Diebner Hans H, Timmesfeld Nina
Biometry and Epidemiology, Department of Medical Informatics, Ruhr-Universität Bochum, 44780 Bochum, Germany.
Infect Dis Rep. 2021 Apr 1;13(2):302-328. doi: 10.3390/idr13020031.
Containment strategies to combat epidemics such as SARS-CoV-2/COVID-19 require the availability of epidemiological parameters, e.g., the effective reproduction number. Parametric models such as the commonly used susceptible-infected-removed (SIR) compartment models fitted to observed incidence time series have limitations due to the time-dependency of the parameters. Furthermore, fatalities are delayed with respect to the counts of new cases, and the reproduction cycle leads to periodic patterns in incidence time series. Therefore, based on comprehensible nonparametric methods including time-delay correlation analyses, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented using publicly available time-series data on prevalence and fatalities. The estimates for Germany are compared with the results for seven other countries (France, Italy, the United States of America, the United Kingdom, Spain, Switzerland, and Brazil). The duration from diagnosis to death resulting from delay-time correlations turns out to be 13 days with high accuracy for Germany and Switzerland. For the other countries, the time-to-death durations have wider confidence intervals. With respect to the German data, the two time series of new cases and fatalities exhibit a strong coherence. Based on the time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated. The temporal median of the instantaneous fatality-case ratio with time lag of 13 days between cases and deaths for Germany turns out to be 0.02. Time courses of asymptotic fatality-case ratios are presented for other countries, which substantially differ during the first half of the pandemic but converge to a narrow range with standard deviation 0.0057 and mean 0.024. Similar results are obtained from comparing time courses of instantaneous fatality-case ratios with optimal delay for the 8 exemplarily chosen countries. The basic reproduction number, R0, for Germany is estimated to be between 2.4 and 3.4 depending on the generation time, which is estimated based on a delay autocorrelation analysis. Resonances at about 4 days and 7 days are observed, partially attributable to weekly periodicity of sampling. The instantaneous (time-dependent) reproduction number is estimated from the incident (counts of new) cases, thus allowing us to infer the temporal behaviour of the reproduction number during the epidemic course. The time course of the reproduction number turns out to be consistent with the time-dependent per capita growth.
对抗诸如SARS-CoV-2/COVID-19等流行病的防控策略需要流行病学参数，例如有效繁殖数。参数模型，如常用的易感染-感染-移除（SIR） compartment模型，拟合观察到的发病时间序列时存在局限性，因为参数具有时间依赖性。此外，死亡人数相对于新病例数存在延迟，并且繁殖周期导致发病时间序列出现周期性模式。因此，基于包括时间延迟相关分析在内的可理解的非参数方法，利用公开可用的患病率和死亡人数时间序列数据，给出了以德国疫情为重点的表征COVID-19大流行的关键参数估计值。将德国的估计值与其他七个国家（法国、意大利、美利坚合众国、英国、西班牙、瑞士和巴西）的结果进行了比较。通过延迟时间相关性得出的德国和瑞士从诊断到死亡的持续时间被证明具有13天的高精度。对于其他国家，死亡时间持续时间的置信区间更宽。就德国的数据而言，新病例和死亡人数的两个时间序列表现出很强的相关性。基于诊断和死亡之间的时间滞后，计算了适当延迟的渐近以及即时病死率。德国病例和死亡之间时间滞后为13天的即时病死率的时间中位数被证明为0.02。给出了其他国家渐近病死率的时间进程，在大流行的前半期有很大差异，但收敛到一个标准差为0.0057、均值为0.024的狭窄范围。通过比较8个示例性选择国家的即时病死率与最佳延迟的时间进程也得到了类似结果。根据代时估计，德国的基本繁殖数R0估计在2.4到3.4之间，代时是基于延迟自相关分析估计的。观察到大约4天和7天的共振，部分归因于采样的每周周期性。从新发病例数估计即时（时间相关）繁殖数，从而使我们能够推断疫情过程中繁殖数的时间行为。繁殖数的时间进程被证明与时间相关的人均增长率一致。
