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Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk

  • CHRISTIAN L. VESTERGAARD (a1), EUGENIO VALDANO (a2), MATHIEU GÉNOIS (a1), CHIARA POLETTO (a2), VITTORIA COLIZZA (a2) (a3) and ALAIN BARRAT (a1) (a3)...
Abstract

The ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of the contacts occurring in a population is however generally unattainable, due for instance to limited participation rates or experimental constraints in spatial coverage. Here, we study the impact of spatially constrained sampling on our ability to estimate the epidemic risk in a population using such detailed data-driven models. The epidemic risk is quantified by the epidemic threshold of the SIRS model for the propagation of communicable diseases, i.e. the critical value of disease transmissibility above which the disease turns endemic. We verify for both synthetic and empirical data of human interactions that the use of incomplete data sets due to spatial sampling leads to the underestimation of the epidemic risk. The bias is however smaller than the one obtained by uniformly sampling the same fraction of contacts: it depends non-linearly on the fraction of contacts that are recorded, and becomes negligible if this fraction is large enough. Moreover, it depends on the interplay between the timescales of population and spreading dynamics.

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[1] Read, J. M., Edmunds, W. J., Riley, S., Lessler, J. & Cummings, D. A. T. (2012) Close encounters of the infectious kind: Methods to measure social mixing behaviour. Epidemiol. Infect 140, 21172130.
[2] Salathé, M. et al. (2010) A high-resolution human contact network for infectious disease transmission. Proc. Natl. Acad. Sci. 107, 2202022025.
[3] Hashemian, M., Stanley, K. & Osgood, N. (2010) Flunet: Automated tracking of contacts during flu season. In: Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, Ad-hoc and Wireless Networks (WIOpt), IEEE, Avignon, France, pp. 348353.
[4] Cattuto, C. et al. (2010) Dynamics of person-to-person interactions from distributed RFID sensor networks. PLoS ONE 5, e11596.
[5] Stehlé, J. et al. (2011) Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Med. 9, 87.
[6] Hornbeck, T. et al. (2012) Using sensor networks to study the effect of peripatetic healthcare workers on the spread of hospital-associated infections. J. Infect. Dis. 206 (10), 15491557.
[7] Gemmetto, V., Barrat, A. & Cattuto, C. (2014) Mitigation of infectious disease at school: targeted class closure vs school closure. BMC Infect. Dis. 14, 110. http://dx.doi.org/10.1186/s12879-014-0695-9.
[8] Stopczynski, A. et al. (2014) Measuring large-scale social networks with high resolution. PLoS ONE 9, e95978.
[9] Obadia, T. et al. (2015) Detailed contact data and the dissemination of staphylococcus aureus in hospitals. PLoS Comput. Biol. 11, e1004170.
[10] Toth, D. J. A. et al. (2015) The role of heterogeneity in contact timing and duration in network models of influenza spread in schools. J. R. Soc. Interface 12, 20150279.
[11] Hui, P. et al. (2005) Pocket switched networks and human mobility in conference environments. In: WDTN '05: Proc. 2005 ACM SIGCOMM Workshop on Delay-Tolerant Networking, ACM, New York, NY, USA.
[12] O'Neill, E. et al. (2006) Instrumenting the city: Developing methods for observing and understanding the digital cityscape. In: Ubicomp, vol. 4206, pp. 315332. Springer Berlin Heidelberg.
[13] Eagle, N. & Pentland, A. (2006) Reality mining: Sensing complex social systems. Pers. Ubiquitous Comput. 10, 255268.
[14] Isella, L. et al. (2011) What's in a crowd? Analysis of face-to-face behavioral networks. J. Theor. Biol. 271, 166180.
[15] Fournet, J. & Barrat, A. (2014) Contact patterns among high school students. PLoS ONE 9, e107878.
[16] Ghani, A. C., Donnelly, C. A. & Garnett, G. P. (1998) Sampling biases and missing data in explorations of sexual partner networks for the spread of sexually transmitted diseases. Stat. Med. 17, 20792097.
[17] Génois, M., Vestergaard, C., Cattuto, C. & Barrat, A. (2015) Compensating for population sampling in simulations of epidemic spread on temporal contact networks. Nat. Commun. 6, 8860.
[18] Granovetter, M. (1976) Network sampling: Some first steps. Am. J. Sociol. 81, pp. 12871303. http://www.jstor.org/stable/2777005.
[19] Frank, O. (1979) Sampling and estimation in large social networks. Soc. Netw. 1, 91–101. http://www.sciencedirect.com/science/article/pii/0378873378900151.
[20] Heckathorn, D. D. (1997) Respondent-driven sampling: A new approach to the study of hidden populations. Soc. Probl. 44, 174199. http://www.jstor.org/stable/3096941.
[21] Achlioptas, D., Clauset, A., Kempe, D. & Moore, C. (2005) On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, STOC '05, ACM, New York, NY, USA, pp. 694703.
[22] Lee, S. H., Kim, P.-J. & Jeong, H. (2006) Statistical properties of sampled networks. Phys. Rev. E 73, 016102.
[23] Kossinets, G. (2006) Effects of missing data in social networks. Soc. Netw. 28, 247268.
[24] Onnela, J.-P. & Christakis, N. A. (2012) Spreading paths in partially observed social networks. Phys. Rev. E 85, 036106.
[25] Blagus, N., Subelj, L. & Bajec, M. (2015) Empirical comparison of network sampling techniques. Preprint arXiv 1506.02449.
[26] Rocha, L. E. C., Thorson, A. E., Lambiotte, R. & Liljeros, F. (2016) Respondent-driven sampling bias induced by community structure and response rates in social networks. J. R. Stat. Soc.: Ser. A (Stat. Soc.) Early view doi: 10.1111/rssa.12180.
[27] Leskovec, J. & Faloutsos, C. (2006) Sampling from large graphs. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining KDD'06, ACM, New York, NY, USA, pp. 631636.
[28] Viger, F., Barrat, A., Dall'Asta, L., Zhang, C.-H. & Kolaczyk, E. (2007) What is the real size of a sampled network? The case of the Internet. Phys. Rev. E 75, 056111.
[29] Bliss, C. A., Danforth, C. M. & Dodds, P. S. (2014) Estimation of global network statistics from incomplete data. PLoS ONE 9, e108471.
[30] Zhang, Y., Kolaczyk, E. D. & Spencer, B. D. (2015) Estimating network degree distributions under sampling: An inverse problem, with applications to monitoring social media networks. Ann. Appl. Stat. 9, 166199.
[31] Ghani, A. C. & Garnett, G. P. (1998) Measuring sexual partner networks for transmission of sexually transmitted diseases. J. R. Stat. Soc.: Ser. A (Stat. Soc.) 161, 227238.
[32] Vestergaard, C. L., Génois, M. & Barrat, A. (2014) How memory generates heterogeneous dynamics in temporal networks. Phys. Rev. E 90, 042805.
[33] Holme, P. & Saramäki, J. (2012) Temporal networks. Phys. Rep. 519, 97125.
[34] Pastor-Satorras, R., Castellano, C., Mieghem, P. V. & Vespignani, A. (2015) Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925.
[35] Valdano, E., Ferreri, L., Poletto, C. & Colizza, V. (2015) Analytical computation of the epidemic threshold on temporal networks. Phys. Rev. X 5, 021005.
[36] Valdano, E., Poletto, C. & Colizza, V. (2015) Infection propagator approach to compute epidemic thresholds on temporal networks: Impact of immunity and of limited temporal resolution. Eur. Phys. J. B 88, 111.
[37] De Domenico, M. et al. (2013) Mathematical formulation of multilayer networks. Phys. Rev. X 3, 041022.
[38] Cozzo, E., Baños, R. A., Meloni, S. & Moreno, Y. (2013) Contact-based social contagion in multiplex networks. Phys. Rev. E 88, 050801.
[39] Wang, H. et al. (2013) Effect of the interconnected network structure on the epidemic threshold. Phys. Rev. E 88, 022801.
[40] Wang, Y., Chakrabarti, D., Wang, C. & Faloutsos, C. (2003) Epidemic spreading in real networks: An eigenvalue viewpoint. In: Proceedings of the 22nd International Symposium on Reliable Distributed Systems, pp. 2534. IEEE.
[41] Gómez, S., Arenas, A., Borge-Holthoefer, J., Meloni, S. & Moreno, Y. (2010) Discrete time Markov chain approach to contact-based disease spreading in complex networks. Europhys. Lett. 89, 38009.
[42] Hanski, I. & Gilplin, M. (1997) Metapopulation Biology: Ecology, Genetics, and Evolution, Academic Press, San Diego.
[43] Grenfell, B. T. & Harwood, J. (1997) (meta)population dynamics of infectious disease. Trends Ecol. Evol. 12, 395399.
[44] Tilman, D. & Kareiva, P. (1997) Spatial Ecology, Princeton University Press, Princeton.
[45] Bascompte, J. & Solé, R. (1998) Modeling Spatio-temporal Dynamics in Ecology, Springer, New York.
[46] Hanski, I. & Gaggiotti, O. (2004) Ecology, Genetics and Evolution of Metapopulations, Elsevier Academic Press, London.
[47] Apolloni, A., Poletto, C. & Colizza, V. (2013) Age-specific contacts and travel patterns in the spatial spread of 2009 H1n1 influenza pandemic. BMC Infect. Dis. 13, 176.
[48] Keeling, M. J., Danon, L., Vernon, M. C. & House, T. A. (2010) Individual identity and movement networks for disease metapopulations. PNAS 107, 88668870. http://www.pnas.org/content/107/19/8866.
[49] Balcan, D. & Vespignani, A. (2011) Phase transitions in contagion processes mediated by recurrent mobility patterns. Nat. Phys. 7, 581586. http://www.nature.com/nphys/journal/v7/n7/full/nphys1944.html.
[50] Belik, V., Geisel, T. & Brockmann, D. (2011) Natural human mobility patterns and spatial spread of infectious diseases. Phys. Rev. X 1, 011001. http://link.aps.org/doi/10.1103/PhysRevX.1.011001.
[51] Poletto, C., Tizzoni, M. & Colizza, V. (2013) Human mobility and time spent at destination: Impact on spatial epidemic spreading. J. Theor. Biol. 338, 4158. http://www.sciencedirect.com/science/article/pii/S0022519313004062.
[52] Mata, A. S., Ferreira, S. C. & Pastor-Satorras, R. (2013) Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks. Phys. Rev. E 88, 042820. http://link.aps.org/doi/10.1103/PhysRevE.88.042820.
[53] Sun, K., Baronchelli, A. & Perra, N. (2015) Contrasting effects of strong ties on sir and sis processes in temporal networks. Eur. Phys. J. B 88, 14346036.
[54] Boguñá, M., Castellano, C. & Pastor-Satorras, R. (2013) Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks. Phys. Rev. Lett. 111, 068701.
[55] Génois, M. et al. (2015) Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers. Netw. Sci. 3, 326347.
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