Temporal Course of 2014 Ebola Virus Disease (EVD) Outbreak in West Africa Elucidated through Morbidity and Mortality Data: A Tale of Three Countries
Temporal Course of 2014 Ebola Virus Disease (EVD) Outbreak in West Africa Elucidated through Morbidity and Mortality Data: A Tale of Three Countries
0 Competing Interests: The author is a PLOS ONE Editorial Board member , this does not in any way
1 Funding: YHH is funded by Taiwan Ministry of Science and Technology (MOST) grants (103-2314- B-039-010-MY3 and 103-2115-M-039-002-MY2). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
2 Editor: Bradley S. Schneider , Metabiota, UNITED STATES
3 Department of Public Health and Center for Infectious Disease Education and Research, China Medical University , Taichung, 40402 , Taiwan
The explosive outbreak of Ebola virus disease (EVD) in West Africa in 2014 appeared to have lessened in 2015, but potentially continues be a global public health threat. A simple mathematical model, the Richards model, is utilized to gauge the temporal variability in the spread of the Ebola virus disease (EVD) in West Africa in terms of its reproduction number R and its temporal changes via detection of epidemic waves and turning points during the 2014 outbreaks in the three most severely affected countries; namely, Guinea, Liberia, and Sierra Leone. The results reveal multiple waves of infection in each of these three countries, of varying lengths from a little more than one week to more than one month. All three countries exhibit marginally fluctuating reproduction numbers during June-October before gradually declining. Although high mobility continues between neighboring populations of these countries across the borders, outbreak in these three countries exhibits decidedly different temporal patterns. Guinea had the most waves but maintained consistently low transmissibility and hence has the smallest number of reported cases. Liberia had highest level of transmission before October, but has remained low since, with no detectable wave after the New Year. Sierra Leone has gradually declining waves since October, but still generated detectable waves up to mid-March 2015, and hence has cumulated the largest number of cases-exceeding that of Guinea and Liberia combined. Analysis indicates that, despite massive amount of international relief and intervention efforts, the outbreak is persisting in these regions in waves, albeit more sparsely and at a much lower level since the beginning of 2015.
An explosive outbreak of Ebola virus disease (EVD) has occurred in Guinea, West Africa since
March 2014. By August, the World Health Organization (WHO) declared the outbreak to be a
“public health emergency of international concern” . The extensive international attention
that followed has not helped to lessen its catastrophic force in three countries (Guinea, Liberia,
and Sierra Leone) that suffer the most. By April 16 2015, WHO reported 25831 confirmed,
probable, or suspected cases in these three countries with 10699 deaths . Local infections of
EVD have occurred outside of Africa, e.g., in the United States of America, United Kingdom,
and Spain, offering indication of its potential for global spread with high mortality rate [3, 4].
Although EVD was first identified in 1976 in Democratic Republic of Congo (DRC) and has
emerged in several countries in the central African region (e.g., DRC, Sudan, Uganda) in the
years since, the 2014 West Africa EVD outbreak was by far the most devastating of all, for
reasons yet to be established.
To ascertain the full threatening potential of the epidemic, many modeling studies have
reported various estimates and projections, by using a wide range of quantitative approaches
and obtaining estimates of transmission potential in the form of the reproduction number [4–
16]. All of these studies were carried out in October or earlier, using Ebola data mainly from
July to October. Several of the studies (e.g., [4–5, 15]) published in late September attempted to
quantify the temporal variations in reproduction number, but with differing results. Some
reported early signs of a decrease in transmission as revealed by estimated effective
reproduction number .
Given the volatilely unstable nature of the outbreaks in these countries under constantly
changing circumstances, it is important to capture the temporal changes and current trending
in the modeling. In this work, a simple mathematical model and EVD case data from Guinea,
Liberia, and Sierra Leone is utilized to fit the Ebola data during various time intervals from
June to late December, in order to pinpoint the occurrence of waves of reported cases and to
trace through the temporal changes of the epidemic in these three countries during the recent
months, in the form of the upturn and downturn of disease incidence during each wave. The
results enable us to elucidate the temporal variations in transmission potential of the Ebola
Due to data collection issues, the data used is subject to changes due to ongoing reclassification,
retrospective investigation and availability of laboratory results . To eliminate artificial
variations in data caused by diagnosis/reporting issues, the suspected cases reported in the WHO
reports are deleted as many other studies had done (e.g., [4–5, 7]), to inaccuracy in the
reporting of cases. Subsequently, the combined number of reported confirmed/probably case and
death data up to March 17/18, 2015 for Guinea, Liberia, and Sierra Leone as made available by
WHO in WHO Situation Summary  on March 20, 2015 are used. The time series of
combined total case number of these three countries up to September 28 is also fitted to the
Richards model, since it was the last date that synchronized case reporting from the three countries
The Richards model  is a simple mathematical model of the form
CðtÞ ¼ K½1 þ e raðt ti ðln aÞ=raÞ 1=a:
In the context of infectious disease modeling [19–20], C(t) is the cumulative number of
reported cases of infections (or any other quantity of disease morbidity/mortality such as
number of deaths, hospitalizations, etc., see ) at week t. K is the final case number over a single
wave of outbreak, r is the per capita growth rate of the cumulative case number, a is the
exponent of deviation of the cumulative case curve, and ti is a turning point of the epidemic
(which signifies the moment of upturn or downturn for the increase in the cumulative case
The basic premise of the Richards model is that the incidence curve of a single wave of cases
consists of a single peak of high incidence which starts initially with exponential growth
followed by saturation, resulting in an S-shaped cumulative case curve and a single turning point
of the outbreak. This turning point ti, which is defined to be the point in time at which the rate
of accumulation changes from increasing to decreasing, or vice versa, can be easily pinpointed
via fitting the Richards model to the cumulative data in question.
When more than one wave of infections occurs, a variation of the S-shaped Richards model
was proposed , which distinguishes two types of turning points. In addition to the
abovementioned turning point signifying the end of exponential growth, a second type of turning
point is present in a multi-wave epidemic where the growth rate of the cumulative case number
begins to increase again, signifying the beginning of the next wave. For further illustrations, the
readers are referred to [20, 22], where the incidence curves for the 2003 Great Toronto Area
(GTA) SARS and the 2007 Taiwan dengue outbreaks containing two peaks (or two turning
points of the first type) and one valley (or a turning point of second type) are investigated.
For the basic reproduction number R0, the formula R0 = exp(rT) is employed, where T is the
generation interval of the disease or the average interval from onset of one individual to the
onset of his/her contacts. It has been shown mathematically  that, given a growth rate r, the
expression R0 = exp(rT) provides an upper bound for basic reproduction number, regardless of
the assumed distribution of the generation interval T. Please note however, that since the aim is
to fit EVD time series data from various time periods during the epidemic, the estimate
obtained is not the basic reproduction number, but the effective reproduction number R of the
fitted time period.
The model parameters of epidemiological importance are K, r, and the turning point ti of
the epidemic. The cumulative epidemic data can be fitted to the Richards model to obtain
estimates of these model parameters, using any standard software with least-squares
approximation tool, e.g., SAS, Matlab, etc. More applications of the Richards model on other infectious
disease outbreaks such as dengue, influenza, HIV also can be found respectively in [22, 24–25].
The Richards model is fitted to the cumulative confirmed/probably case and death data at
different time intervals for each country as well as for the combined total numbers, and was able
to detect multiple waves for each country. Details of the data fitting procedure are provided in
S1 File. By fitting the EVD case and death data of Guinea, Liberia, and Sierra Leone to the
Richards model (Fig 1), one is able to detect seven small waves from case data and four waves from
death data during June 5 to February 18, 2015 in Guinea. For Liberia, four waves of cases and
two waves of deaths between July 20 and December 28 are pinpointed. For Sierra Leon seven
waves of cases and three waves of deaths during June 30 to March 15, 2015 are detected. By
combining the total case number of the three countries, two waves of cases and two waves of
deaths from July 20 to December 31 have been obtained. The resulting time intervals in which
the Richards model is fitted, and the corresponding turning points and reproduction numbers
with the 95% confidence interval (CI) from model fitting, are summarized in Table 1, with R
computed using a generation time of T = 15.3±9.3 .
Fig 1. Richards model fit for each wave of 2014 EVD outbreak data in (a) Guinea, (b) Liberia, (c) Sierra Leone, and (d) total. For each figure, black dot
denotes reported death data, blue dot denotes reported confirmed/probable case data, red curve denotes model-fitted number of deaths, and green curve
denotes model-fitted confirmed/probably case number.
To further illustrate the temporal changes of transmission potential of Ebola virus in each
country since June, Fig 2 shows the time periods in which a reproduction number R was obtain.
Here the data used to obtain the estimate was shown in color, with green for case number and
red for number of deaths. To further highlight the temporal progression of the outbreak in
each country, chronological timelines of the waves were provided in Fig 3.
Due to data collection issues, the data used is subject to changes due to ongoing reclassification,
retrospective investigation and availability of laboratory results  which often occurs during
the course of an epidemic outbreak . In attempt to eliminate artificial variations in data
caused by diagnosis/reporting issues, the subsequent deletion of suspected cases reported in the
WHO reports (e.g., [4–5, 7]) might led to an underreporting of cases, in addition to many
more unreported or asymptomatic cases. More precisely, the waves that were pinpointed
through modeling are waves of reported cases/deaths, which does not necessarily correspond
exactly to waves of infections, but nonetheless give indication to the variations in the temporal
Table 1. Summary table for time intervals of Richards model fit, data fitted, and estimates of the turning point and reproduction number with 95%
confidence intervals in parenthesis.
Reproduction number R
course of the epidemic that had occurred. Therefore, the results need to be interpreted
qualitatively rather than quantitatively, in the sense that the relative temporally variation in the
reproduction number is more revealing than the actual magnitude.
On the other hand, if these artificial diagnosis/reporting issues remain consistent
throughout the epidemic, any underreporting that had indeed occurred would not have too much
actual impact on the detection of waves or the timing of the turning points. Furthermore, note
that while previous modeling studies of infectious disease outbreaks in literature have been
shown that multiple estimates can be obtained from distinct epidemic data (case,
hospitalization, and deaths), the estimates of reproduction number are often comparable [21, 26–27].
However, clinical progression of an infected person from diagnosis/reporting to death/
recovery dictates that a wave detected using case data (in green color in Fig 3) must temporally
precede the same wave detected through death data (in red color). Some of these waves in
Table 1 are redundant. That is, since death is a consequence of a reported case after a time lag,
some waves of reported deaths that were capture by the Richards model were in fact the same
Fig 2. Reproduction number R and its corresponding 95% CI for each wave in (a) Guinea, (b) Liberia, (c) Sierra Leone, and (d) total. The middle bar
denotes the mean estimate for R, while the upper and lower bars denote the upper and lower bounds for 95% CI. Green denotes estimates using the
confirmed/probable case data, and red denotes estimates using the number of deaths.
waves that had previously been detected from the reported case data, after a lag of average time
from reporting to death. For a case in point, the wave of cases in Sierra Leone during December
17-January 4, 2015 is clearly the same wave that results in reported deaths during December
20-January 12, 2015. Hence, these redundant waves are deleted from Figs 2 and 3, and the
discussions, in order to elucidate what the results truly inform us.
Country-specific transmissibility of EVD
The initial waves for Liberia and Sierra Leone exhibit significantly wider 95% CIs comparing to
latter waves of these two country, perhaps an indication of the volatility and uncertainty
surrounding case diagnosis/reporting during the early phase of the outbreak in July. Hence we
discard these two early waves. Subsequently, the reproduction number ranges between 1.05–1.31
for Guinea, between 1.05–2.22 in Liberia, between 1.06–1.70 in Sierra Leone, and between
1.11–1.62 for the combined total of the three countries.
Both Guinea and Sierra Leone data generated multiple waves that remain at a low level of
transmissibility with mean reproduction number between 1 and 2. However, the lower bound
of reproduction number during this initial wave (1.14) is consistently similar to the lower
bounds of subsequent waves detected in Sierra Leone, and hence might have been caused by
Fig 3. Chronological timelines for the waves of 2014 EVD outbreak between June 5 2014 to March 15 2015 in (a) Guinea, (b) Liberia, (c) Sierra
Leone, and (d) total. Green bar denotes a wave of confirmed/probably case number and Red bar denotes a wave of deaths.
greater uncertainty in diagnosis/reporting during the initial stage of epidemic, rather than
being a true indication of greater transmissibility.
Interestingly, the three waves for combined total numbers of cases and deaths coincide with
three of the four waves detected using the case and death data for Liberia (see Fig 3), with the
lone exception occurring when the data for combined total was unavailable in November. This
gives indication that the epidemic in these three countries in West Africa basically follows a
similar temporal pattern as that of Liberia. However, both the numbers of reported cases and
deaths in Liberia are actually smaller than those of Sierra Leone, showing that the country with
the largest outbreak (Sierra Leone) does not necessarily dictates the overall temporal changes
of the epidemic in that region.
From Table 1 and Fig 2, the transmission potential of EVD in all three countries, as
quantified by the estimated reproduction number R, fluctuated slightly but remained relatively
consistent during all waves of the epidemic for Guinea and Sierra Leone, but only from August to
September in Liberia. The observed variations in range of 95% CIs is mainly due to the varying
lengths of the waves resulting and thus the number of data points for the model fit. The
Fisman et al.  (9/8)
Nishiura and Chowell  (9/11)
Towers et al.  (9/23)
WHO Ebola Response Team  (9/23)
Webb et al.  (1/30)
*Reported data including suspected cases.
reproduction number for Liberia decreased significantly after November, an indication of
improved situation for Liberia.
Reproduction number for 2014 West Africa EVD
To compare the results of this study with previous modeling studies, Table 2 lists results on
estimates of reproduction number for 2014 West Africa Ebola outbreak. The date of
publication/online is given as an indication of the timeline of the data that is available at the time
when these studies were carried out. The results for the time periods before October (row 1 in
Table 2) are in general agreement with the other estimates in the literature. Estimate for Liberia
tends to be higher than most other studies, while estimates are somewhat lower for Guinea and
Sierra Leone as well as the combined total number. However, estimates for Liberia for August
and September (mean R: 2.09–2.22) is close to estimates for Montserrado County, Liberia
during June 4 to September 23 using a transmission model (2.49 in ) and for Liberia in August
using a logistic growth model (2.4 in ), corroborating the results of this study that the
transmissibility of EVD was at its highest during August-September in Liberia. This study also
finds that the reproduction numbers in all countries declined after September, corroborated by
a recent modeling study using district-level data in Sierra Leone found that the reproduction
number in all districts declined between August and December .
There does not seem to be a significant change in the ranges of reproduction numbers
during the time period in any of the three countries. Although in comparison, Guinea has the
smallest, between 1.05–1.31, while Liberia has the largest reproduction number with mean
estimate between 2.09–2.22 in August-September but significantly lower reproduction number
(1.05–1.08) after November. Sierra Leone has most reported cases and deaths, but does not
have a significantly larger reproduction number than other 2 countries, ranging between 1.06–
1.70 after August, with the low being most recent wave in February-March, 2015. The mean
reproduction number for three countries combined total is range between 1.48–1.62.
Temporally, although each country exhibits different pattern in its transmissibility (see Fig
2), reproduction numbers for each country fluctuate without any noticeable trend before
November, likely an indication of stochastic variations that existed in reporting of earlier cases
in each country. Mover, Sierra Leone has the most cases among the 3 countries, although its
reproduction number was lower than that of Liberia until after November. Therefore, although
reproduction number provides an indication of transmission potential of an infectious disease
in a particular community during a particular time period (wave), one should not simply
equate its magnitude with actual outbreak severity or duration of the wave.
Moreover, it has been proposed in earlier studies (e.g., ) that any outbreak is in fact a
single realization of an underlying stochastic process that could exhibit considerable variability
among repeated realizations, and hence the same stochastic process produces a range of
realizations that each yields a different R0 estimate. The different R0 estimates listed in Table 2 are
the results of different estimation procedures using data from a single realization of a stochastic
process. For a lucid discussion on reliability of model fit with regard to West Africa ebola data,
the readers are referred to .
Country-level vs. local
The present study, similar to most other modeling studies on West Africa EVD outbreak, make
use of the national case data, although some studies using local data have yielded similar results
on reproduction number (e.g., , ). A recent study using national, subnational, and
regional data  has found significant differences in the growth patterns, perhaps due to local
differences in important factors such as reporting, behavior change, impact of intervention,
etc., factors that tend to be suppressed when combining them in a national total. The epidemic
data from these three countries clearly reflect a complex spatial structure, i.e., spatial spread of
the disease across neighboring regions of these three countries, as pointed out in several studies
(e.g., [28, 31]). Although modeling complex spatial structure often requires incorporating
spatial structure in model construction and, more importantly, information on spatial movement
of the populations across different regions, our multi-wave results and aggregated estimates for
R0 using aggregated country-specific and combined total data highlight the nature of spatial
heterogeneity that had existed during the epidemic.
In this study, by combining the national totals, the temporal course of the West Africa
outbreak (as quantified by waves and turning points detected via the Richards model) tends to
follow a similar pattern as that of Liberia, although Liberia did not have the most reported cases
among the three countries. On the other hand, the transmission potential of EVD (as
quantified by reproduction number R) estimated from the combined total case number of the three
countries (range of mean R: 1.48–1.62) appears to fall consistently between the estimates for
Liberia (which tends to have comparatively higher R) and the other two countries, whenever
the waves in these countries coincide, until December when mean estimates of R for all
countries as well as the combined total are around 1.10 with narrow 95% CIs, perhaps the result of
some synchronization of local control and international relief taking efforts.
In summary, the outbreak in these three countries exhibits decidedly different temporal
patterns, despite high mobility among the populations. Guinea has had the most waves but
maintained a low level of transmission, and hence has smallest number of reported cases and deaths.
Liberia had highest level of transmission before October, but has remained at low level since
then and no detectable wave since the New Year. Sierra Leone had gradually declining waves
since October, but still generated detectable waves up to March 2015, and hence has cumulated
the largest number of cases, exceeding that of Guinea and Liberia combined since end of the
year. The EVD epidemic is still persisting in waves in West Africa, albeit more sparsely and at a
much lower level since the beginning of 2015.
The main limitation for this study is the data quality, due to data collection issues by local
health authority, including: reporting of numbers subject to change due to ongoing
reclassification, retrospective investigation and availability of laboratory results; data not reported due to
the high proportion of probable and suspected cases that are reclassified; data not being
available; and data missing for some dates in some countries . Some of these issues are common
in infectious disease outbreak data collection and real-time modeling ; although for the
current Ebola epidemic in West Africa the problem is magnified due to instability in the
The author is grateful to the reviewers and editors for their constructive comments and
suggestions which led to significant improvements in this manuscript.
Conceived and designed the experiments: YHH. Analyzed the data: YHH. Contributed
reagents/materials/analysis tools: YHH. Wrote the paper: YHH.
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