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, 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 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.

中文翻译：

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非光滑凸优化估计 Covid-19 复制数时空演化，对低质量数据具有鲁棒性

日常大流行监测，通常通过估计繁殖数量来实现，对国家卫生当局设计对策构成了重大挑战。在早期的工作中，我们提出将再现数的估计公式化为一个优化问题，结合数据模型保真度和时空规律性约束，通过非光滑凸近端最小化来解决。尽管很有希望，但对于 Covid-19 数据的低质量（不相关或缺失的计数、伪季节性等）来说，虽然很有希望，但由于紧急情况和危机背景，这严重损害了准确的大流行演变评估。目前的工作旨在通过仔细制作功能许可来克服这些限制，以便在一个步骤中联合估计，为模拟低质量数据而定义的再现数和异常值。此功能还强制再现数估计的流行病学驱动的规律性属性，同时保持凸性，从而允许设计有效的最小化算法，基于分析得出的邻近算子。理论上证明了所提出算法的显式收敛性。其相关性通过真实的 Covid-19 数据进行量化，包括 200 多个国家和法国 96 个大都市县的每日新增感染人数，这些数据可在约翰霍普金斯大学和 Santé-Publique-France 公开获得。该程序允许通过动画和交互式地图报告这些估计值的自动每日更新。开源估算程序将公开发布。