Outbreak size distributions in epidemics with multiple stages

TL;DR

This paper analyzes the outbreak size distributions in multistage epidemic models, especially the critical multistage SIR process, providing asymptotic results and scaling laws applicable to finite populations.

Contribution

It introduces analytical methods for outbreak size distributions in multistage epidemic models and extends asymptotic results to more general branching processes.

Findings

Derived outbreak size distributions for multistage SIR models

Established asymptotic results applicable to general multistage processes

Proposed scaling laws for finite population epidemic outbreaks

Abstract

Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical multistage Susceptible-Infected-Recovered (SIR) infection process. In the infinite population limit, we compute the outbreak size distributions and show that asymptotic results apply to more general multiple-type critical branching processes. Finally using heuristic arguments and simulations we establish scaling laws for a multistage SIR model in a finite population.