Extreme outbreak dynamics in epidemic models

TL;DR

This paper develops a comprehensive mathematical framework to analyze the probability and dynamics of extreme epidemic outbreaks in large populations, applicable to models like SIR, revealing complex underlying path structures.

Contribution

It introduces a novel Hamiltonian path approach to compute the likelihood of all extensive outbreaks, including extreme cases, in stochastic epidemic models.

Findings

Probability distribution for extreme outbreaks derived

Reveals continuum of Hamiltonian paths underlying outbreak statistics

Provides insights into rare event dynamics in epidemic models

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.