Description of historic epidemic data analyzed.

Description of historic epidemic data analyzed.</p

Comparison of estimating real-time transmission dynamics of the COVID-19 epidemic between Jan 23, 2020 and Apri 5, 2021, in Hongkong, China.

Transmission dynamics (i.e., reproduction number R and dispersion number k) were assumed constant over a window of 14 days, and the estimates were obtained by analyzing the incidence data of the time window. Solid lines show the mean estimates from two methods. Red curves and blue curves represent the estimation from the instant-individual heterogeneity model (IIH) and the instant-level heterogeneity (ILH) model respectively. The shaded areas show the 95% high probability density (HPD) intervals. A: Incidence data of the confirmed cases and government stringency data in South Africa; B: Estimation of reproduction number (Rt); C: Estimation of dispersion number (kt).</p

Comparison of estimating transmission dynamics of three epidemics with the instant-individual heterogeneity (IIH) model and the instant-level heterogeneity (ILH) model in [22].

During each epidemic, transmission dynamics (i.e., reproduction number R and dispersion number k) were assumed constant. Colored areas showed the posteriors of the estimates by analyzing incidence times series. Black solid lines represented the estimates in literatures obtained by analyzing the contact tracing data of these epidemics [10, 33, 34]. A: Estimation of reproduction number (R); B: Estimation of dispersion number (k).</p

Further details on the simulation study and analysis of real epidemic datasets.

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Estimation of real-time transmission dynamics of the COVID-19 epidemic between 2021-05-01 and 2022-01-09 in South Africa.

Transmission dynamics (i.e., reproduction number R and dispersion number k) were assumed constant over a window of 7 days, and the estimates were obtained by analyzing the incidence data of the time window. Solid lines show the mean estimates and the shaded areas show the 95% high probability density (HPD) intervals. A: Incidence data of the confirmed cases and government stringency data in South Africa; B: Estimation of reproduction number (Rt); C: Estimation of dispersion number (kt).</p

Accuracy of the instant-individual heterogeneity model in estimating transmission dynamics with simulated data.

Incidence data were generated with the instant-individual heterogeneity model (4) with given reproduction number and dispersion number. Each simulation began with 10 cases and stopped at 24 days. The relative MADs and the coverage of 95% high probability density interval were calculated for the estimation of reproduction number R and dispersion number k respectively. The probability of identification (defined in the section of methods) was also calculated for the estimation of dispersion number k. A, B, and C. Estimation with daily reported incidence data of different time lengths, i.e., window size = 7 days (A), 14 days (B), and 21 days (C); D. Estimation with irregularly reported incidence data, where the incidence data were generated every day or every three days iteratively.</p

Effects of underreporting rates and misspecification of the serial interval on estimating transmission dynamics with the instant-individual heterogeneity model.

Synthetic data incorporating missing cases were generated on the basis of the incidence data from the Ebola epidemic between Aug 04, 2014 (week 36), and March 29, 2015 (week 13), in the capital Freetown of Sierra Leone. Colored lines show the mean estimates and the shaded areas show the 95% high probability density intervals under the true values. A and B: Estimation under different reporting rates (ρ). Dashed lines represent the estimates under the scenario with time-varying reporting rate. C and D: Estimation from different specification of the serial interval mean (μSI); E and F: Estimation from different specification of the serial interval standard deviation (σSI).</p

Comparison of estimating real-time transmission dynamics of the COVID-19 epidemic between March 1, 2020 and May 3, 2020, in five counties of Georgia state, USA.

Transmission dynamics (i.e., reproduction number R and dispersion number k) were assumed constant over a window of 7 days, and the estimates were obtained by analyzing the incidence data of the time window. Solid lines show the mean estimates from two methods, i.e., red curves and blue curves represent the estimation from the instant-individual heterogeneity model (IIH) and the instant-level heterogeneity (ILH) model respectively. The shaded areas show the 95% high probability density (HPD) intervals. As in [9], the reference time was set as April 3rd, 2021 when the shelter-in-place order was announced. The whole study period was divided into three periods, i.e., before April 3rd, between April 3rd and April 17th, after April 17th. A: Incidence data of the confirmed and probable cases; B: Estimation of reproduction number (Rt); C: Estimation of dispersion number (kt).</p

Comparison of estimating real-time transmission dynamics of the Ebola epidemic between Aug 04, 2014 (week 36), and March 29, 2015 (week 13), in the capital Freetown of Sierra Leone.

Transmission dynamics (i.e., reproduction number R and dispersion number k) were assumed constant over a window of 7 weeks, and the estimates were obtained by analyzing the incidence data of the time window. Solid lines show the mean estimates from two methods. Red curves and blue curves represent the estimation from the instant-individual heterogeneity model (IIH) and the instant-level heterogeneity (ILH) model respectively. The shaded areas show the 95% high probability density (HPD) intervals. As in [16], the reference time tref was set as 2014-11-01, and the whole time period was divided into five periods as: from 2014-10-20 to tref (period 1), tref to tref +20 days (period 2), tref +20 days to tref +50 days (period 3), tref + 50 days to tref + 100 days (period 4), and thereafter (period 5).A: Incidence data of the confirmed and probable cases; B: Estimation of reproduction number (Rt); C: Estimation of dispersion number (kt).</p

Synergetic Extraction of Phytic Acid from HCl Extract of Rapeseed Meal with Alamine 336 and <i>n</i>-Octanol Dissolved in Sulfonated Kerosene

Extraction of phytic acid from HCl extract of rapeseed meal using Alamine 336/n-octanol/sulfonated kerosene was investigated. The results showed that the addition of n-octanol can significantly enhance the extraction of phytic acid by Alamine 336/sulfonated kerosene, indicating the synergetic effect between Alamine 336 and n-octanol. The key affecting factors of the extraction include pH and the concentration of the extractants, whose effects on the distribution ratio were quantitatively analyzed. Phytic acid extracted into the organic solutions can be well strip extracted back by using a dilute NaOH solution. At the optimum operating conditions, the extraction efficiency from a 0.03 mol/L phytic acid solution can reach 85.4%, and the corresponding single strip-extraction efficiency is 74.6%, while the total strip-extraction efficiency after three strip extractions can reach 96.4%