Inference of R(0) and transmission heterogeneity from the size distribution of stuttering chains

PLoS Comput Biol. 2013;9(5):e1002993. doi: 10.1371/journal.pcbi.1002993. Epub 2013 May 2.


For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, [Formula: see text] and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring [Formula: see text] and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer [Formula: see text], but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, [Formula: see text]) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both [Formula: see text] and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for [Formula: see text] is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in [Formula: see text] is detectable. In addition, by allowing for superspreading events, inference of [Formula: see text] shifts the threshold above which a transmission chain should be considered anomalously large for a given value of [Formula: see text] (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Cluster Analysis
  • Computer Simulation
  • Contact Tracing*
  • Democratic Republic of the Congo
  • Disease Transmission, Infectious*
  • Humans
  • Models, Biological*
  • Models, Statistical*
  • Monkeypox / transmission
  • Zoonoses / transmission

Grant support

Financial support was provided by the RAPIDD program of the Science and Technology Directorate, Department of Homeland Security, and the Fogarty International Center, National Institutes of Health, and by the National Science Foundation under grants EF-0928690 and PHY05-51164. JOLS is grateful for the support of the De Logi Chair in Biological Sciences. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.