The deterministic Kermack-McKendrick model bounds the general stochastic epidemic

TL;DR

This paper demonstrates that the deterministic Kermack-McKendrick SIR model provides bounds on the expected number of susceptibles and recoveries in the stochastic epidemic with Poisson processes, using message passing techniques.

Contribution

It establishes rigorous bounds for stochastic SIR epidemics based on the classical deterministic model, leveraging message passing methods.

Findings

Deterministic SIR model bounds stochastic epidemic outcomes

Provides strict bounds on expected susceptibles and recoveries

Uses message passing representation for proof

Abstract

We prove that, for Poisson transmission and recovery processes, the classic Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of suscpetibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.