There are currently intensified efforts by the scientific community world-wide to analyze the dynamics of the Covid-19 pandemic in order to predict key epidemiological effects and assist the proper planning for its clinical management, as well as guide sociopolitical decision-making regarding proper mitigation measures. Most efforts follow variants of the established SIR methodological framework that divides a population into “Susceptible”, “Infectious” and “Recovered/Removed” fractions and defines their dynamic inter-relationships with first-order differential equations. Goal: This paper proposes a novel approach based on data-guided detection and concatenation of infection waves – each of them described by a Riccati equation with adaptively estimated parameters. Methods: This approach was applied to Covid-19 daily time-series data of US confirmed cases, resulting in the decomposition of the epidemic time-course into five “Riccati modules” representing major infection waves to date (June 18th). Results: Four waves have passed the time-point of peak infection rate, with the fifth expected to peak on July 20th. The obtained parameter estimates indicate gradual reduction of infectivity rate, although the latest wave is expected to be the largest. Conclusions: This analysis suggests that, if no new waves of infection emerge, the Covid-19 epidemic will be controlled in the US (<5000 new daily cases) by September 26th, and the maximum of confirmed cases will reach 4,160,000. Importantly, this approach can be used to detect (via rigorous statistical methods) the emergence of possible new waves of infections in the future. Analysis of data from individual states or countries may quantify the distinct effects of different mitigation measures.

中文翻译：

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美国 Covid-19 数据的预测建模：自适应相空间方法

目前，全世界的科学界都在加紧努力，分析 Covid-19 大流行的动态，以预测关键的流行病学影响，协助对其临床管理进行适当规划，并指导有关适当缓解措施的社会政治决策措施。大多数努力都遵循已建立的 SIR 方法框架的变体，该框架将人群分为“易感”、“传染”和“恢复/移除”部分，并用一阶微分方程定义它们的动态相互关系。目标：本文提出了一种基于数据引导检测和感染波串联的新方法——每个感染波都由具有自适应估计参数的 Riccati 方程描述。方法：该方法应用于美国确诊病例的 Covid-19 每日时间序列数据，导致将流行病时间过程分解为五个“Riccati 模块”，代表迄今为止（6 月 18 日）的主要感染浪潮。结果：已经有四波感染高峰时间点过去了，第五波预计在7月20日达到高峰。获得的参数估计表明传染率逐渐降低，尽管预计最新一波是最大的。结论：该分析表明，如果不出现新的感染浪潮，到 9 月 26 日，Covid-19 疫情将在美国得到控制（每日新增病例<5000 例），确诊病例最多将达到 416 万例。重要的是，这种方法可用于检测（通过严格的统计方法）未来可能出现的新一波感染。来自个别州或国家的数据分析可以量化不同缓解措施的不同影响。