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

Publication by Laboratoire de physique and IXXI, in MedRxiv on June 15, 2020.

Abstract: 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 counties and their joint analysis, leading to dynamic maps revealing the temporal co-evolution of their reproduction numbers.

Source: . Patrice Abry, Nelly Pustelnik, Stéphane Roux, Pablo Jensen, Patrick Flandrin, Rémi Gribonval, Charles G. Lucas, Eric Guichard, Pierre Borgnat, Nicolas Garnier, Benjamin Audit. MedRxiv, June 15, 2020.

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