Journal of Mathematical Biology

, Volume 63, Issue 4, pp 691–734

Epidemic growth rate and household reproduction number in communities of households, schools and workplaces

  • Lorenzo Pellis
  • Neil M. Ferguson
  • Christophe Fraser
Article

DOI: 10.1007/s00285-010-0386-0

Cite this article as:
Pellis, L., Ferguson, N.M. & Fraser, C. J. Math. Biol. (2011) 63: 691. doi:10.1007/s00285-010-0386-0

Abstract

In this paper we present a novel and coherent modelling framework for the characterisation of the real-time growth rate in SIR models of epidemic spread in populations with social structures of increasing complexity. Known results about homogeneous mixing and multitype models are included in the framework, which is then extended to models with households and models with households and schools/workplaces. Efficient methods for the exact computation of the real-time growth rate are presented for the standard SIR model with constant infection and recovery rates (Markovian case). Approximate methods are described for a large class of models with time-varying infection rates (non-Markovian case). The quality of the approximation is assessed via comparison with results from individual-based stochastic simulations. The methodology is then applied to the case of influenza in models with households and schools/workplaces, to provide an estimate of a household-to-household reproduction number and thus asses the effort required to prevent an outbreak by targeting control policies at the level of households. The results highlight the risk of underestimating such effort when the additional presence of schools/workplaces is neglected. Our framework increases the applicability of models of epidemic spread in socially structured population by linking earlier theoretical results, mainly focused on time-independent key epidemiological parameters (e.g. reproduction numbers, critical vaccination coverage, epidemic final size) to new results on the epidemic dynamics.

Keywords

Stochastic epidemic modelsReal-time growth rateHousehold reproduction numberStructured populationsTwo levels of mixingEpidemic dynamics

Mathematics Subject Classification (2000)

92D30

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Lorenzo Pellis
    • 1
  • Neil M. Ferguson
    • 1
  • Christophe Fraser
    • 1
  1. 1.Medical Research Council Centre for Outbreak Analysis and Modelling, Department of Infectious Disease EpidemiologyImperial College London, St. Mary’s HospitalLondonUK