Message passing approach for general epidemic models

Brian Karrer and M. E. J. Newman
Phys. Rev. E 82, 016101 – Published 2 July 2010

Abstract

In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for transmission and recovery. Time intervals for real diseases, however, have distributions that in most cases are far from exponential, which leads to disagreements, both qualitative and quantitative, with the models. In this paper, we study a generalized version of the susceptible-infected-recovered model of epidemic disease that allows for arbitrary distributions of transmission and recovery times. Standard differential equation approaches cannot be used for this generalized model, but we show that the problem can be reformulated as a time-dependent message passing calculation on the appropriate contact network. The calculation is exact on trees (i.e., loopless networks) or locally treelike networks (such as random graphs) in the large system size limit. On non-tree-like networks we show that the calculation gives a rigorous bound on the size of disease outbreaks. We demonstrate the method with applications to two specific models and the results compare favorably with numerical simulations.

  • Figure
  • Figure
  • Figure
  • Received 6 April 2010

DOI:https://doi.org/10.1103/PhysRevE.82.016101

©2010 American Physical Society

Authors & Affiliations

Brian Karrer1 and M. E. J. Newman1,2

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 2Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 82, Iss. 1 — July 2010

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×