Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Nonparametric Methods

Abstract

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.

Spatio-Temporal Patterns of the SARS-CoV-2 Epidemic in Germany

“…Taken together, we try to provide as comprehensive a picture of the complexity of the pandemic as possible, using only available incidence data. Some facets of the complexity of the COVID-19 epidemic have been published recently [23,24] and we ask the readers to combine these previous results mainly focusing on temporal features with the new findings presented here, which put more emphasis on spatial patterns.…”

“…Broadly speaking, the work provides a kind of atlas for spatio-temporal patterns of the epidemic, which now need to be interpreted with expertise from different disciplines. We encourage readers to combine the results presented here with those in [23,24] to obtain an even more comprehensive picture on COVID-19 pandemic dynamics. In particular, we urge sociologists and policy makers to associate the observed processes of change with both sociocultural characteristics of individual regions and local policy-making processes.…”

Study of the Deep Processes of COVID-19 in Russia: Finding Ways to Identify Preventive Measures

“…The dynamics of the ratio of daily new COVID-19 deaths to daily new infections from day 430 to day 650 of the pandemic in Russia also support this. An essential element of the epidemic process is the ratio of daily new cases of COVID-19 infection to daily new fatalities because it can indicate the severity of the illness and, indirectly, the efficacy of preventive efforts [ 27 ].…”

Application of distributed lag models and spatial analysis for comparing the performance of the COVID-19 control decisions in European countries

“…In present study the Distributed Lag Model (DLM) was used for predicting future deaths according to the daily number of new cases in previous days. Also, this model could be estimating both important indices: the mean delay and AFR of COVID-19 in socio-economic and epidemiological studies 21 , 22 . So, the interest of this study is to estimate the mean delay and AFR of COVID-19 among European countries and their spatial distributions with new application of DLMs that anticipate the delay effect of the number of COVID-19 cases on fatality rate.…”