Nonsmooth convex optimization to estimate the Covid-19 reproduction number space-time evolution with robustness against low quality data

Abstract

Daily pandemic surveillance, often achieved through the estimation of the reproduction number, constitutes a critical challenge for national health authorities to design counter-measures. In an earlier work, we proposed to formulate the estimation of the reproduction number as an optimization problem, combining data-model fidelity and space-time regularity constraints, solved by nonsmooth convex proximal minimizations. Though promising, that first formulation significantly lacks robustness against the Covid-19 data low quality (irrelevant or missing counts, pseudoseasonalities,. . . ) stemming from the emergency and crisis context, which significantly impairs accurate pandemic evolution assessments. The present work aims to overcome these limitations by carefully crafting a functional permitting to estimate jointly, in a single step, the reproduction number and outliers defined to model low quality data. This functional also enforces epidemiology-driven regularity properties for the reproduction number estimates, while preserving convexity, thus permitting the design of efficient minimization algorithms, based on proximity operators that are derived analytically. The explicit convergence of the proposed algorithm is proven theoretically. Its relevance is quantified on real Covid-19 data, consisting of daily new infection counts for 200+ countries and for the 96 metropolitan France counties, publicly available at Johns Hopkins University and Santé-Publique-France. The procedure permits automated daily updates of these estimates, reported via animated and interactive maps. Open-source estimation procedures will be made publicly available..

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

“…Many papers dedicated to the computation of R t use this model, for example [32][33][34], who also assume that R t is a Poisson variable, and [35] who also assume that R t also is a random variable following a Gamma distribution. In [36], the authors use the stochastic form of the renewal Equation (13) where they call Φ s causal serial interval. Then R t is estimated jointly on all regions of a country by a variational model containing a spatial total variation regularization to ensure that R t is piecewise constant, and the L 1 norm of its time Laplacian to ensure time regularity.…”

Modeling Covid-19 incidence by the renewal equation after removal of administrative bias and noise

“…Many papers dedicated to the computation of R t use this model, for example [32], [33] and [34], who also assume that R t is a Poisson variable, and [35] who also assume that R t also is a random variable following a Gamma distribution. In [36], the authors use the stochastic form of the renewal equation (13) where they call Φ s causal serial interval. Then R t is estimated jointly on all regions of a country by a variational model containing a spatial total variation regularization to ensure that R t is piecewise constant, and the L 1 norm of its time Laplacian to ensure time regularity.…”