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

TL;DR

This paper introduces a robust convex optimization method to accurately estimate Covid-19 reproduction numbers from low-quality data, incorporating outlier detection and epidemiological regularity, with proven convergence and real-world application.

Contribution

It develops a novel convex functional that jointly estimates reproduction numbers and outliers, improving robustness against data issues in pandemic surveillance.

Findings

Effective estimation of reproduction numbers across 200+ countries and French counties.

Algorithm convergence is theoretically proven.

Open-source tools for automated daily updates are provided.

Abstract

Daily pandemic surveillance, often achieved through the estimation of the reproduction number, constitutes a critical challenge for national health authorities to design countermeasures. 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, pseudo-seasonalities,.. .) 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 Sant{\'e}-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.