtained at finite heterogeneity strength. This second-order phase transition, universal for all network distributions with finite standardized moments, indicates that network heterogeneity can greatly increase the final outbreak size. We also show that this effect can be enhanced by adding population heterogeneity, in the form of varying interindividual susceptibility and infectiousness. Our results provide key insight as to the predictability of the well-mixed SIR model for the final outbreak size, in realistic scenarios.

Original languageAmerican English
Article numberL012010
JournalPhysical Review Research
Issue number1
StatePublished - Jan 2024

Bibliographical note

Publisher Copyright:
© 2024 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.


Dive into the research topics of 'Heterogeneity can markedly increase final outbreak size in the SIR model of epidemics'. Together they form a unique fingerprint.

Cite this