Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations

Nature Physics (2024)Cite this article

Subjects

Abstract

Accurate estimates of the reproduction ratio are crucial for projecting the evolution of an infectious disease epidemic and for guiding the public health response. Here we prove that estimates of the reproduction ratio based on inference from surveillance data can be inaccurate if the population comprises spatially distinct communities, as the space–mobility interplay may hide the true evolution of the epidemic from surveillance data. Consequently, surveillance may underestimate the reproduction ratio over long periods, even mistaking growing epidemics as subsiding. To address this, we use the spectral properties of the matrix describing the spatial epidemic spread to reweight surveillance data. We propose a correction that removes the bias across all epidemic phases. We validate this correction against simulated epidemics and use COVID-19 as a case study. However, our results apply to any epidemic in which mobility is a driver of circulation. Our findings may help improve epidemic monitoring and surveillance and inform strategies for public health responses.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Convergence to the equilibrium spatial distribution of infections.
Fig. 2: Comparison of the reference and measured reproduction ratios.
Fig. 3: Corrected reproduction ratio.
Fig. 4: Application of the proposed correction to COVID-19 data for France.

Similar content being viewed by others

Data availability

Meta Colocation Maps, which were used to reconstruct the reproduction operators and to infer between- and within-community mixing for stochastic simulations can be requested at https://dataforgood.facebook.com/dfg/tools/colocation-maps. Meta Movement Range Maps used to correct within-community colocations are available at https://data.humdata.org/dataset/movement-range-maps. Hospital admission data in France are available at https://www.data.gouv.fr. French census data can be found at https://www.insee.fr. Shapefiles for French departments are available at https://www.data.gouv.fr/en/datasets/carte-des-departements-2-1/. All websites were accessed in November 2023.

Code availability

The code used in this study is available here: https://github.com/ev-modelers/birello-surveillance (ref. 70). A continuously developed and maintained library allowing us to implement our corrections to estimates of the reproduction ratio from surveillance data can be found at https://github.com/ev-modelers/rt-from-surveillance (ref. 60).

References

  1. Keeling, M. J. & Rohani, P. Modeling Infectious Diseases in Humans and Animals (Princeton Univ. Press, 2007).

  2. Nishiura, H. & Chowell, G. in Mathematical and Statistical Estimation Approaches in Epidemiology (eds Chowell, G. et al.) 103–121 (Springer, 2009).

  3. Wallinga, J., van Boven, M. & Lipsitch, M. Optimizing infectious disease interventions during an emerging epidemic. Proc. Natl Acad. Sci. USA 107, 923–928 (2010).

    Article  ADS  Google Scholar 

  4. Ridenhour, B., Kowalik, J. M. & Shay, D. K. Unraveling R0: considerations for public health applications. Am. J. Public Health 108, S445–S454 (2018).

    Article  Google Scholar 

  5. Thompson, R. N., Gilligan, C. A. & Cunniffe, N. J. Control fast or control smart: when should invading pathogens be controlled? PLoS Comput. Biol. 14, e1006014 (2018).

    Article  ADS  Google Scholar 

  6. Dhillon, R. S., Srikrishna, D. & Chowell, G. Getting to zero in the DR Congo Ebola outbreak. Lancet Infect. Dis. 20, 395–397 (2020).

    Article  Google Scholar 

  7. Pan, A. et al. Association of public health interventions with the epidemiology of the COVID-19 outbreak in Wuhan, China. J. Am. Med. Assoc. 323, 1915–1923 (2020).

    Article  Google Scholar 

  8. Wallinga, J. & Lipsitch, M. How generation intervals shape the relationship between growth rates and reproductive numbers. Proc. R. Soc. B 274, 599–604 (2007).

    Article  Google Scholar 

  9. Davoudi, B. et al. Early real-time estimation of the basic reproduction number of emerging infectious diseases. Phys. Rev. X 2, 031005 (2012).

    Google Scholar 

  10. Obadia, T., Haneef, R. & Boëlle, P.-Y. The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks. BMC Med. Inform. Decis. Mak. 12, 147 (2012).

    Article  Google Scholar 

  11. Cori, A., Ferguson, N. M., Fraser, C. & Cauchemez, S. A new framework and software to estimate time-varying reproduction numbers during epidemics. Am. J. Epidemiol. 178, 1505–1512 (2013).

    Article  Google Scholar 

  12. Thompson, R. N. et al. Improved inference of time-varying reproduction numbers during infectious disease outbreaks. Epidemics 29, 100356 (2019).

    Article  Google Scholar 

  13. Biggerstaff, M., Cauchemez, S., Reed, C., Gambhir, M. & Finelli, L. Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature. BMC Infect. Dis. 14, 480 (2014).

    Article  Google Scholar 

  14. Thompson, R., Wood, J. G., Tempia, S. & Muscatello, D. J. Global variation in early epidemic growth rates and reproduction number of seasonal influenza. Int. J. Infect. Dis. 122, 382–388 (2022).

    Article  Google Scholar 

  15. Guerra, F. M. et al. The basic reproduction number (R0) of measles: a systematic review. Lancet Infect. Dis. 17, e420–e428 (2017).

    Article  Google Scholar 

  16. Li, Y. et al. The temporal association of introducing and lifting non-pharmaceutical interventions with the time-varying reproduction number (R) of SARS-CoV-2: a modelling study across 131 countries. Lancet Infect. Dis. 21, 193–202 (2021).

    Article  Google Scholar 

  17. Maganga, G. D. et al. Ebola virus disease in the Democratic Republic of Congo. N. Engl. J. Med. 371, 2083–2091 (2014).

    Article  Google Scholar 

  18. Mukandavire, Z. et al. Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe. Proc. Natl Acad. Sci. USA 108, 8767–8772 (2011).

    Article  ADS  Google Scholar 

  19. Codeço, C. T., Villela, D. A. M. & Coelho, F. C. Estimating the effective reproduction number of dengue considering temperature-dependent generation intervals. Epidemics 25, 101–111 (2018).

    Article  Google Scholar 

  20. Routledge, I. et al. Estimating spatiotemporally varying malaria reproduction numbers in a near elimination setting. Nat. Commun. 9, 2476 (2018).

    Article  ADS  Google Scholar 

  21. Introducing a Coherent European Framework for Tuning COVID-19 Response Measures (ECDC, 2021); https://www.ecdc.europa.eu/sites/default/files/documents/Framework-for-tuning-COVID-19-response-measures.pdf

  22. Pastor-Satorras, R., Castellano, C., Van Mieghem, P. & Vespignani, A. Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925–979 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  23. Hufnagel, L., Brockmann, D. & Geisel, T. Forecast and control of epidemics in a globalized world. Proc. Natl Acad. Sci. USA 101, 15124–15129 (2004).

    Article  ADS  Google Scholar 

  24. Balcan, D. & Vespignani, A. Phase transitions in contagion processes mediated by recurrent mobility patterns. Nat. Phys. 7, 581–586 (2011).

    Article  Google Scholar 

  25. Soriano-Paños, D., Lotero, L., Arenas, A. & Gómez-Gardeñes, J. Spreading processes in multiplex metapopulations containing different mobility networks. Phys. Rev. X 8, 031039 (2018).

    Google Scholar 

  26. Gómez-Gardeñes, J., Soriano-Paños, D. & Arenas, A. Critical regimes driven by recurrent mobility patterns of reaction–diffusion processes in networks. Nat. Phys. 14, 391–395 (2018).

    Article  Google Scholar 

  27. Chang, S. et al. Mobility network models of COVID-19 explain inequities and inform reopening. Nature 589, 82–87 (2020).

    Article  ADS  Google Scholar 

  28. Coletti, P., Poletto, C., Turbelin, C., Blanchon, T. & Colizza, V. Shifting patterns of seasonal influenza epidemics. Sci. Rep. 8, 12786 (2018).

    Article  ADS  Google Scholar 

  29. Scarpino, S. V. & Petri, G. On the predictability of infectious disease outbreaks. Nat. Commun. 10, 898 (2019).

    Article  ADS  Google Scholar 

  30. Castro, M., Ares, S., Cuesta, J. A. & Manrubia, S. The turning point and end of an expanding epidemic cannot be precisely forecast. Proc. Natl Acad. Sci. USA 117, 26190–26196 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  31. Li, Y. & Nair, H. Trends in the global burden of lower respiratory infections: the knowns and the unknowns. Lancet Infect. Dis. 22, 1523–1525 (2022).

    Article  Google Scholar 

  32. Messina, J. P. et al. The current and future global distribution and population at risk of dengue. Nat. Microbiol. 4, 1508–1515 (2019).

    Article  Google Scholar 

  33. Romanello, M. et al. The 2022 report of the Lancet Countdown on health and climate change: health at the mercy of fossil fuels. Lancet 400, 1619–1654 (2022).

    Article  Google Scholar 

  34. Carlson, C. J. et al. Climate change increases cross-species viral transmission risk. Nature 607, 555–562 (2022).

    Article  ADS  Google Scholar 

  35. Watson, H. W. & Galton, F. On the probability of the extinction of families. J. Anthropol. Inst. G. B. Irel. 4, 138–144 (1875).

    Google Scholar 

  36. Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E. & Getz, W. M. Superspreading and the effect of individual variation on disease emergence. Nature 438, 355–359 (2005).

    Article  ADS  Google Scholar 

  37. Hellewell, J. et al. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob. Health 8, e488–e496 (2020).

    Article  Google Scholar 

  38. Kucharski, A. J. et al. Effectiveness of ring vaccination as control strategy for Ebola virus disease. Emerg. Infect. Dis. 22, 105–108 (2016).

    Article  Google Scholar 

  39. de Meijere, G. et al. Attitudes towards booster, testing and isolation, and their impact on COVID-19 response in winter 2022/2023 in France, Belgium, and Italy: a cross-sectional survey and modelling study. Lancet Reg. Health Eur. 28, 100614 (2023).

    Article  Google Scholar 

  40. Susswein, Z. et al. Ignoring spatial heterogeneity in drivers of SARS-CoV-2 transmission in the US will impede sustained elimination. Preprint at medRxiv https://doi.org/10.1101/2021.08.09.21261807 (2021).

  41. Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990).

    Article  MathSciNet  Google Scholar 

  42. Nishiura, H., Chowell, G., Safan, M. & Castillo-Chavez, C. Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009. Theor. Biol. Med. Model. 7, 1 (2010).

    Article  Google Scholar 

  43. Mazzoli, M., Valdano, E. & Colizza, V. Projecting the COVID-19 epidemic risk in France for the summer 2021. J. Travel Med. 28, taab129 (2021).

    Article  Google Scholar 

  44. Jourdain, F. et al. From importation to autochthonous transmission: drivers of chikungunya and dengue emergence in a temperate area. PLoS Negl. Trop. Dis. 14, e0008320 (2020).

    Article  Google Scholar 

  45. Iyer, S. et al. Large-scale measurement of aggregate human colocation patterns for epidemiological modeling. Epidemics 42, 100663 (2023).

    Article  Google Scholar 

  46. White, L. F., Archer, B. & Pagano, M. Estimating the reproductive number in the presence of spatial heterogeneity of transmission patterns. Int. J. Health Geogr. 12, 35 (2013).

    Article  Google Scholar 

  47. Trevisin, C. et al. Spatially explicit effective reproduction numbers from incidence and mobility data. Proc. Natl Acad. Sci. USA 120, e2219816120 (2023).

    Article  Google Scholar 

  48. Nishiura, H., Castillo-Chavez, C., Safan, M. & Chowell, G. Transmission potential of the new influenza A(H1N1) virus and its age-specificity in Japan. Euro Surveill. 14, 19227 (2009).

    Article  Google Scholar 

  49. Bansal, S., Grenfell, B. T. & Meyers, L. A. When individual behaviour matters: homogeneous and network models in epidemiology. J. R. Soc. Interface 4, 879–891 (2007).

    Article  Google Scholar 

  50. Chowell, G., Viboud, C., Simonsen, L. & Moghadas, S. M. Characterizing the reproduction number of epidemics with early subexponential growth dynamics. J. R. Soc. Interface 13, 20160659 (2016).

    Article  Google Scholar 

  51. Liu, Q.-H. et al. Measurability of the epidemic reproduction number in data-driven contact networks. Proc. Natl Acad. Sci. USA 115, 12680–12685 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  52. Nishiura, H. & Roberts, M. G. Estimation of the reproduction number for 2009 pandemic influenza A(H1N1) in the presence of imported cases. Euro Surveill. 15, 19622 (2010).

    Article  Google Scholar 

  53. Mercer, G. N., Glass, K. & Becker, N. G. Effective reproduction numbers are commonly overestimated early in a disease outbreak. Stat. Med. 30, 984–994 (2011).

    Article  MathSciNet  Google Scholar 

  54. COVID-19: point épidémiologique du 11 février 2021 (Santé Publique France, 2021).

  55. Di Domenico, L., Sabbatini, C. E., Pullano, G., Lévy-Bruhl, D. & Colizza, V. Impact of January 2021 curfew measures on SARS-CoV-2 B.1.1.7 circulation in France. Euro Surveill. 26, 2100272 (2021).

    Article  Google Scholar 

  56. Nishiura, H. Correcting the actual reproduction number: a simple method to estimate R0 from early epidemic growth data. Int. J. Environ. Res. Public Health 7, 291–302 (2010).

    Article  Google Scholar 

  57. Gostic, K. M. et al. Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput. Biol. 16, e1008409 (2020).

    Article  Google Scholar 

  58. Sherratt, K. et al. Exploring surveillance data biases when estimating the reproduction number: with insights into subpopulation transmission of COVID-19 in England. Philos. Trans. R. Soc. Lond. B 376, 20200283 (2021).

    Article  Google Scholar 

  59. Jorge, D. C. P., Oliveira, J. F., Miranda, J. G. V., Andrade, R. F. S. & Pinho, S. T. R. Estimating the effective reproduction number for heterogeneous models using incidence data. R. Soc. Open Sci. 9, 220005 (2022).

    Article  ADS  Google Scholar 

  60. Birello, P. & Valdano, E. Compute Rt from surveillance data. GitHub https://github.com/ev-modelers/rt-from-surveillance (2024).

  61. Wesolowski, A., Eagle, N., Noor, A. M., Snow, R. W. & Buckee, C. O. The impact of biases in mobile phone ownership on estimates of human mobility. J. R. Soc. Interface 10, 20120986 (2013).

    Article  Google Scholar 

  62. Tizzoni, M. et al. On the use of human mobility proxies for modeling epidemics. PLoS Comput. Biol. 10, e1003716 (2014).

    Article  Google Scholar 

  63. Wesolowski, A., Buckee, C. O., Engø-Monsen, K. & Metcalf, C. J. E. Connecting mobility to infectious diseases: the promise and limits of mobile phone data. J. Infect. Dis. 214, S414–S420 (2016).

    Article  Google Scholar 

  64. Lai, S. et al. Exploring the use of mobile phone data for national migration statistics. Palgrave Commun. 5, 34 (2019).

    Article  Google Scholar 

  65. Sekara, V. et al. in Guide to Mobile Data Analytics in Refugee Scenarios: The ‘Data for Refugees Challenge’ Study (eds Salah, A. A. et al.) 53–66 (Springer, 2019).

  66. Colizza, V. & Vespignani, A. Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations. J. Theor. Biol. 251, 450–467 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  67. Balcan, D. et al. Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. Natl Acad. Sci. USA 106, 21484–21489 (2009).

    Article  ADS  Google Scholar 

  68. Faucher, B. et al. Agent-based modelling of reactive vaccination of workplaces and schools against COVID-19. Nat. Commun. 13, 1414 (2022).

    Article  ADS  Google Scholar 

  69. Diekmann, O., Heesterbeek, J. A. P. & Roberts, M. G. The construction of next-generation matrices for compartmental epidemic models. J. R. Soc. Interface 7, 873–85 (2009).

    Article  Google Scholar 

  70. Birello, P., Wang, B., Valdano, E. Code for 'Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations'. GitHub https://github.com/ev-modelers/birello-surveillance (2024).

Download references

Acknowledgements

Colocation data were available thanks to Data For Good at Meta.

Author information

Authors and Affiliations

  1. Sorbonne Université, INSERM, Institut Pierre Louis d’Epidémiologie et de Santé Publique, Paris, France

    Piero Birello, Boxuan Wang, Vittoria Colizza & Eugenio Valdano

  2. Department of Applied Science And Technology (DISAT), Politecnico di Torino, Turin, Italy

    Michele Re Fiorentin

  3. Department of Biology, Georgetown University, Washington, DC, USA

    Vittoria Colizza

Authors
  1. Piero Birello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michele Re Fiorentin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Boxuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vittoria Colizza
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eugenio Valdano
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

E.V. conceived and designed the study. E.V. and M.R.F. developed the theory. P.B. developed the code and the publicly available library, performed the numerical simulations and analysed the results. B.W. analysed the surveillance data and reconstructed infections from them. P.B., M.R.F., B.W., V.C. and E.V. interpreted the results. E.V. drafted the article. P.B., M.R.F., B.W., V.C. and E.V. contributed to and approved the final version of the article.

Corresponding author

Correspondence to Eugenio Valdano.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Emily Harvey, Aram Vajdi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Methods Sections 1.1–1.5, Figs. 1–13 and references.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Birello, P., Re Fiorentin, M., Wang, B. et al. Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02471-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41567-024-02471-7

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing