Outbreak Size Distribution in Stochastic Epidemic Models

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Outbreak Size Distribution in Stochastic Epidemic Models

Jason Hindes, Michael Assaf, and Ira B. Schwartz

Phys. Rev. Lett. 128, 078301 – Published 15 February 2022

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.

Received 27 July 2021
Revised 10 November 2021
Accepted 26 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.078301

Physics Subject Headings (PhySH)

Diseases Diseases, physiology & pathology Ecological population dynamics Fluctuations & noise Irreversible processes Mathematical physics Nonequilibrium & irreversible thermodynamics Nonequilibrium statistical mechanics Population dynamics Scaling laws of complex systems Stochastic processes

Nonlinear DynamicsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsPhysics of Living Systems

Authors & Affiliations

Jason Hindes¹, Michael Assaf ^2,3, and Ira B. Schwartz ¹

¹U.S. Naval Research Laboratory, Washington, D.C. 20375, USA
²Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
³Institute for Physics and Astronomy, University of Potsdam, Potsdam 14476, Germany