Epidemic growth rate and household reproduction number in communities of households,schools and workplaces |
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Authors: | Lorenzo Pellis Neil M Ferguson Christophe Fraser |
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Institution: | (1) Julius Centre for Health Sciences and Primary Care, University Medical Centre Utrecht, Utrecht, The Netherlands;(2) Center for Infectious Disease Control, RIVM, Bilthoven, The Netherlands |
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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. |
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Keywords: | |
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