Projections of Ebola outbreak size and duration with and without vaccine use in Équateur, Democratic Republic of Congo, as of May 27, 2018
Projections of Ebola
outbreak size and duration with and without
vaccine use in E?quateur, Democratic Republic of
Congo, as of May
Projections of Ebola outbreak size and duration with and without vaccine use in ?Equateur, Democratic Republic of Congo, as of May 27, 2018
J. Daniel Kelly 0 1 3
Lee WordenID 0 1 3
S. Rae WannierID 0 1 3
Nicole A. Hoff 1 3
Patrick Mukadi 1 3
Cyrus Sinai 1 3
Sarah Ackley 0 1 3
Xianyun Chen 1 3
Daozhou Gao 1 3
Bernice Selo 1 3
Mathais Mossoko 1 3
Emile Okitolonda-Wemakoy 1 3
Eugene T. Richardson 1 2 3
George W. Rutherford 0 1 3
Thomas M. Lietman 0 1 3
Jean Jacques Muyembe-Tamfum 1 3
Anne W. Rimoin 1 3
Travis C. Porco 0 1 3
0 School of Medicine, University of California , San Francisco (UCSF), San Francisco, CA , United States of America , 2 F.I. Proctor Foundation, UCSF, San Francisco, CA , United States of America, 3 School of Public Health, University of California, Los Angeles , Los Angeles, CA , United States of America, 4 National Institute of Biomedical Research, Kinshasa, Democratic Republic of Congo, 5 Mathematics and Science College, Shanghai Normal University , Shanghai, China, 6 Ministry of Health , Kinshasa, Democratic Republic of Congo, 7 School of Public Health, University of Kinshasa , Kinshasa , Democratic Republic of Congo
1 Editor: John Schieffelin, Tulane University , UNITED STATES
2 Harvard Medical School , Boston, MA , United States of America, 9 Brigham and Women's Hospital , Boston, MA , United States of America
3 Institute of General Medical Sciences, U01- GM087728, Dr. Lee Worden, Dr. Travis C Porco; Faucett Catalyst Fund, Dr. Anne W Rimoin. The funders had no role in study design , data collection
As of May 27, 2018, 6 suspected, 13 probable and 35 confirmed cases of Ebola virus disease (EVD) had been reported in E? quateur Province, Democratic Republic of Congo. We used reported case counts and time series from prior outbreaks to estimate the total outbreak size and duration with and without vaccine use. We modeled Ebola virus transmission using a stochastic branching process model that included reproduction numbers from past Ebola outbreaks and a particle filtering method to generate a probabilistic projection of the outbreak size and duration conditioned on its reported trajectory to date; modeled using high (62%), low (44%), and zero (0%) estimates of vaccination coverage (after deployment). Additionally, we used the time series for 18 prior Ebola outbreaks from 1976 to 2016 to parameterize the Thiel-Sen regression model predicting the outbreak size from the number of observed cases from April 4 to May 27. We used these techniques on probable and confirmed case counts with and without inclusion of suspected cases. Probabilistic projections were scored against the actual outbreak size of 54 EVD cases, using a log-likelihood score. With the stochastic model, using high, low, and zero estimates of vaccination coverage, the median outbreak sizes for probable and confirmed cases were 82 cases (95% prediction respectively. With the Thiel-Sen regression model, the median outbreak size was estimated to be 65.0 probable and confirmed cases (95% PI: 48.8, 119.7). Among our three mathematical models, the stochastic model with suspected cases and high vaccine coverage predicted total outbreak sizes closest to the true outcome. Relatively simple mathematical
and analysis, decision to publish, or preparation of
Competing interests: The authors have declared
that no competing interests exist.
models updated in real time may inform outbreak response teams with projections of total
outbreak size and duration.
On May 8, 2018, the World Health Organization (WHO) announced the occurrence of an
outbreak of Ebola virus disease (EVD) in the Democratic Republic of Congo (DRC).[
April 4 through May 7, 21 suspected EVD cases were reported in Iboko and Bikoro, E? quateur
Province. On May 7, blood samples from five hospitalized patients had been sent to Kinshasa
for Ebola-PCR testing, and two were confirmed PCR-positive.[
] On May 21, vaccination of
healthcare workers started.[
] By May 27, the ring vaccination campaign was being rolled out
as 906 contacts and contacts of contacts were being actively monitored. Six suspected, 13
probable and 35 confirmed EVD cases had been reported, and 25 (52%) of 48 probable and
confirmed EVD cases had died.[
This outbreak had several features that were worrisome for widespread transmission. Cases
were reported over a 168-kilometer distance, including four confirmed cases in the
~1,200,000-inhabitant provincial capital of Equateur, Mbandaka, which is situated on the
Congo River and bordering Congo-Brazzaville.[
] Moreover, travel to Kinshasa is frequent
from Mbandaka. Given these risk factors, early epidemic growth profiles,[
] and evidence of
unreported infection from previous outbreaks,[
] the risk of a substantially larger outbreak
could not be ignored.
The factors causing epidemic growth to peak have been debated. Delayed detection of EVD
outbreaks and resulting widespread distributions of EVD have significantly contributed to
epidemic growth. In addition to traditional burial practices, Ebola treatment units with low
quality care and/or high mortality rates have discouraged Ebola suspects from presenting to
care and contribute to community-based transmission.[
] Fragile, overwhelmed public
health surveillance systems have also contributed to higher rates of unreported cases, who
endanger urban communities,[
] which potentially have had higher transmission rates than
] Change to subcritical transmission (reproduction number below 1)
tends to occur when Ebola response organizations deploy control, prevention and care
] communities adopt more protective behaviors,[15,16] and/or transmission
decreases in a social network.[
] Scientific advances with rapid diagnostics and vaccines
from the West Africa outbreak were deployed in the April-July 2018 EVD outbreak in DRC
and had the potential to limit Ebola virus transmission.[
We used reported case counts during EVD outbreak in DRC and/or time series from 18
prior outbreaks to estimate the total outbreak size and duration with and without the use of
vaccines. These projections were intended to help organizations anticipate and allocate
sufficient resources for the duration of the April-July 2018 EVD outbreak.
The following methods were used to generate projections: a stochastic branching process
] statistical regression based on prior outbreaks, and Gott?s Law.[
] On May 27, 54
EVD cases (6 suspected, 13 probable and 35 confirmed) were reported in three locations
(Iboko, Bikoro, and Mbandaka) (Fig 1). Based on EVD situation reports from DRC, we
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Fig 1. Map of cases of Ebola virus disease per health zone in E?quateur Province, Democratic Republic of Congo,
as of May 27, 2018 (Source: Hansen/UMD/Google/USGS/NASA[
assumed the ring vaccination program started the week of May 21, so we used May 23 as the
time point that vaccines were implemented in the model at high and low coverage levels.
Data on suspected, probable, and confirmed case counts were available from WHO situation
reports in May 2018 and used as the basis for analysis. The published situation reports reflected
data available up until May 11, 13, 16, 23, and 27, respectively. During the outbreak, the Ebola
response team tested suspected cases for EVD and depending on positive or negative results,
cases were classified as confirmed or not a case. The final outbreak case count was 54 probable
and confirmed cases (no suspected cases).[
] Due to this reporting process, probable and
confirmed cases were used to parameterize the stochastic branching process model, regression
models, and Gott?s law. We added suspected cases to create an additional projection, using
stochastic branching process model.
Stochastic branching process model
We modeled Ebola virus transmission using a stochastic branching process model,
parameterized by transmission rates estimated from the dynamics of prior EVD outbreaks, and
conditioned on agreement with reported case counts from the 2018 EVD outbreak to date. We
incorporated high and low estimates of vaccination coverage into this model. Then we
generated a set of probabilistic projections of the size and duration of simulated outbreaks in the
To estimate the reproduction number R as a function of the number of days from the
beginning of the outbreak, we included reported cases by date from thirteen prior outbreaks and
excluded the first historical outbreak reported in those countries (e.g., 1976 outbreak in
Yambuko, DRC) (S1 Table).[
] As there is a difference in the Ebola response system as well as
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community sensitization to EVD following a country?s first outbreak, we employed this
inclusion criterion to reflect the Ebola response system in DRC during what is now its ninth
outbreak. The Wallinga-Teunis technique was used to estimate R for each case and therefore for
each reporting date in the outbreak.
The serial interval was defined as the interval between disease onset in an index case and
disease onset in a person infected by that index case. The serial interval distribution used for
this estimation was a gamma distribution with a mean of 14.5 days and a standard deviation of
5 days, with intervals rounded to the nearest whole number of days, consistent with the
understanding that the serial interval of EVD cases ranges from 3 to 36 days with mean 14 to 15
] Given that serial interval distribution, which we can denote as a probability w
(t) of a t-day interval between given primary and secondary cases, Wallinga-Teunis estimation
works by defining a relative likelihood pij for each possible source j of a given case i:
pij ? w?ti
and then deriving from that an estimated reproduction number Rj for each case:
After using this technique to derive estimated reproduction numbers for each case in an
outbreak, we use these estimated R values and cases? onset dates d to estimate an initial
reproduction number R0 and quenching rate ? for each past outbreak by fitting an exponentially
Rj ? Si pij:
R ? Ro e td;
to each outbreak?s R and d values (S1 Fig).
Transmission was modeled using a stochastic branching process model in which the
number of secondary cases Si caused by any given primary case i was drawn from a negative
binomial distribution whose mean is the reproduction number R:[
where R is reproduction number as a function of day, k is a dispersion parameter, and Nb()
denotes the negative binomial distribution. All transmission events were assumed to be
independent. The serial interval between date of detection of each primary case and that of each of
its secondary cases is assumed gamma distributed with mean 14.5 days and standard deviation
5 days, rounded to the nearest whole number of days, as above. The pair of parameters R0 and
? estimated for the different past outbreaks used, and dispersion parameter k, were used in all
possible combinations (with R0 and ? taken as a unit) to simulate outbreaks.
This model generated randomly varying simulated outbreaks with a range of case counts
per day. After the Ministry of Health and WHO conducted epidemiological investigations
about the beginning of the EVD outbreak in E?quateur Province, they concluded that the
outbreak began on April 4, 2018, with a single case.[
] The simulation process occurs as follows:
proposed epidemic trajectories are generated in an initial step based on the above branching
process, and these are then subsequently filtered by discarding all but those whose cumulative
case counts match the known counts of the April-July 2018 EVD outbreak on known dates.
The filtration accepts epidemics within a range of 3 cases more or less than each recorded
value. This one-step particle filtering technique produced an ensemble of model outbreaks,
filtered on agreement with the recorded trajectory of the outbreak to date. This filtered ensemble
is then used to generate projections of the eventual outcome of the outbreak.[
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To model vaccination coverage with respect to total transmission (unreported and
reported), we multiplied the estimate of vaccine effectiveness by low and high estimates of
reported cases. In a ring vaccination study at the end of the West Africa outbreak, the overall
estimated rVSV-vectored vaccine efficacy was 100% and vaccine effectiveness was 64.6% in
protecting all contacts and contacts of contacts from EVD in the randomized clusters,
including unvaccinated cluster members.[
] Estimates of vaccine effectiveness were used in our
stochastic model. The ring vaccination study found the vaccine to be effective against cases with
onset dates 10 days or more from the date of vaccine administration, so we modeled the
vaccination program as a proportionate reduction in the number of new cases with onsets 10 days
or more after the program start date.
Then, past estimates of the proportion of unreported cases were used to estimate the
proportion of exposed individuals not covered by the vaccination process. Based on a Sierra
Leonean study from the 2013?2016 outbreak,[
] we estimated that the percentage of reported
cases in DRC would rise over time from a low of 68% to a high of 96%. Given these low and
high estimates of reported cases and the estimate of vaccine effectiveness (64.6%), a low
estimate of vaccination program coverage was 44% (68% multiplied by 64.6%) and a high estimate
of vaccination program coverage was 62% (96% multiplied by 64.6%). The course of the
outbreak with and without the vaccination program was modeled based on approximate dates
available from situation reports.[
For simulation based on probable and confirmed cases, from 122,683,392 simulated
outbreaks, 21,036 were retained after filtering on approximate agreement with DRC case counts.
For simulation based on probable, confirmed, and suspected cases, from 122,683,392
simulated outbreaks, 32,431 were retained after filtering. The simulated outbreaks that were
retained after filtering were continued until they generated no further cases. This ensemble
was used to derive a distribution of outbreak sizes and durations. Mean and median values
and 95% prediction intervals were calculated using the 2.5 and 97.5 percentiles of simulated
outbreak size and duration. These analyses were conducted using R 3.4.2 (R Foundation for
Statistical Computing, Vienna, Austria).
For contrast with the stochastic model above, a simple regression forecast was conducted
based solely on outbreaks of size 10 or greater. Time series for all 18 such prior outbreaks were
obtained, including seven prior ones from DRC, dating back to 1976 (S1 Table; S2 Fig).[
] One (5.6%) of the 18 prior outbreaks in our sample (the 2013?2016 West Africa
outbreak) achieved a large size (over 28,000 cases). No exclusions were made; no attempt to
model specific features of the April-July 2018 outbreak was conducted. The regression model
predicted the outbreak size based on values of the outbreak size at a specific earlier time. The
beginning of each outbreak was not reliably characterized; therefore, all time-series were
aligned on the day they reached 10 cases. In the April-July 2018 outbreak, we observed cases
over the period from April 4 to May 27 (day 0 to day 53). May 27 corresponded to day 34 since
reaching 10 reported cases. For the prior 18 outbreaks, linear interpolation was used to obtain
the number of cases on day 34 (after reaching 10 cases). To reduce the influence of outliers
and high leverage points, and to improve linearity, we calculated the pseudologarithm
transform f(x) = arcsinh(x/2), asymptotically logarithmic but well-behaved at 0. We used
nonparametric Theil-Sen regression (R-package mblm) followed by calculation of the resulting
prediction interval for a new observation.[
] Finally, we reported the median and 95%
central coverage intervals for the prediction distribution conditional on the value being no
smaller than the observed value on day 34. Sensitivity analysis was conducted using ordinary
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least squares regression. These analyses were conducted using R 3.4.2 (R Foundation for
Statistical Computing, Vienna, Austria).
Gott?s Law was used to estimate the outbreak size using data through May 27 and May 11. We
included a projection using data through May 11 because we hypothesized that this method
performs better when the first situation report is posted than at later in the outbreak period.
] Then we included a projection with the regression models using data through May 11 for
comparison. With Gott?s Law, we assume we have no special knowledge of our position on the
epidemic curve. If we assume a non-informative uniform prior for the portion of the epidemic
that still remains, the resulting probability distribution for the remaining number of cases y is:
P?Y ? y? ? Yo=y2:
The median outbreak size was estimated, along with the two-sided 95% prediction interval.
Each of the above models assigned a probability to any possible value of the total outbreak size.
The final outbreak size was 54 probable and confirmed cases, so we identified the probability
of this equivalent number (53) from each model, as of May 27. Probabilistic projections were
scored using a log-likelihood (ignorance) score.[
As of May 27, 2018, there were 6 suspected, 13 probable and 35 confirmed EVD cases. Bikoko
had ten confirmed cases, 11 probable cases, and one suspected case. Iboko had 21 confirmed
cases, two probable cases, and one suspected case. Mbandaka had four confirmed cases and
one suspected case (Fig 1).
With the stochastic model, we projected outbreak size and duration of probable and
confirmed cases. In the absence of any vaccination program, the projected median outbreak size
was 213.0 cases (mean 360.2; 95% prediction interval: 64.8, 1450.2). Median duration of
projected outbreaks was 175.0 days (mean 182.8; 95% prediction interval: 86.0, 282.0). Using a
lower estimate of 44% vaccination coverage, the median outbreak size was 104.0 cases (mean
118.8; 95% prediction interval: 58.0, 271.0) and median duration was 121.0 days (mean 124.6;
95% prediction interval: 74.0, 187.0). Using a higher estimate of 62% vaccination coverage, the
median size was 82.0 EVD cases (mean 88.1; 95% prediction interval: 55.0, 156.0), and the
median duration was 101.0 days (mean 103.4; 95% prediction interval: 68.0, 153.0). These
projections with the stochastic model were repeated to estimate suspected, probable and
confirmed cases (Table 1 and Table 2; Figs 2 & 3).
With the regression based on past outbreaks, the median outbreak size was estimated to be
65.0 probable and confirmed cases (95% prediction interval: 48.8, 119.7), while use of ordinary
least squares produced a median size of 97.9 probable and confirmed cases (95% prediction
interval: 58.3, 169.9). Outbreak projections were also reported using data through May 11 in
Gott?s Law suggests that given 48 probable and confirmed cases, the median estimate of
outbreak size was 96.0 cases (95% CI: 49.0, 1920.0). Using the 34 probable and confirmed cases
as of May 11, the median estimate of outbreak size was 68.0 cases (95% CI: 35.0, 1360.0).
Of the mathematical models employed, the stochastic model that included suspected cases
and high vaccination coverage had the best probabilistic score (log likelihood of -1.31).
Likelihood scores of each model can be found in Table 4.
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When we were conducting our projections in late May, this outbreak still had the potential to
become the largest outbreak in DRC since 2007. Vaccine use, regardless of coverage levels, was
projected to prevent more than half of the total outbreak size. Vaccines, however, were only
part of concurrent prevention, control, and care strategies.[
] We also found that the
stochastic model with vaccine use projected that rare, large outbreaks (tail of the distribution
of the model without vaccinations) were prevented, suggesting that repeat epidemics such as
the 2013?2016 West African outbreak may have been highly unlikely once vaccines were rolled
Multiple models were used to estimate total outbreak size. This study exemplified how
mathematical models, including simple regressions, can be useful for advising real-time
decision making because they provided rapid projections and similar estimates of R as compared
to complex models, even though real-time modeling projections historically overestimated
outbreak size and duration.[
] Our projections that included suspected cases did not
suggest that vaccines had as much of an impact as our model using only probable and confirmed
cases. The trends associated with suspected cases were subject to several factors, including
operational choices of response teams and maturity of the outbreak. Nevertheless, suspected
case counts may at times provide a better glimpse into the near future of an outbreak than the
confirmed and probable case counts. In our case, use of the time series of confirmed, probable,
and suspect cases yielded a forecast closer to the final outbreak size. However, as model
projections can be highly sensitive to inclusion of suspected cases and use of exact case counts,
particularly the last few counts in the available data, conclusions must be taken with caution.
Thus far, there had been a strong local and international response, and deployment of
vaccines and rapid diagnostic tests (RDT) occurred early in response efforts.[
] RDTs were being
used to screen Ebola suspects while the vaccines are being administered to high-risk groups
for EVD, including healthcare workers, contacts, and contacts of contacts. To further limit
epidemic growth from unreported cases, particularly those who have non-specific symptoms but
95% Prediction Interval
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Fig 2. Cumulative case counts used in filtering stochastic branching process model.
are screened negative by the WHO case definition, more decentralized use of RDTs should be
considered. In addition, formal evaluations of vaccine use and coverage on transmission
reduction are needed.
There are limitations to our projections. Projection distributions were right-skewed, with
long tails (and we therefore reported the median instead of the mean). While there have been
22 observed EVD outbreaks with a case count greater than ten cases, we were unable to include
all prior outbreaks in our estimates due to data availability.[
] Note that the simple
regression projection is based entirely on past outbreaks of EVD (measured and reported in different
ways), and cannot account for the improved control measures and vaccination in the way that
a mechanistic model does. We included, however, as much real-time information into our
estimates as possible, but situations such as the introduction of EVD into a large urban population
and implementation of RDTs and vaccines are new to DRC. We did not include vaccination of
healthcare workers in the stochastic model. Our estimates of vaccination effectiveness and
reported cases were obtained from West Africa because these estimates were not available for
the EVD outbreak in E?quateur. These modeling assumptions may not have been consistent
with estimates in DRC and should be carefully considered prior to use in other EVD
A strength of our approach was the use of multiple methods to estimate the outbreak size,
although we note that Gott?s Law has not been validated for outbreak projections in other
EVD outbreaks. Additional limitations of the models were that they did not include
parameters to address spatial spread, urban settings, conflict zone, or other factors that may have
influenced the accuracy of the predictions, particularly in the 2018?2019 EVD outbreak in
Northeastern DRC (ongoing in January 2019). While it can also be useful and achievable to
use models of these kinds to make short-term forecasts for evaluation of model performance
and to inform outbreak response, the present study was limited to projections of final
outbreak size and duration.
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Fig 3. Distribution of outbreak projections from stochastic branching process model. a. Mean and prediction interval of cumulative probable/
confirmed case count by day in model projections, by proportion of vaccine coverage. Target case numbers and dates are marked with + signs; b. Mean
and prediction interval of cumulative probable/confirmed/suspected case count by day in model projections, by proportion of vaccine coverage. Target
case numbers and dates are marked with + signs; c. Mean and prediction interval of weekly average of per-day probable/confirmed case count in model
projections; and d. Mean and prediction interval of weekly average of per-day probable/confirmed/suspected case count in model projections.
Among our three mathematical models, the model that performed the best (stochastic
model with suspected cases and high vaccine coverage) predicted total outbreak sizes close to
the true outcome. When EVD cases were introduced into Mbandaka, there was concern that
the total outbreak size could exceed most prior EVD outbreaks in DRC. Indeed, our
projections were consistent with this concern because models without vaccine coverage projected
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higher total outbreak sizes. In our stochastic model projections, vaccine use reduced mean
total outbreak size by more than half, regardless of coverage levels (p<0.001, Welch?s t-test).
As vaccine coverage was scaled up, an influx of support was warranted to support and bolster
the evolving rapid response; however, continued efforts to strengthen the health system are
equally as warranted so that we can respond to future outbreaks before they become
epidemics. Relatively simple mathematical models updated in real time may inform outbreak response
teams with projections of total outbreak size and duration.
S1 Table. List of 21 prior Ebola outbreaks from 1976 to 2016 by time period, country,
confirmed/probable reported and time series case count, outbreak inclusion into the
regression and stochastic models.
S1 Fig. Estimates of temporal change in reproduction number R in thirteen past Ebola
outbreaks. To each series of R estimates we fit an exponentially decaying curve, to be used in our
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S2 Fig. Time-series of 18 prior Ebola outbreaks from 1976 to 2016 was depicted.
cratic Republic of Congo.
We thank the Ebola responders for their efforts in the 2018 EVD outbreak in E? quateur,
DemoConceptualization: J. Daniel Kelly, Lee Worden, Eugene T. Richardson, George W.
Rutherford, Thomas M. Lietman, Anne W. Rimoin, Travis C. Porco.
Data curation: J. Daniel Kelly, S. Rae Wannier, Cyrus Sinai, Xianyun Chen, Daozhou Gao,
Bernice Selo, Mathais Mossoko, Emile Okitolonda-Wemakoy.
Formal analysis: J. Daniel Kelly, Lee Worden, S. Rae Wannier, Thomas M. Lietman, Travis C.
Investigation: J. Daniel Kelly, S. Rae Wannier.
Methodology: J. Daniel Kelly, Lee Worden, S. Rae Wannier.
Project administration: J. Daniel Kelly, Lee Worden.
Software: Lee Worden, S. Rae Wannier, Travis C. Porco.
Supervision: Travis C. Porco.
Validation: J. Daniel Kelly, Lee Worden, S. Rae Wannier, Nicole A. Hoff, Patrick Mukadi,
Eugene T. Richardson, Thomas M. Lietman, Jean Jacques Muyembe-Tamfum, Anne W.
Rimoin, Travis C. Porco.
Visualization: J. Daniel Kelly, Lee Worden, S. Rae Wannier.
Writing ? original draft: J. Daniel Kelly, Lee Worden.
Writing ? review & editing: J. Daniel Kelly, Lee Worden, S. Rae Wannier, Nicole A. Hoff,
Patrick Mukadi, Cyrus Sinai, Sarah Ackley, Xianyun Chen, Daozhou Gao, Bernice Selo,
Mathais Mossoko, Emile Okitolonda-Wemakoy, Eugene T. Richardson, George W.
Rutherford, Thomas M. Lietman, Jean Jacques Muyembe-Tamfum, Anne W. Rimoin, Travis C.
11 / 14
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