Submitted to ArXiv on 6 May 2020

As humanity struggles to contain the global Covid-19 infection, prophylactic actions are grandly slowed down by the shortage of testing kits. Governments have taken several measures to work around this shortage: the FDA has become more liberal on the approval of Covid-19 tests in the US. In the UK emergency measures allowed to increase the daily number of locally produced test kits to 100,000. China has recently launched a massive test manufacturing program. However, all those efforts are very insufficient and many poor countries are still under threat. A popular method for reducing the number of tests consists in pooling samples, i.e. mixing patient samples and testing the mixed samples once. If all the samples are negative, pooling succeeds at a unitary cost. However, if a single sample is positive, failure does not indicate which patient is infected. This paper describes how to optimally detect infected patients in pools, i.e. using a minimal number of tests to precisely identify them, given the a priori probabilities that each of the patients is healthy. Those probabilities can be estimated using questionnaires, supervised machine learning or clinical examinations. The resulting algorithms, which can be interpreted as informed divide-and-conquer strategies, are non-intuitive and quite surprising. They are patent-free. Co-authors are listed in alphabetical order.​

Submitted to ArXiv on 14 May 2020

Sample pooling consists in combining samples from multiple individuals into a single pool that is then tested using a unique test-kit. A positive test means that at least one individual within the pool is infected. Here, we propose an analysis and applications of sample pooling to the epidemiologic monitoring of COVID-19. We first introduce a model of the RT-qPCR process used to test for the presence of virus in a sample and construct a statistical model for the viral load in a typical infected individual inspired by the clinical data from Jones et. al. (2020). We then propose a method for the measure of the prevalence in a population, based on group testing, taking into account the increased number of false negatives associated with this method. Finally, we present an application of sample pooling for the prevention of epidemic outbreak in closed connected communities (e.g. nursing homes).

9 April 2020

Now that a large part of the world’ population is in lockdown to fight against the global spread of the new coronavirus, the crucial question is: What’s next? As lock-down measures will progressively be lifted, the key to avoid second and third waves of the pandemics will be massive and rapid testing, combined with case tracking and targeted quarantining. Unfortunately, the testing capacity of most countries is currently not nearly enough.

Des compétences en mathématiques et en informatique mises d’une gestion optimisée des stocks de tests de dépistage:

Professeur, spécialiste de la sécurité informatique à l’ENS-PSL, David Naccache s’est engagé dans la lutte contre le Covid-19 enDes compétences en mathématiques et en informatique mises d’une gestion optimisée des stocks de tests de dépistage mobilisant au pied levé une équipe de chercheurs et de normaliens en informatique et mathématiques. En combinant algorithmes et techniques de group testing développées par Robert Dorfman dans les années 40, ces informaticiens et mathématiciens sont parvenus à proposer une méthode de contrôle de la pandémie moins gourmande en tests.
Déjà déployée dans plusieurs pays, elle a permis de réduire par 3 à 4 le nombre de tests nécessaires pour une population. Elle est particulièrement précieuse à l’heure où la pandémie touche indifféremment pays développés et pays pauvres.

Submitted to BioRxiv 13 April 2020

Am J Clin Pathol. 18​ Apr 2020; XX:1–4

Journal of Clinical Virology, 104382. 23 April 2020

Clinical Infectious Diseases, 2 May 2020

Submitted to MedRxiv on 7 May 2020

Submitted to ArXiv 3 June 2020

Submitted to MedRxiv 11 June 2020

Submitted to MedRxiv 3 July 2020

Submitted to ArXiv 22 July 2020

Submitted to ArXiv 27 July 2020