Mathematical basis for the assessment of antibiotic resistance and administrative counter-strategies

Diebner, Hans H.; Kather, Anna; Roeder, Ingo

doi:10.1371/journal.pone.0238692

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…For details on interpreting the diversity function, confer [ 38 ], and for an analogous application within an epidemiological context, see [ 39 ]. Briefly, for a given age class a at time point t , equal incidences over all counties give maximum entropy, hence maximum diversity

.…”

Section: Materials and Methodsmentioning

confidence: 99%

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

Diebner

2023

Entropy

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Results from an explorative study revealing spatio-temporal patterns of the SARS-CoV-2/ COVID-19 epidemic in Germany are presented. We dispense with contestable model assumptions and show the intrinsic spatio-temporal patterns of the epidemic dynamics. The analysis is based on COVID-19 incidence data, which are age-stratified and spatially resolved at the county level, provided by the Federal Government’s Public Health Institute of Germany (RKI) for public use. Although the 400 county-related incidence time series shows enormous heterogeneity, both with respect to temporal features as well as spatial distributions, the counties’ incidence curves organise into well-distinguished clusters that coincide with East and West Germany. The analysis is based on dimensionality reduction, multidimensional scaling, network analysis, and diversity measures. Dynamical changes are captured by means of difference-in-difference methods, which are related to fold changes of the effective reproduction numbers. The age-related dynamical patterns suggest a considerably stronger impact of children, adolescents and seniors on the epidemic activity than previously expected. Besides these concrete interpretations, the work mainly aims at providing an atlas for spatio-temporal patterns of the epidemic, which serves as a basis to be further explored with the expertise of different disciplines, particularly sociology and policy makers. The study should also be understood as a methodological contribution to getting a handle on the unusual complexity of the COVID-19 pandemic.

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.…”

Section: Materials and Methodsmentioning

confidence: 99%

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

Diebner

2023

Entropy

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“…However, Shannon entropy and the related Kullback–Leibler divergence, which serve as a basis for mutual information, tend to discriminate small differences relatively less in favour of discriminating larger differences of the two time series (cf. [ 26 ]).…”

Section: Methodsmentioning

confidence: 99%

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

Diebner

Timmesfeld

2021

Infectious Disease Reports

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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.

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“…For details on interpreting the diversity function, confer [38], and for an analogous application within an epidemiological context, see [39]. Briefly, for a given age class a at time point t, equal incidences over all counties give maximum entropy, hence maximum diversity D(a, t) = 1.…”

Section: Spatial Heterogeneitymentioning

confidence: 99%

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

Diebner¹

2023

Preprint

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Results from an explorative study revealing spatio-temporal patterns of the SARS-CoV-2/COVID-19 epidemic in Germany are presented. We dispense with contestable model assumptions and show the intrinsic spatio-temporal patterns of the epidemic dynamics. The analysis is based on COVID-19 incidence data, which are age-stratified and spatially resolved at the county level, provided by the Federal Government’s Public Health Institute of Germany (RKI) for public use. Although the 400 county-related incidence time series show enormous heterogeneity both with respect to temporal features as well as spatial distributions, the counties’ incidence curves organise into well distinguished clusters that coincide with East and West Germany. The analysis is based on dimensionality reduction, multidimensional scaling, network analysis, and diversity measures. Dynamical changes are captured by means of difference-in-difference methods which are related to fold changes of the effective reproduction numbers. The age-related dynamical patterns suggest a considerably stronger impact of children, adolescents and seniors on the epidemic activity than previously expected. Besides these concrete interpretations, the work mainly aims at providing an atlas for spatio-temporal patterns of the epidemic which serves as a basis to be further explored with the expertise from different disciplines, particularly sociology and policy makers. The study should also be understood as a methodological contribution to getting a handle on the unusual complexity of the COVID-19 pandemic.

show abstract

Mathematical basis for the assessment of antibiotic resistance and administrative counter-strategies

Cited by 4 publications

References 24 publications

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

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

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

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

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