2018.06.18 A. Lambert & E. Scherzte - Probabilistic models related to the SARS-CoV-2 pandemic
Channel: One World Probability
Date: 2020-06-18

In this talk, we will discuss three projects initiated by the SMILE
group (Collège de France/Sorbonne Université) during the SARS-CoV-2 pandemic.
(1) We will present Alcov2, a large-scale survey to study the transmission of
SARS-CoV-2 within French households. In particular, we will show how to use
micro-epidemic models (at the household level) to extract precise estimates on
various epidemiological parameters (fraction of asymptomatics, probability of
transmission within households).
(2) We will study a model where infected individuals can be symptomatic or
asymptomatic, use a contact tracing mobile app or not. 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. We 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.
(3) We will present a general and tractable framework for modeling and
"nowcasting" the epidemic at a national scale.  Our approach is based on a
fairly general stochastic model at the individual level capturing the main
features of the epidemic (presence of asymptomatics, large heterogeneity in
the population etc.). We show that despite the underlying complexity of our
microscopic model, the global scale of the epidemic (i.e., when the number of
infected gets large) is well captured by a deterministic McKendrick—Van
Foerster 1-d PDE, and that such an approximation allows us to make robust
predictions on the fate of the epidemic. Finally, we will discuss the effect
of stochasticity by means of Central Limit Theorems. From a practical point of
view, such approach aims at quantifying the uncertainty of various lockdown
strategies, e.g., can we predict the fate of the epidemics (death toll etc.)
if populations are re-confined after recording x number of deaths,
hospitalized etc.? Finally, and if time permits, we will discuss some spatial
aspects of the epidemics.