Geodesic
A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic
Amaury Lambert1, 2
1 Laboratoire de Probabilités, Statistique & Modélisation (LPSM), Sorbonne Université, CNRS UMR8001, Université de Paris, Paris, France.
2 Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR7241, INSERM U1050, PSL Research University, Paris, France.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 53 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic (A) or symptomatic (I), and use a contact tracing mobile phone application (Y ) or not (N). We denote by R0 the average number of secondary infections from a random infected individual. We investigate the effect of non-digital interventions (voluntary isolation upon symptom onset, quarantining private contacts) and of digital interventions (contact tracing thanks to the app), depending on the willingness to quarantine, parameterized by four cooperating probabilities. For a given ‘effective’ R0 obtained with non-digital interventions, we use non-negative matrix theory and stopping line techniques to characterize mathematically the minimal fraction y0 of app users needed to curb the epidemic, i.e., for the epidemic to die out with probability 1. We show that under a wide range of scenarios, the threshold y0 as a function of R0 rises steeply from 0 at R0 = 1 to prohibitively large values (of the order of 60−70% up) whenever R0 is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce R0 but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions.
DOI : 10.1051/mmnp/2021042

Amaury Lambert 1, 2

1 Laboratoire de Probabilités, Statistique & Modélisation (LPSM), Sorbonne Université, CNRS UMR8001, Université de Paris, Paris, France.
2 Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR7241, INSERM U1050, PSL Research University, Paris, France. 
@article{10_1051_mmnp_2021042,
     author = {Amaury Lambert},
     title = {A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the {COVID-19} epidemic},
     journal = {Mathematical modelling of natural phenomena},
     eid = {53},
     year = {2021},
     volume = {16},
     doi = {10.1051/mmnp/2021042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2021042/}
}
TY  - JOUR
AU  - Amaury Lambert
TI  - A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic
JO  - Mathematical modelling of natural phenomena
PY  - 2021
VL  - 16
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2021042/
DO  - 10.1051/mmnp/2021042
LA  - en
ID  - 10_1051_mmnp_2021042
ER  - 
%0 Journal Article
%A Amaury Lambert
%T A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic
%J Mathematical modelling of natural phenomena
%D 2021
%V 16
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2021042/
%R 10.1051/mmnp/2021042
%G en
%F 10_1051_mmnp_2021042
Amaury Lambert. A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 53. doi: 10.1051/mmnp/2021042

[1] Q. Bi, Y. Wu, S. Mei, C. Ye, X. Zou, Z. Zhang, X. Liu, L. Wei, S.A. Truelove, T. Zhang Epidemiology and transmission of COVID-19 in Shenzhen China: analysis of 391 cases and 1, 286 of their close contacts MedRxiv 2020

[2] B. Chauvin Product martingales and stopping lines for branching Brownian motion Ann. Probab 1991 1195 1205

[3] L. Ferretti, C. Wymant, M. Kendall, L. Zhao, A. Nurtay, L. Abeler-Dörner, M. Parker, D. Bonsall, C. Fraser Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing Science 2020

[4] C. Fraser, S. Riley, R.M. Anderson, N.M. Ferguson Factors that make an infectious disease outbreak controllable Proc. Natl. Acad. Sci 2004 6146 6151

[5] J. Hellewell, S. Abbott, A. Gimma, N.I. Bosse, C.I. Jarvis, T.W. Russell, J.D. Munday, A.J. Kucharski, W.J. Edmunds, F. Sun Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts Lancet Global Health 2020

[6] D. Klinkenberg, C. Fraser, H. Heesterbeek The effectiveness of contact tracing in emerging epidemics PloS one 2006

[7] E. Lavezzo, E. Franchin, C. Ciavarella, G. Cuomo-Dannenburg, L. Barzon, C. Del Vecchio, L. Rossi, R. Manganelli, A. Loregian, N. Navarin Suppression of a SARS-CoV-2 outbreak in the Italian municipality of vo Nature 2020 425 429

[8] M. Lv, X. Luo, J. Estill, Y. Liu, M. Ren, J. Wang, Q. Wang, S. Zhao, X. Wang, S. Yang Coronavirus disease (COVID-19): a scoping review Eurosurveillance 2020 2000125

[9] S. Ma, J. Zhang, M. Zeng, Q. Yun, W. Guo, Y. Zheng, S. Zhao, M.H. Wang, Z. Yang Epidemiological parameters of coronavirus disease 2019: a pooled analysis of publicly reported individual data of 1155 cases from seven countries medRxiv 2020

[10] K. Mizumoto, K. Kagaya, A. Zarebski, G. Chowell Estimating the asymptomatic proportion of coronavirusdisease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020 Eurosurveillance 2020 2000180

[11] C.J. Mode, Vol. 34 of Multitype branching processes: theory and applications. American Elsevier Pub. Co. (1971).

[12] H. Nishiura, T. Kobayashi, T. Miyama, A. Suzuki, S.-M. Jung, K. Hayashi, R. Kinoshita, Y. Yang, B. Yuan, A.R. Akhmetzhanov Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19) Int. J. Infectious Diseases 2020 154

[13] C.M. Peak, L.M. Childs, Y.H. Grad, C.O. Buckee Comparing nonpharmaceutical interventions for containing emerging epidemics Proc. Natl. Acad. Sci 2017 4023 4028

[14] H. Qian, T. Miao, L. Liu, X. Zheng, D. Luo, Y. Li Indoor transmission of SARS-CoV-2 Indoor Air 2021 639 645

[15] M. Salathé, M. Kazandjieva, J.W. Lee, P. Levis, M.W. Feldman, J.H. Jones A high-resolution human contact network for infectious disease transmission Proc. Natl. Acad. Sci 2010 22020 22025

[16] H. Salje, C.T. Kiem, N. Lefrancq, N. Courtejoie, P. Bosetti, J. Paireau, A. Andronico, N. Hozé, J. Richet, C.-L. Dubost Estimating the burden of SARS-CoV-2 in France Science 2020 208 211

[17] E. Yoneki, J. Crowcroft Epimap: Towards quantifying contact networks for understanding epidemiology in developing countries Ad Hoc Netw 2014 83 93

Cité par Sources :