Math. Model. Nat. Phenom.
Volume 16, 2021
Coronavirus: Scientific insights and societal aspects
|Number of page(s)||23|
|Published online||05 October 2021|
A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic
Laboratoire de Probabilités, Statistique & Modélisation (LPSM), Sorbonne Université, CNRS UMR8001, Université de Paris,
2 Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS UMR7241, INSERM U1050, PSL Research University, Paris, France.
* Corresponding author: email@example.com
Accepted: 24 July 2021
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.
Mathematics Subject Classification: 92D30 / 60J80 / 60J85 / 91A12 / 91D30
Key words: Multitype branching process / leading eigenvalue / stopping line / epidemiology / personal data
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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