The deterministic Kermack-McKendrick model bounds the general stochastic epidemic

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 exp...

Full description

Bibliographic Details
Main Authors: Wilkinson, Robert R., Ball, Frank G., Sharkey, Kieran J.
Format: Article
Published: Applied Probability Trust 2016
Subjects:
Online Access:https://eprints.nottingham.ac.uk/40422/
Description
Summary: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.