Mathematical Biosciences and Engineering, 2009, 6(2): 239-259. doi: 10.3934/mbe.2009.6.239.

Primary: 58F15, 58F17; Secondary: 53C35.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

The reproduction number $R_t$ in structured and nonstructured populations

1. Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, NM 87545
2. School of Human Evolution and Social Change, Arizona State University, Box 872402, Tempe, AZ 85287


Using daily counts of newly infected individuals, Wallinga and Teunis (WT) introduced a conceptually simple method to estimate the number of secondary cases per primary case ($R_t$) for a given day. The method requires an estimate of the generation interval probability density function (pdf), which specifies the probabilities for the times between symptom onset in a primary case and symptom onset in a corresponding secondary case. Other methods to estimate $R_t$ are based on explicit models such as the SIR model; therefore, one might expect the WT method to be more robust to departures from SIR-type behavior. This paper uses simulated data to compare the quality of daily $R_t$ estimates based on a SIR model to those using the WT method for both structured (classical SIR assumptions are violated) and nonstructured (classical SIR assumptions hold) populations. By using detailed simulations that record the infection day of each new infection and the donor-recipient identities, the true $R_t$ and the generation interval pdf is known with negligible error. We find that the generation interval pdf is time dependent in all cases, which agrees with recent results reported elsewhere. We also find that the WT method performs essentially the same in the structured populations (except for a spatial network) as it does in the nonstructured population. And, the WT method does as well or better than a SIR-model based method in three of the four structured populations. Therefore, even if the contact patterns are heterogeneous as in the structured populations evaluated here, the WT method provides reasonable estimates of $R_t$, as does the SIR method.
  Article Metrics

Keywords reproduction number; generation interval; structured population.

Citation: Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences and Engineering, 2009, 6(2): 239-259. doi: 10.3934/mbe.2009.6.239


This article has been cited by

  • 1. Quan-Hui Liu, Marco Ajelli, Alberto Aleta, Stefano Merler, Yamir Moreno, Alessandro Vespignani, Measurability of the epidemic reproduction number in data-driven contact networks, Proceedings of the National Academy of Sciences, 2018, 201811115, 10.1073/pnas.1811115115

Reader Comments

your name: *   your email: *  

Copyright Info: 2009, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved