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 mon- itoring 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 observa- tions. The novelty of the proposed approach is twofold: 1) the estimation of the repro- duction 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: Spatial and temporal regularization to estimate COVID-19 Reproduction Number R(t): Promoting piecewise smoothness via convex optimization. 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.