Outbreak Size Distribution in Stochastic Epidemic Models

Jason Hindes, Michael Assaf, Ira B. Schwartz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with demographic noise, including the susceptible-infected-recovered (SIR) model and its general extensions. In the limit of large populations, we compute the probability distribution for all extensive outbreaks, including those that entail unusually large or small (extreme) proportions of the population infected. Our approach reveals that, unlike other well-known examples of rare events occurring in discrete-state stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths, each satisfying unique boundary conditions with a conserved probability flux.

Original languageAmerican English
Article number078301
JournalPhysical Review Letters
Volume128
Issue number7
DOIs
StatePublished - 18 Feb 2022

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