Journal Article

Spatial and temporal regularization to estimate COVID-19 reproduction number R(t): Promoting piecewise smoothness via convex optimization

Gribonval, Rémi, Flandrin, Patrick, Borgnat, Pierre, Garnier, Nicolas, Roux, Stéphane, Jensen, Pablo, Guichard, Éric, Abry, Patrice, Lucas, Charles-Gérard, Pustelnik, Nelly

2020

Overview

Among the different indicators that quantify the spread of an epidemic such as the on-going COVID-19, stands first the reproduction number which measures how many people can be contaminated by an infected person. In order to permit the monitoring of the evolution of this number, a new estimation procedure is proposed here, assuming a well-accepted model for current incidence data, based on past observations. The novelty of the proposed approach is twofold: 1) the estimation of the reproduction number is achieved by convex optimization within a proximal-based inverse problem formulation, with constraints aimed at promoting piecewise smoothness; 2) the approach is developed in a multivariate setting, allowing for the simultaneous handling of multiple time series attached to different geographical regions, together with a spatial (graph-based) regularization of their evolutions in time. The effectiveness of the approach is first supported by simulations, and two main applications to real COVID-19 data are then discussed. The first one refers to the comparative evolution of the reproduction number for a number of countries, while the second one focuses on French departments and their joint analysis, leading to dynamic maps revealing the temporal co-evolution of their reproduction numbers.

• Publisher: Public Library of Science,Public Library of Science (PLoS)
• Subject: Algorithms / Betacoronavirus / Computer and Information Sciences / Computer Science / Computer simulation / Convex analysis / Convexity / Coronavirus Infections - epidemiology / Coronavirus Infections - transmission / Coronavirus Infections - virology / Coronaviruses / COVID-19 / Databases, Factual / Disease transmission / Disease Transmission, Infectious - statistics & numerical data / Earth Sciences / Engineering and Technology / Epidemics / Evolution / France / France - epidemiology / Humans / Inverse problems / Medical supplies / Medicine and Health Sciences / Methods / Models, Statistical / Optimization / Pandemics / Parameter estimation / People and places / Physical Sciences / Pneumonia, Viral - epidemiology / Pneumonia, Viral - transmission / Pneumonia, Viral - virology / Poisson Distribution / Regularization / Reproduction / Research and Analysis Methods / Risk factors / SARS-CoV-2 / Sentinel surveillance / Signal and Image Processing / Smoothness / Software / Spatio-Temporal Analysis / Statistics