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Barrat A, Cattuto C, Kivelä M, Lehmann S, Saramäki J. Effect of manual and digital contact tracing on COVID-19 outbreaks: a study on empirical contact data. J R Soc Interface 2021. [PMID: 33947224 DOI: 10.1101/2020.07.24.20159947] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/19/2023] Open
Abstract
Non-pharmaceutical interventions are crucial to mitigate the COVID-19 pandemic and contain re-emergence phenomena. Targeted measures such as case isolation and contact tracing can alleviate the societal cost of lock-downs by containing the spread where and when it occurs. To assess the relative and combined impact of manual contact tracing (MCT) and digital (app-based) contact tracing, we feed a compartmental model for COVID-19 with high-resolution datasets describing contacts between individuals in several contexts. We show that the benefit (epidemic size reduction) is generically linear in the fraction of contacts recalled during MCT and quadratic in the app adoption, with no threshold effect. The cost (number of quarantines) versus benefit curve has a characteristic parabolic shape, independent of the type of tracing, with a potentially high benefit and low cost if app adoption and MCT efficiency are high enough. Benefits are higher and the cost lower if the epidemic reproductive number is lower, showing the importance of combining tracing with additional mitigation measures. The observed phenomenology is qualitatively robust across datasets and parameters. We moreover obtain analytically similar results on simplified models.
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Affiliation(s)
- A Barrat
- Aix Marseille Univ., CNRS, CPT, Turing Center for Living Systems, Université de Toulon, Marseille, France
- Tokyo Tech World Research Hub Initiative (WRHI), Tokyo Institute of Technology, Tokyo, Japan
| | - C Cattuto
- Computer Science Department, University of Turin, Turin, Italy
- ISI Foundation, Turin, Italy
| | - M Kivelä
- Department of Computer Science, Aalto University, Aalto, Finland
| | - S Lehmann
- Technical University of Denmark, Copenhagen, Denmark
| | - J Saramäki
- Department of Computer Science, Aalto University, Aalto, Finland
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Barrat A, Cattuto C, Kivelä M, Lehmann S, Saramäki J. Effect of manual and digital contact tracing on COVID-19 outbreaks: a study on empirical contact data. J R Soc Interface 2021; 18:20201000. [PMID: 33947224 PMCID: PMC8097511 DOI: 10.1098/rsif.2020.1000] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 04/13/2021] [Indexed: 12/25/2022] Open
Abstract
Non-pharmaceutical interventions are crucial to mitigate the COVID-19 pandemic and contain re-emergence phenomena. Targeted measures such as case isolation and contact tracing can alleviate the societal cost of lock-downs by containing the spread where and when it occurs. To assess the relative and combined impact of manual contact tracing (MCT) and digital (app-based) contact tracing, we feed a compartmental model for COVID-19 with high-resolution datasets describing contacts between individuals in several contexts. We show that the benefit (epidemic size reduction) is generically linear in the fraction of contacts recalled during MCT and quadratic in the app adoption, with no threshold effect. The cost (number of quarantines) versus benefit curve has a characteristic parabolic shape, independent of the type of tracing, with a potentially high benefit and low cost if app adoption and MCT efficiency are high enough. Benefits are higher and the cost lower if the epidemic reproductive number is lower, showing the importance of combining tracing with additional mitigation measures. The observed phenomenology is qualitatively robust across datasets and parameters. We moreover obtain analytically similar results on simplified models.
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Affiliation(s)
- A. Barrat
- Aix Marseille Univ., CNRS, CPT, Turing Center for Living Systems, Université de Toulon, Marseille, France
- Tokyo Tech World Research Hub Initiative (WRHI), Tokyo Institute of Technology, Tokyo, Japan
| | - C. Cattuto
- Computer Science Department, University of Turin, Turin, Italy
- ISI Foundation, Turin, Italy
| | - M. Kivelä
- Department of Computer Science, Aalto University, Aalto, Finland
| | - S. Lehmann
- Technical University of Denmark, Copenhagen, Denmark
| | - J. Saramäki
- Department of Computer Science, Aalto University, Aalto, Finland
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Barrat A, Cattuto C, Kivelä M, Lehmann S, Saramäki J. Effect of manual and digital contact tracing on COVID-19 outbreaks: a study on empirical contact data. J R Soc Interface 2021. [PMID: 33947224 DOI: 10.1101/2020.07.24.20159947v1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2023] Open
Abstract
Non-pharmaceutical interventions are crucial to mitigate the COVID-19 pandemic and contain re-emergence phenomena. Targeted measures such as case isolation and contact tracing can alleviate the societal cost of lock-downs by containing the spread where and when it occurs. To assess the relative and combined impact of manual contact tracing (MCT) and digital (app-based) contact tracing, we feed a compartmental model for COVID-19 with high-resolution datasets describing contacts between individuals in several contexts. We show that the benefit (epidemic size reduction) is generically linear in the fraction of contacts recalled during MCT and quadratic in the app adoption, with no threshold effect. The cost (number of quarantines) versus benefit curve has a characteristic parabolic shape, independent of the type of tracing, with a potentially high benefit and low cost if app adoption and MCT efficiency are high enough. Benefits are higher and the cost lower if the epidemic reproductive number is lower, showing the importance of combining tracing with additional mitigation measures. The observed phenomenology is qualitatively robust across datasets and parameters. We moreover obtain analytically similar results on simplified models.
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Affiliation(s)
- A Barrat
- Aix Marseille Univ., CNRS, CPT, Turing Center for Living Systems, Université de Toulon, Marseille, France
- Tokyo Tech World Research Hub Initiative (WRHI), Tokyo Institute of Technology, Tokyo, Japan
| | - C Cattuto
- Computer Science Department, University of Turin, Turin, Italy
- ISI Foundation, Turin, Italy
| | - M Kivelä
- Department of Computer Science, Aalto University, Aalto, Finland
| | - S Lehmann
- Technical University of Denmark, Copenhagen, Denmark
| | - J Saramäki
- Department of Computer Science, Aalto University, Aalto, Finland
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Abstract
Human activity follows a circadian rhythm. In online activity, this rhythm is visible both at the level of individuals as well as at the population level from Wikipedia edits to mobile telephone calls. However, much less is known about circadian patterns at the level of network structure, that is, beyond the day-night cycle of the frequency of activity. Here, we study how the temporal connectivity of communication networks changes through the day, focusing on sequences of communication events that follow one another within a limited time. Such sequences can be thought to be characteristic of information transfer in the network. We find that temporal connectivity also follows a circadian rhythm, where at night a larger fraction of contacts is associated with such sequences and where contacts appear more independent at daytime. This result points out that temporal networks show richer variation in time than what has been known thus far.
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Affiliation(s)
- T Alakörkkö
- Department of Computer Science, Aalto University, 02150 Espoo, Finland
| | - J Saramäki
- Department of Computer Science, Aalto University, 02150 Espoo, Finland
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Satokangas I, Martin SH, Helanterä H, Saramäki J, Kulmuni J. Multi-locus interactions and the build-up of reproductive isolation. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190543. [PMID: 32654649 PMCID: PMC7423273 DOI: 10.1098/rstb.2019.0543] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 05/26/2020] [Indexed: 12/15/2022] Open
Abstract
All genes interact with other genes, and their additive effects and epistatic interactions affect an organism's phenotype and fitness. Recent theoretical and empirical work has advanced our understanding of the role of multi-locus interactions in speciation. However, relating different models to one another and to empirical observations is challenging. This review focuses on multi-locus interactions that lead to reproductive isolation (RI) through reduced hybrid fitness. We first review theoretical approaches and show how recent work incorporating a mechanistic understanding of multi-locus interactions recapitulates earlier models, but also makes novel predictions concerning the build-up of RI. These include high variance in the build-up rate of RI among taxa, the emergence of strong incompatibilities producing localized barriers to introgression, and an effect of population size on the build-up of RI. We then review recent experimental approaches to detect multi-locus interactions underlying RI using genomic data. We argue that future studies would benefit from overlapping methods like ancestry disequilibrium scans, genome scans of differentiation and analyses of hybrid gene expression. Finally, we highlight a need for further overlap between theoretical and empirical work, and approaches that predict what kind of patterns multi-locus interactions resulting in incompatibilities will leave in genome-wide polymorphism data. This article is part of the theme issue 'Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers'.
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Affiliation(s)
- I. Satokangas
- Organismal & Evolutionary Biology Research Programme, University of Helsinki, Viikinkaari 1, PO Box 65, 00014 Helsinki, Finland
| | - S. H. Martin
- Institute of Evolutionary Biology, University of Edinburgh, Ashworth Laboratories, Edinburgh EH9 3FL, UK
| | - H. Helanterä
- Ecology and Genetics research unit, University of Oulu, PO Box 3000, 90014 Oulu, Finland
| | - J. Saramäki
- Department of Computer Science, Aalto University, PO Box 11000, 00076 Aalto, Espoo, Finland
| | - J. Kulmuni
- Organismal & Evolutionary Biology Research Programme, University of Helsinki, Viikinkaari 1, PO Box 65, 00014 Helsinki, Finland
- Tvärminne Zoological Station, University of Helsinki, J. A. Palménin tie 260, 10900 Hanko, Finland
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Karsai M, Kivelä M, Pan RK, Kaski K, Kertész J, Barabási AL, Saramäki J. Small but slow world: how network topology and burstiness slow down spreading. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 83:025102. [PMID: 21405879 DOI: 10.1103/physreve.83.025102] [Citation(s) in RCA: 238] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2010] [Revised: 11/08/2010] [Indexed: 05/16/2023]
Abstract
While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible-infected model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.
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Affiliation(s)
- M Karsai
- BECS, School of Science and Technology, Aalto University, P.O. Box 12200, FI-00076, Finland.
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Toivonen R, Castelló X, Eguíluz VM, Saramäki J, Kaski K, San Miguel M. Broad lifetime distributions for ordering dynamics in complex networks. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:016109. [PMID: 19257109 DOI: 10.1103/physreve.79.016109] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2008] [Indexed: 05/27/2023]
Abstract
We search for conditions under which a characteristic time scale for ordering dynamics toward either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks with mesoscale community structure built up from randomly connected cliques. We find that large heterogeneity at the mesoscale level of the network appears to be a sufficient mechanism for the absence of a characteristic time for the dynamics. Such heterogeneity results in dynamical metastable states that survive at any time scale.
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Affiliation(s)
- R Toivonen
- Department of Biomedical Engineering and Computational Science (BECS), Helsinki University of Technology, FIN-02015 HUT, Finland.
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Onnela JP, Saramäki J, Hyvönen J, Szabó G, Lazer D, Kaski K, Kertész J, Barabási AL. Structure and tie strengths in mobile communication networks. Proc Natl Acad Sci U S A 2007; 104:7332-6. [PMID: 17456605 PMCID: PMC1863470 DOI: 10.1073/pnas.0610245104] [Citation(s) in RCA: 473] [Impact Index Per Article: 27.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2006] [Indexed: 11/18/2022] Open
Abstract
Electronic databases, from phone to e-mails logs, currently provide detailed records of human communication patterns, offering novel avenues to map and explore the structure of social and communication networks. Here we examine the communication patterns of millions of mobile phone users, allowing us to simultaneously study the local and the global structure of a society-wide communication network. We observe a coupling between interaction strengths and the network's local structure, with the counterintuitive consequence that social networks are robust to the removal of the strong ties but fall apart after a phase transition if the weak ties are removed. We show that this coupling significantly slows the diffusion process, resulting in dynamic trapping of information in communities and find that, when it comes to information diffusion, weak and strong ties are both simultaneously ineffective.
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Affiliation(s)
- J-P Onnela
- Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9203, FI-02015 TKK, Helsinki, Finland.
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