A Quantitative Assessment of Dynamic
Intervention Capacity Effectiveness in
the 2014 Ebola Epidemic
Willem L. Auping (HCSS)*, Erik Pruyt (NIAS & TU Delft), Jan H. Kwakkel (TU Delft), Michel
Rademaker (HCSS)
*Corresponding author: willemauping@HCSS.nl
Abstract
Background: The current outbreak of the Ebola Virus (EBOV) is characterized by
inadequate intervention capacities. In this theoretical paper, we research what the influence of
limitations in the intervention capacity are on the effective reproduction number, and what the
effectiveness would be of a more proactive approach in expanding the intervention capacities.
Methodology: We use a transmission model extended with dynamical intervention
capacities of isolation, health workers, tracing officers, and eventually vaccines. We generate a
set of plausible scenarios explaining the current reported Ebola Virus Disease (EVD) cases taking
into account a bandwidth for potential underreporting. We use these scenarios to test the
effectiveness of a more proactive approach in extending intervention capacities.
Results and conclusions: We show that a reactive approach in extending intervention
capacities leads to under-capacity for isolating EVD cases. This under-capacity can lead to a
significant increase in the effective reproduction number, leading to faster transmission of
EBOV. A more proactive approach, which takes into account development delays of capacities,
the doubling time of the disease, and the factor of potential underreporting of the number of
cases, helps in any scenario in limiting the total number of EVD cases and deaths.
Keywords: Ebola Virus Disease, Intervention capacity, Reproduction number, Scenario
Discovery
Introduction
The 2014 outbreak of Ebola Virus (EBOV) and, consequently, Ebola Virus Disease (EVD)
in Liberia, Sierra Leone, Guinea, Senegal, Mali, Nigeria, Spain, and the United States of
America®? is by far the largest observed to date;3 The number of cases and deaths outnumbers
the sum of all previous outbreaks of EVD. The outbreak distinguishes itself from earlier
outbreaks by occurring in densely populated urban areas.3 Earlier outbreaks took place in rural
or otherwise sparsely populated areas.4!2
Dynamic transmission models can be used for intervention capacity planning for
epidemics like the 2014 EVD epidemic. These models have been used for estimating the
reproduction number of Ebola, and projecting the future development of the epidemic.3"3-4
However, projecting the dynamics of EBOV is complicated by the uncertainty about many input
factors.'5 Examples include the case fatality ratio,® and the basic reproduction number Ro.378
Further, the actual number of cases during this epidemic is believed to be considerably higher
than the reported number of cases," since the infrastructure to diagnose new cases and identify
contamination epicenters is insufficient, as is demonstrated by the continued spreading of the
disease.
When EBOV was spreading exponentially, medical staff, hospitals, isolation facilities, and
tracing officers were trying to limit the further spreading of the virus, and an effort was started to
develop Ebola vaccines and medication as quickly as possible. Therefore, it makes sense to
incorporate these intervention capacities in transmission models aimed at projecting the future
development of the epidemic. For example, Bachinksy & Nizolenko combine a SEIR model with
capacities.2° They model bed capacity as isolation capacity and kept the number of available beds
constant. Further, several studies of influenza look at the influence of anti-viral medication and
vaccination programs.2?!25
In this paper, we present a model that incorporates EBOV propagation in an extended
SEIR model. We incorporate endogenously modeled intervention capacities, and parameterize
the model for Liberia. The parameterization happens in a Scenario Discovery approach where we
sample over a broad bandwidth of input parameter values to account for the uncertainty
characterizing the current EVD outbreak. This allows us to evaluate the influence of dynamic
limits of EVD interventions on the effective reproductive number. As such, the effective
reproduction number is modeled as the result of a SEIR model extended with endogenous
intervention capacities. This theoretical paper thus tries to explain how the epidemic risk and the
necessary intervention interact, what the consequences are of this interaction, and how the use
of dynamic transmission models with integrated dynamic intervention capacities may inform
planning of intervention capacities during future large outbreaks.
The setup of this paper is as follows. First, we explain how we developed the model,
extending the SEIR model structure with limiting intervention capacities of isolation, health
workers, tracing officers, and eventually vaccines, and the experimental setup. Second, we
present the results of our analysis for the reproduction number, cumulative number of cases,
cumulative number of deaths, cases in isolation, and cases not in isolation. Third, we discuss our
findings and potential future research directions, followed by the conclusions.
Methodology
We present a model combining a SEIR core with possible interventions aimed at stopping
the Ebola epidemic in West Africa. The model is represented using System Dynamics
(henceforth called SD).2°28 We use the model in a Scenario Discovery approach”? to explore the
consequences of the different combinations of uncertainties on the dynamics of the epidemic,
and test the effects of different intervention strategies.
Model description
The SD model extends the traditional SEIR model by including a set of endogenous
interventions. SD is a method for modeling and simulating dynamically complex systems or
issues characterized by causal relations, feedback loops, accumulations, and delays. Although
Causal Loop Diagrams and Stock-Flow Diagrams are used to explain the complexity of the
system, which is characterized by feedback and accumulation effects, in an understandable
way,3° SD models are essentially systems of differential equations. Numerically integrating these
equations results in a simulation of the dynamically complex behavior of the modeled system.
This simulation can be used to analyze problems related to the system, and to evaluate the effects
of policy interventions in these systems. SD is regularly used to study disease dynamics and
health policy.273!
The central structure of the model contains a Susceptible, Exposed, Infectious, and
Recovered population (Figure 1). We made several changes to this basic structure. We divided
the infectious population in a critical phase, where patients may either recover or die. The
recovering patients are still infectious. Therefore, they are modeled using a second stock
variable, the infectious survived population, who are recovering and will survive. We subdivided
(i.e., vectorized or subscripted) these population stocks to take into account that the population
may start to apply some self-quarantining. We assume that infecting the self-quarantined
population is more difficult than infecting the rest of the population, and that the self-
quarantined infectious outside isolation are less infectious to their surroundings. The S, E, and I
stocks outside isolation, and the flows between these stocks, thus contains this subdivision. In
Figure 1, these stocks have a bold border. Introducing this structure is important, as a succesful
societal reaction to an outbreak leads to a significant decrease in necessary intervention
capacities like isolation capacity. Next to this, motivating the population to change behavior in
this way can be seen as an intervention itself.
Further, we added isolation capacity to the model, containing again two stocks for the
critical and the survived infectious population. Treating and burying of the formally isolated
happens at a lower infectivity rate, while the non-isolated deceased may still infect the
susceptible population before their burial takes place. We, therefore, added a stock for the
unburied deceased population. Finally, we included a stock for those who will be vaccinated
when vaccines become available. This vaccinated population, and the recovered population, are
assumed to be no longer susceptible to EBOV.
[Tsotated—] Teoied
infectious
population Isolated
surviving
Salle dying and
‘burying isolated
Isolated
recovering
Buried
deceased
opulation
Unsafe burying tie?
- ues
Population Sotetion spaleton
self-quarentining Non-isolated
recovering
Ss E Nom isolated
Exposed suring
Leoeuaton J infecting Teno] Incubation
DklImmunization
Tmmur
population
Figure 1. Stock-flow structure of the extended (other factors and causal relations are not shown) SEIR model
containing isolated population stocks, and the immune population due to vaccination. SEIR elements are indicated
with their respective letters as well. Subscripted stocks have a bold border, infectious stocks are red, and the exposed
population is blue.
All interventions are limited in their capacity. Therefore, we included in this model the
endogenous development of the availability of isolation capacity (i.e., beds), health workers,
tracing officers, and vaccines. All intervention capacities are modeled as aging chains containing
stocks for the preparation of capacity and the available capacity. These stocks are separated by
delay time that may hinder timely reaction to an epidemic.3233
The capacities for isolation and other interventions are modeled adaptively: if needed,
they are expanded, albeit delayed. In this way, the numbers of health workers, tracing officers,
and available vaccines increase. For health workers, the possibility of getting infected by EBOV
and consequentially dying of EVD is taken into consideration,#4 thus reducing their availability.
We assume that fully recovered healthcare workers will try to continue their efforts after an
extensive recovery time. Further, healthcare workers may be recruited domestically or from
outside the region. All physicians needed are assumed to be foreign. Only a small portion of the
susceptible population is considered suitable for nursing since they are not trained to protect
themselves properly, but a larger part of the recovered population is suitable for nursing, since
they are immune.
Finally, if the medical staff capacity is not sufficient for the isolation capacity, the
isolation capacity will be limited following the available staff numbers. This represents the
closing down of EVD treatment centers due to illness of staff.
Experimental setup
The model was implemented in the Vensim modeling softwares and parameterized for
the Liberian situation. The model contains 161 variables, of which 20 were subdivided for
hygienic and normal behaving population (i.e., vectorized or subscripted), and 35 were
considered uncertain. We simulated the model for 400 days, with a time step of 0.25 days using
the Runge-Kutta 4 auto numerical integration method. For the 35 uncertain parameters, we used
a Latin Hypercube sampling approach, based on the ranges in Table 1. We generated 10.000
samples. The model and scripts for the analysis can be found in the supplementary material.
Table 1. Uncertainties used as model input. Factors for which no literature reference exists, are indicated as
assumption.
Variable name Unit Min Max References
“Average contact rate infectious bs 3 3
population Day. 3 9 3,17, 37
Average development timeisoation yy, ad a8 eaiveateacapenatine gs
“Average infectivity for medical staff _1/Day 0.0087 0.046 Derived from analysis; 36
“Average extra recovery time — oid
Averages Day 0.5 4.66 3; Derived from analysis
“Average time staff active Day 185 341 Derived from analysis
“Average time until burial Day 0.5 2 37
Average time until return diseased ’ .
ripeness Day 21 60 ‘Assumption
“Average period critical condition Day 4 9 3
Case fatality rate in isolation relative py. i ace Broad bandwidth around data from 3;
to outside isolation Dimensionless = 0.43 0.73 Derived from:analysis
Case fatality rate outside isolation Dimensionless 0.45 0.86 3:
Contact rate before funeral 4/Day 0.32 0.97 Derived from 236;
Contacts to be traced per f - a 3
umn ee Contact/Person 5.47 40 Bachinsky and Nizolenko (20)
_ ope | Contact/ a :
Contacts traceable per tracer perday GME 10 40 Bachinsky and Nizolenko (20)
Delay time development new ; Assuming that vaccines will be available
vaccines Day 250 350 in first or second quarter of 2015
Doctors per nurse Dimensionless 0.12 0.46 Assumption; Derived from analysis
Effect of self: behavior Dit 2.28 20 Assumption
Fraction recovered population useful yi nensionless 0.000458 0.043 Assumption; Derived from analysis
as medical sta
Fraction susceptible population oe 7 a a
en ee Dimensionless 1.86E-06 0.000189 _ Assumption; Derived from analysis
Incubation period Day 7 45 WHO Ebola Response Team 3
Initial exposed population Person 50 100 WHO"
Initial isolation capacity Person 120 600 WHO"
Initial relative susceptible hygienic py: wancionless oot 02 assoiptlbn
population
Initial tracing personnel Person 5 30 Assumption
Initial vaccines in preparation Vaccine 4 20 ‘Assumption
Lifetime isolation capacity Day 180 360 Assumption; Derived from analysis
Medical staff creating awareness 4/Day 5 100 Assumption
Medical staff per new case 4/Day 0.2 05 WHO"
Preparing time foreign staff Day 14 60 Assumption; Derived from analysis,
iHiou sate diseased Dimension 02 0.95 Broad bandwidth around WHO *"
Relative reduction in infectivity due nencionless 0.7 5 Ascuropition
to isolation
‘Training time new staff Day 3 10 ‘Assumption
Vaccination speed Vaccine/ 50 240 Assumption (estimate)
(Person"Day)
Results
Scenario selection
The epidemiological data provided by the WHO presents the number of cases and deaths
measured to date. However, it is plausible that this data considerable underreports the actual
number of EVD cases.'9 The WHO acknowledges this in its roadmaps.37 Therefore, we used both
the measured cumulative cases and the actual cumulative cases as indicators for selecting the
plausible scenarios from the total set of runs. The measured cumulative cases are the cases
reported and found by tracing officers and the cases that report themselves. The actual
cumulative cases are all cumulative EBOV infected cases. The measured cumulative cases was
required to be minimally the reported number of cases, while the actual number of cases was
required to be maximally 4 times the reported cases. Therefore, we take a slightly broader
bandwidth than the potential underreporting correction factor of 2.5.9 Following this recipe, we
were able to select 16 scenarios out of a total of 10000 model simulation runs.
Measured cases
Actual cases
Tie (day) Tie (ay)
Figure 2. Dynamics for measured cases, historic data Figure 3. Dynamics for actual cases, historic data from
from WHO ts indicated in dashed lines. The figure hasa — WHO is indicated with dashed lines. The figure has a
logarithmic y axis. logarithmic y axis.
The 16 scenarios visible in Figure 2 and Figure 3 each provide a different internally
consistent explanation of the measured data by the WHO. The runs start at the moment when
the WHO reported 51 cases in Liberia, so t=o can be interpreted as 22 June 2014. In the best-
case scenario, the underreporting of cases is limited due to relatively sufficient tracing officers
capacities. Consequentially, the required additional capacities for isolation and medical staff, as
well as for the additional tracing officers, can be estimated adequately, resulting in a situation
where the disease can be controlled before the whole population becomes infected.
In the worst-case scenarios, the tracing capacity is inadequate, which leads to inadequate
development of isolation and medical staff capacity. This can be seen by comparing Figure 4 and
Figure 5. Figure 4 shows the total non-isolated infectious population, while Figure 5 shows the
isolated infectious population. First, the peak in the non-isolated population is considerably
earlier than the peak in the isolated population. In these instances, the intervention capacity has
missed the real peak in the epidemic. Second, missing this peak makes that an order of
magnitude difference exists between the maximum non-isolated infectious and the maximum
isolated infectious in the worst-case scenarios.
In the worst-case scenarios, changes in population behavior (e.g., when part of the
diseased actively seek help at treatment centers, even when they were not traced) will have less
effect, as the required isolation capacity and treatment is not available. Therefore, it is the
weakest link in the intervention capacities that determines the strength of the intervention
capability.
8.8 8 8
Total quarantined infectious
population (thousand)
Time (day)
Figure 4. Total non-isolated infectious population Figure 5. Total isolated infectious population dynamics
dynamics
Limits in EBOV intervention capability influences the speed with which the virus is
transmitted. The assumption underlying these dynamics is solely that an isolated EVD case is
less infectious than a non-isolated EVD case. The results of this are illustrated in Figure 6, which
shows how the reproduction number develops in the 16 scenarios. In the best-case scenario, the
reproduction number will gradually decline as intervention becomes more effective. In the
worst-case scenarios, however, we see that a failure to isolation a majority of EVD cases leads to
a considerable increase in the reproduction rate of the disease, causing a significant increase in
the effective reproduction number. As a result, we see that the doubling time of the number of
cases declines (Figure 7). This indicates an increased spreading of EBOV, which leads to the
break in current trends visible in Figure 2 and Figure 3. When the EBOV transmission is over its
peak, the doubling time will quickly rise as the effective reproduction number falls below 1.0.
Effective reprocuction number
Doubling time (day)
50 700 Bo oo 30 800 ae aDO
BOO 200
Tima (cay) Timo (cay)
Figure 6. Effective reproduction number dynamics Figure 7. Doubling time dynamics
For two distinct reasons, scenarios showing an increased effective reproduction number
may be plausible in the case of the 2014 West Africa EBOV epidemic. First, the reproductive
number is the result of infectious people having contact with their surroundings (e.g., as they are
being treated by family members, or in the case of unsafe burials). Therefore, if the relative share
of infectious population that cannot be isolated increases, due to limitations in either available
beds or available trained and well-equipped staff, then the effective reproduction number is also
expected to increase. Second, many studies estimating the base reproductive number of EBOV or
similar diseases assume that the intervention capability is not available at the beginning of the
epidemic, while its adequacy increases over time (e.g., 338). In the case of the 2014 EBOV
epidemic in West Africa, however, it seems as though the intervention capability is getting less
adequate over time (compare data in 37), potentially resulting in the dynamics simulated here.
Effect of a more proactive approach
The response to the EBOV epidemic was initially inadequate, leading to a situation in
which the outbreak could become out of control . The exponential character of the spreading of
EBOV in the early phases of the outbreak might explain this. Since the response leading to an
increase of the intervention capability is delayed, the capacities that become available will often
fall short of the capacity required, especially when, for example, insufficient tracing capacities
further increase the underreporting of the speed with which the virus propagates through
society. Therefore, it may be needed to use a more proactive approach in increasing the
intervention capacities, trying to be ahead of future increases in cases, while taking irreducible
delays in the development of new capacities, into account. The following formula captures this
kind of proactive planning:
Te
Cert = Cu * Craes *( 1+ (=) —C
2
Where:
Ct41 is the capacity to develop;
C, is the expected underestimation factor of the number of EVD cases;
Czaes is the presently desired capacity;
Tc is the delay on capacity development;
Tz is the doubling time for the number of EVD cases;
C, is current available capacity.
The motivation for this formula is that while preparing new intervention capacities, one
should be prepared for those EVD cases that will arise during the preparation time, as well as the
exposed population that will become infectious after the deployment of the additional capacities.
If the preparation time is relatively short compared to the doubling time, the necessary extra
capacity is, therefore, smaller. Existing capacity may be subtracted from the capacity to develop.
It should be noted, however, that in the case of probable underreporting of the number of EVD
cases, the presently desired capacity should be multiplied with the expected underestimation
factor.
In any scenario, a more proactive approach will lead to a decrease in both the total
number of cases (Figure 8) and the total number of deaths. However, the effectiveness of this
change in intervention capacity development depends largely on the phase of the epidemic;
when the spread of the virus is already decreasing and the doubling time is increasing (Figure 9),
the potential gains are smaller.
Actual cases (milion)
Doubling time (day)
30 o_O 300-380 aDO
Time (day) Time (day)
— Reactive response — Reacte response
~ Proactive response starting at ey 110 ~~ Proactiv response starting at day 110
Figure 8. Total cases with proactive intervention Figure 9. Doubling time dynamics with proactive
expansion from day 110 intervention from day 110
The effectiveness of a more proactive approach is especially clear when it is applied
earlier in the exponential growth phase of the epidemic (Figure 10 and Figure 11). These figures
show the result of starting the proactive approach at day 50. The worst case is now logically the
scenario in which an initial underestimation of the size of the epidemic leads to an early increase
in the reproductive number of the virus. Consequentially, it becomes more difficult to control the
EBOV outbreak. An early proactive approach in building up the total spectrum of intervention
capacities thus decreases the final scale of the epidemic, characterized by the cumulative cases,
considerably.
Actual cases (milion)
Effective reproduction number
Time (day)
page
SE ee ren RL Tl Re eo aneialst
Figure 10. Total cases with proactive intervention Figure 11. Total deceased with proactive intervention
expansion from day 110 from day 110
Discussion
The results presented in this study provide plausible scenarios for the spread of the
EBOV in Liberia, but should not be interpreted as forecasts of the future number of cases or
deaths. Rather, we present an extended what-if analysis to explain how the epidemic might
evolve under circumstances similar to the situation in Liberia in between June and October
2014.
For several reasons, the actual disease spread may be less dramatic than the worst-case
scenarios presented in this study suggest. First, the geographic spread of the population may
lead to a slower virus transmission. Within certain areas, the susceptible population may be,
therefore, actually smaller than the assumption underlying our simulation model that the
susceptible and infectious populations outside isolation are perfectly mixed. Further, this model
does not contain possible social and psychological dynamics of the population that may
considerably slow down EBOV transmission, nor the existence of asymptomatic infections and
acquired immunity.39
Finally, this research is not exhaustive in the possible intervention measures. We have
not modeled essential medical supplies besides the medical staff and bed capacity in isolation.
Further, we have assumed that the intervention capacities developed will not be hindered by lack
of available resource, for example skilled medical personnel, in foreign countries. However, the
same principle applies to these other measures: Any under capacity will harm the effectiveness of
the total intervention capability. The entire intervention capability is as strong as the weakest
capacity in the chain.
Conclusions
In this article, we have demonstrated that the current under capacity in intervention
measures for combatting the 2014 West Africa EBOV epidemic may lead to an increased effective
reproduction number. The consequence of such a situation may be that the growth in the actual
number of EVD cases accelerates significantly. This finding is derived from an extended SEIR
model that includes key intervention capacities endogenously, parameterized for the situation in
Liberia.
This research suggests that the reproduction number of the current Ebola epidemic may
increase compared to the measured base reproduction number: if the capacities of the different
interventions are not brought to the minimally required level. Such a situation with sufficient
intervention capacities is in contrast with the situation in the first half of October 2014 in
Liberia, which shows a significant shortfall in bed capacity, caused by both a lack of health care
staff and a lack of operational bed capacity in Ebola treatment units.4°
This under capacity may be caused by an overly reactive response to the initial
exponential growth of the number of EVD cases. A more proactive approach in expansion of the
intervention capacities may, therefore, help in controlling the 2014 West Africa EBOV epidemic,
as well as future epidemics. A proactive approach takes into account how the development time
of these capacities relates to the doubling time of the disease, and the factor by which the
measured cases may be underreported. A proactive and faster reaction is especially important
before the EBOV becomes endemic in the West African region.4
Acknowledgements
The authors would like to thank Michiel van Boven and Jacco Wallinga of the
Netherlands National Institute for Public Health and the Environment (RIVM) for their valuable
feedback, Artur Usanoy (strategic analyst at HCSS) for his feedback during the modeling phase,
and Roberta Coelho (assistant analyst at HCSS) for their help during the research.
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