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Superspreading and the effect of individual variation on disease emergence

Abstract

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups1,2. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R0, which is defined as the mean number of infections caused by an infected individual in a susceptible population3,4. Population estimates of R0 can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous ‘superspreading events’ in which certain individuals infected unusually large numbers of secondary cases5,6,7,8,9,10. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear2,10,11. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R0 is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

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Figure 1: Evidence for variation in individual reproductive number ν.
Figure 2: Outbreak dynamics with different degrees of individual variation in infectiousness.
Figure 3: Implications for control measures.

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Acknowledgements

We are grateful for comments and data suggestions from B. Bolker, J. Edmunds, N. Ferguson, A. Galvani, R. Gani, N. Gay, J. Gog, B. Grenfell, H. Hethcote, D. Heymann, A. Hubbard, N. Jewell, J. Lauer, R. May, T. Porco, C. Roth, D. Smith and B. Williams. We thank R. Gani for providing unpublished data from a previous publication, and L. Matthews for sharing work ahead of print. Our research was supported by the NSF, NIH-NIDA, the James S. McDonnell Foundation, the NSF/NIH Ecology of Infectious Disease Program, and the South African Centre for Epidemiological Modelling and Analysis (SACEMA). Author Contributions J.O.L.-S. and W.M.G. conceived the study. J.O.L.-S. collected and analysed outbreak data, conducted dynamic modelling, and drafted and revised the text. S.J.S. conducted formal analysis of branching processes and control measures. W.M.G. provided technical input on superspreading and control analyses. All authors contributed conceptually, and edited or commented on the text.

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Correspondence to J. O. Lloyd-Smith.

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Supplementary information

Supplementary Notes

This file contains additional discussion of factors contributing to individual variation in infectiousness, methodological details on statistical and modelling analyses, and details of outbreak datasets and superspreading events. (PDF 435 kb)

Supplementary Figures

The file includes Supplementary Figures 1 to 4, with captions. The figures address the prediction of superspreading event frequency, further results on outbreak dynamics and control, and estimation of the dispersion parameter k with limited data. (PDF 322 kb)

Supplementary Table 1

A summary of results from our statistical analysis of uncontrolled outbreaks (corresponds to Figure 1a–c). (PDF 71 kb)

Supplementary Table 2

Detailed results from our statistical analysis of uncontrolled outbreaks (elaborating on Supplementary Table 1), and the analysis of data before and after control measures were applied in four outbreaks. (PDF 94 kb)

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Lloyd-Smith, J., Schreiber, S., Kopp, P. et al. Superspreading and the effect of individual variation on disease emergence. Nature 438, 355–359 (2005). https://doi.org/10.1038/nature04153

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