Fig 1.
A demonstration of instantaneous reproduction number estimation by rtestim and the corresponding predicted incident cases.
The example is the Covid-19 epidemic in Canada during the period from January 23, 2020 to June 28, 2023. In the top panel, the blue curve is the estimated piecewise quadratic and the colorful ribbon is the corresponding 95% confidence band. The colors represent the variants whose serial interval distributions are used to estimate
. In the bottom panel, the black curve is the observed Covid-19 daily confirmed cases, and the orange curve on top of it is the predicted incident cases corresponding to the estimated
. The three vertical dashed lines represent the beginning of a new dominant variant.
Fig 2.
This figure displays example realizations for each setting.
Top row: the instantaneous reproduction numbers. Middle row: synthetic measles incidence (Poisson in blue, negative binomial in red) incidence. Bottom row: synthetic SARS incidence. The 4 scenarios are shown in the columns.
Fig 3.
Boxplot of mean KL divergence between and true
across 50 synthetic measles epidemics.
Performance of each approach given Poisson incidence is in top panels and negative binomial incidence is in bottom panels. The average excludes the first week in all settings, since EpiEstim with a weekly sliding window does not provide estimates for the first week. Outliers beyond 1.5 × IQR of each box are excluded for the sake of comparison with full range of the y-axis deferred to Fig A.3.1 in S1 Appendix.
Fig 4.
Boxplot of mean KL divergence between and true
across 50 synthetic SARS epidemics.
Performance of each approach given Poisson incidence is in top panels and negative binomial incidence is in bottom panels. The average excludes the first week in all settings, since EpiEstim with a weekly sliding window does not provide estimates for the first week. Outliers beyond 1.5 × IQR of each box are excluded for the sake of comparison with full range of the y-axis deferred to Fig A.3.1 in S1 Appendix.
Fig 5.
estimates for realizations of a measles epidemic with Poisson observations.
An expanded visualization with each estimated curve displayed in a separate panel is provided in Fig A.6.1 in S1 Appendix.
Fig 6.
estimates for realizations of a SARS epidemic with negative binomial observations.
An expanded visualization with each estimated curve displayed in a separate panel is provided in Fig A.6.4 in S1 Appendix.
Fig 7.
Estimated instantaneous reproduction number based on Covid-19 daily confirmed incident cases.
The epidemic is between January 23rd, 2020 and June 28th, 2023 in Canada. The left panels show estimates corresponding to 50 tuning parameters. The right panels show the CV-tuned estimate along with approximate 95% confidence bands. The top, middle and bottom panels show the estimated using the Poisson trend filtering in Eq (5) with degrees k = 1, 2, 3 respectively. All estimates use a constant serial interval distribution, which is the weighted sum of probabilities of the 4 dominant variants used in Fig 1.
Fig 8.
Daily incident influenza cases in Baltimore, Maryland between September and November 1918.
Fig 9.
Estimated instantaneous reproduction numbers for influenza in Baltimore, Maryland in 1918.
The left panels show estimates for a set of 50 tuning parameters. The right column displays the CV-tuned estimates with approximate 95% confidence bands. The rows (top to bottom) show using Poisson trend filtering with k = 1, 2, 3 respectively.