Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany

The effective reproductive number R$_t$ has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of R$_t$ may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates

<span style="font-size:15.0pt;mso-bidi-font-size: 14.0pt" lang="EN-GB">Low cost single-step purification of endoglucanase from <i style="mso-bidi-font-style:normal">Aspergillus fumigatus </i>ABK-9 </span>

954-959<span style="font-size: 9.0pt;mso-bidi-font-size:11.0pt" lang="EN-GB">Low cost agro-waste was used as adsorption support for single-step purification of endoglucanase from the culture filtrate of A. fumigatus ABK-9. Among various agro-waste substrates, 1% NaOH pretreated rice bran was proved to be the best for adsorbing about 74.8 and 71.1% of endoglucanase at 4 °C and 10 °C respectively. Langmuir type adsorption isotherm at 4 °C showed maximum adsorption of enzyme at pH 5.0, which was in the range of optimum pH of the enzyme. The rice bran column bound enzyme was maximally eluted by a mixture of acetate buffer (0.05 M, pH 5.5) and ethanol (40%, v/v) at a ratio of 3:2 and a flow rate of 1 mL/min. A 5.52-fold purification of the enzyme was achieved from culture supernatant. The specific activity and recovery yield after purification were <span style="mso-bidi-font-weight: bold">294.0 U/mg and 40.15%, respectively, which were comparable with other contemporary protocols. The homogeneity of the enzyme was tested through sodium dodecyl sulphate polyacrylamide gel electrophoresis and a single band of 56.3 kDa was observed. Zymogram analysis finally confirmed the occurrence of endoglucanase in the single band. </span

<span style="font-size:11.0pt;font-family: "Times New Roman","serif";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: Mangal;mso-ansi-language:EN-GB;mso-fareast-language:EN-US;mso-bidi-language: HI" lang="EN-GB">Keratinase production by <i>Bacillus weihenstephanensis</i> PKD5 in solid-state fermentation and its milk clotting potential</span>

200-207<span style="font-size:11.0pt;font-family: " times="" new="" roman","serif";mso-fareast-font-family:"times="" roman";mso-bidi-font-family:="" mangal;mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:="" hi"="" lang="EN-GB">A low cost and energy intensive solid-state fermentation medium was formulated by employing poultry feather for the production of keratinase by Bacillus weihenstephanensis PKD5 following ‘one variable at a time’ (OVAT) and response surface methodology (RSM). After OVAT optimization, four most critical factors were identified with significant increase of enzyme production (2.95-fold). Among them, incubation period, incubation temperature, pH and nitrogen source (ammonium chloride) were further optimized statistically by Box-Behnken RSM. The results of analysis of variance and regression of the second-order model of RSM showed that among the parameters, fermentation time (2.85 d), temperature (34.12<span style="font-size:11.0pt; font-family:Symbol;mso-ascii-font-family:" times="" new="" roman";mso-fareast-font-family:="" "times="" roman";mso-hansi-font-family:"times="" roman";mso-bidi-font-family:="" mangal;mso-ansi-language:en-gb;mso-fareast-language:en-us;mso-bidi-language:="" hi;mso-char-type:symbol;mso-symbol-font-family:symbol"="" lang="EN-GB">°C), pH (7.79) and ammonium chloride (0.5%) had the significant influences on keratinase production. Under the optimized conditions, a maximum enzyme production of 164.9 U/g was achieved, which was 3.17-fold higher. During further investigation on milk clotting property, the enzyme had shown the clotting activity of 43.6 SU/mL, suggesting its usefulness as new source of milk-coagulant for cheese making.</span

Synthesis and structure of iron (III) and iron (II) complexes in S₄P₂ environment created by diethyldithiocarbamate and 1,2-bis(diphenylphosphino)ethane chelation: Investigation of the electronic structure of the complexes by Mössbauer and magnetic studies

Iron (II) and iron (III) complexes, [FeII(DEDTC)2(dppe)] · CH2Cl2 (1), [FeII(ETXANT)2(dppe)] (2) (DEDTC = diethyldithiocarbamate, ETXANT = ethyl xanthate, dppe = 1,2-bis (diphenylphosphino) ethane), and [FeIII(DEDTC)2(dppe)] [FeIIICl4] (3) have been synthesized and characterized. Since 3 contains two magnetic centers, an anion metathesis reaction has been conducted to replace the tetrahedral FeCl4− by a non-magnetic BPh4− ion producing [FeIII(DEDTC)2(dppe)]BPh4 (4) for the sake of unequivocal understanding of the magnetic behavior of the cation of 3. With the similar end in view, the well-known FeCl4− ion, the counter anion of 3, is trapped as PPh4[FeIIICl4] (5) and its magnetic property from 298 to 2 K has been studied. Besides the spectroscopic (IR, UV–Vis, NMR, EPR, Mass and XPS) characterization of the appropriate compounds, especially 2, others viz. 1, 3 and 4 have been structurally characterized by X-ray crystallography. While FeII complexes, 1 and 2, are diamagnetic, the FeIII systems, namely the cations of 3, and 4 behave as low-spin (S = 1/2) paramagnetic species from 298 to 50 K. Below 50 K 3 shows gradual increase of χMT up to 2 K suggesting ferromagnetic behavior while 4 exhibits gradual decrease of magnetic moment from 60 to 2 K, indicating the occurrence of weak antiferromagnetic interaction. These conclusions are supported by the Mössbauer studies of 3 and 4. The Mössbauer pattern of 1 exhibits a doublet site for diamagnetic (2–400 K) FeII. The compounds 1, 2 and 4 encompass interesting cyclic voltammetric responses involving FeII, FeIII and FeIV

Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany.

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates

Comparison of uncertainty intervals after standardization of analytical choices.

The figure shows 95% uncertainty intervals corresponding to Fig 6, Step 4.</p