IEEE Computational Intelligence Magazine - November 2020 - 30

We observed that the ground-truth Rt is well estimated
within our confidence interval. In particular, the sharp
change of Rt caused by the intervention is captured
immediately by our approach while there is a lag
using the sliding window-based method.
suppression and mitigation factors, respectively. The results are
demonstrated in Table 1.
VI. Results
A. Validation with Simulated Data

We simulated an artificial epidemic outbreak with a time-varying infectiousness profile using the renewal process. The generation time intervals were adapted from Ferretti et al. [5]. The
simulation period includes 50 days, and an intensive intervention measure is induced on day 35 altering the transmission
dynamics. Before the intervention, the ground-truth R t followed Gaussian random walk with a mean of 2.5. After the
intervention (50% p t reduction and 67% D t reduction), the
mean of R t was reduced to 0.5 (black line).
We validate the effectiveness of our approach in capturing
the sudden change of R t evolution induced by interventions,
which is difficult to detect using traditional sliding windowbased methods (Figure 5). We compared the results using our
approach (red line with 95% confidence intervals) to the results
computed by the R package 'EpiEstim v2.2' [11] (blue) which
is a sliding window-based method widely used for R t estimation. We observed that the ground-truth R t is well estimated
within our confidence interval. In particular, the sharp change
of R t caused by the intervention is captured immediately by

our approach while there is a lag using the
sliding window-based method.
B. Evaluation of Intervention
Measures in Europe

In this part, we applied the proposed framework to analyze the epidemic evolution in the
14 European Countries and also Wuhan. With
the inferred , we can then assess
the impacts of intervention measures.
Figure 6 demonstrates the reconstruction of daily infections
in the UK from the reported confirmed cases. The infected-toreport delay between report and infected time is composed of
the incubation period (a lognormal distribution with a mean of
5.5 days and a standard deviation of 2.1 days [5]) and the onsetto-report period (a gamma distribution with a mean of 4.9
days and a standard deviation of 3.3 days [10]). The blue bars in
Figure 6 indicate the numbers of confirmed cases. After deconvolving the confirmed numbers using infected-to-report delay,
we obtained the infection curve (curve of estimated daily
infected instances), which is colored in red in Figure 6. To
check the reliability of the deconvolution results, we convolve
the inferred infection curve (in red) with the infected-toreport delay to recover the confirmed curve (in black). We can
see that the black curve matches well to the original blue bars,
and is much smoother. With the above observation, we can see
the effectiveness of the infection curve inference. Figure 7
shows the results of estimating R t of the UK from the infection curve. The missing values in the infection curve are
replaced by the average mean of the neighboring numbers. The
green bar is the posterior mean of estimated R t .
To quantitatively show the impacts of different strength levels of interventions, Table 1 summarizes the statistical analysis

10,000

United Kingdom
Confirmed Cases
Deconvoluted
Recovered

9,000

3
2.5
2

6,000
5,000
4,000

2,000
0

0.5
10

30
Days

FIGURE 5 Validation of the proposed Bayesian updating scheme on
simulated data with intensive intervention measure.

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2020

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1,000

7,000

3,000

1.5

8,000

Cases

Ground-Truth
EpiEstim
Proposed
95% CI

3.5

Date
FIGURE 6 Reconstruction of daily infections from the report of confirmed cases in UK. The forward convolution on reconstructed data
(black line) matches well with actual reported data (blue bars), validating the correctness of the deconvolution method.

IEEE Computational Intelligence Magazine - November 2020

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