# Abstract

Background: The 2014 West African Ebola outbreak has evolved into an epidemic of historical proportions and catastrophic scope. Prior outbreaks have been contained through the use of personal protective equipment, but such an approach has not been rapidly effective in the current epidemic. Several candidate vaccines have been developed against the Ebola virus, and are undergoing initial clinical trials.

Methods: As removal of population-level susceptibility through vaccination could be a highly impactful control measure for this epidemic, we sought to estimate the number of vaccine doses and timing of vaccine administration required to reduce the epidemic size. Our base model was fit using the IDEA approach, a single equation model that has been successful to date in describing Ebola growth. We projected the future course of the Ebola epidemic using this model. Vaccination was assumed to reduce the effective reproductive number. We evaluated the potential impact of vaccination on epidemic trajectory under different assumptions around timing of vaccine availability.

Results: Using effective reproductive (Re) number estimates derived from this model, we estimate that 3-4 million doses of vaccine, if available and administered, could reduce Re to 0.9 in the interval from January-March 2015. Later vaccination would be associated with a progressively diminishing impact on final epidemic size; in particular, vaccination to the same Re at or after the epidemic is projected to peak (April-May 2015) would have little impact on final epidemic size, though more intensive campaigns (e.g., Re reduced to 0.5) could still be effective if initiated by summer 2015. In summary, there is a closing window of opportunity for the use of vaccine as a tool for Ebola epidemic control.

Conclusions: Effective vaccination, used before the epidemic peaks, would be projected to prevent tens of thousands of deaths; this does not minimize the ethical challenges that would be associated with wide-scale application of vaccines that have undergone only limited evaluation for safety and efficacy.

# Funding Statement

Ms. Tuite is funded by a Banting and Best Doctoral Award from the Canadian Institutes of Health Research. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors have declared that no competing interests exist.## Introduction

The 2014 West African Ebola epidemic has evolved into a human catastrophe of historical proportions ^{1} ; as of October 22, 2014, nearly 10,000 reported infections, and over 4,800 deaths, had been reported ^{13}. While Ebola virus has a low reproductive number, and prior outbreaks have been controlled through use of personal protective equipment (PPE) and stringent burial practices ^{2} , the current epidemic has continued to grow despite these interventions. It has been noted that the speed with which Ebola treatment centres (ETC) can be constructed could easily be outstripped by growth in case numbers at rates that have been seen throughout the epidemic ^{11}, and the most recent available World Health Organization situation report suggests that the number of staffed ETC beds in most-affected countries is remains smaller than promised, and is insufficient to permit care of all incident Ebola cases, with only 13% of cases in Sierra Leone cared for in ETC ^{19} .

An important driver of epidemic spread is the presence of abundant susceptible individuals who are both themselves at risk for infection, and who then infect others, resulting in the exponential growth in incidence that characterizes epidemics ^{3}. While reducing transmission through PPE and case isolation can reduce the reproductive number to less than one (causing incidence to decelerate), an abundant supply of susceptible individuals means that such efforts need to be maintained indefinitely. By contrast, immunization in the context of an outbreak or epidemic has the attractive property of both preventing acquisition of infection by susceptible individuals, but also reducing the force of infection (rate at which susceptibles become infected, by reducing numbers of infectious cases); if sufficient fractions of the population are immunized, an epidemic should end rapidly.

Several promising candidate vaccines against Ebola virus are currently in clinical trials ^{12} . Although these trials are ongoing, and consequently, information about vaccine efficacy is unavailable, it would be desirable to approximate how many doses of vaccine would be required to substantially change the trajectory of this epidemic, and what the impact would be of delays in time to immunize substantial numbers of people. We used an existing mathematical model of the 2014 West African Ebola epidemic to model the quantity of a hypothetical highly effective vaccine needed to substantially decrease epidemic size, and also to simulate the impact of vaccination timing and dosing with a hypothetical vaccine on the future contours of the epidemic.

## Methods

*The Effective Reproductive Number (R _{e}) and Its Relation to Immunity*

The basic reproductive number (R_{0}) for a communicable disease can be defined as the average number of secondary infections produced by a primary infection in a wholly susceptible population, and in the absence of intervention. Many mathematical models heavily emphasize the role of susceptibility in maintaining transmission, such that the effective reproductive number (R_{e}) is represented as:

*R _{e} = S·R_{0}* [Eq. 1]

Here *S* is the susceptible fraction of the population. Using a well-fitting mathematical model (the Incidence Decay with Exponential Adjustment (IDEA) model ^{4}^{,}^{5} ), we observe that the West African Ebola epidemic is well-characterized as a process where R_{e }is declining over time even as susceptibility in the population remains high; if *S* remains close to 1, declining *R _{e}* must represent a combination of behavioral change and public health and medical intervention, or the presence of large numbers of unrecognized infections

^{6}. However, even in the presence of four-fold under-reporting (i.e., with 40,000 cases rather than approximately 10,000 cases in the region as of mid-October 2014), the fraction of immune individuals in the population would still be < 1%; as described below,

*R*has fallen by over 20%. In the presence of an

_{e}*R*when susceptibility is widespread, we can estimate the likely impact of a hypothetical 100% effective vaccine based on the relation:

_{e}<R_{0 }
*R _{e}‘ = R_{e}(1-V)* [Eq. 2]

*R _{e}‘* is the effective reproductive number in the presence of vaccination and V is the proportion of the population vaccinated. This relation can be rescaled based on vaccine efficacy (

*E*) less than 100%, such that:

*R _{e}‘ = R_{e}(1-VE)* [Eq. 3]

*IDEA Model and Projection of Re*

We projected the future course of the epidemic using the IDEA model ^{4}^{,}^{5} , as described elsewhere. Briefly, this descriptive single equation model describes epidemics as processes characterized by exponential growth (a function of *R _{0}*), with corresponding exponential “control” parameter (

*d*), according to the relation:

*I _{t}= [R_{0}/(1+d)^{t}]^{t }*[Eq. 4]

Here *t *is the epidemic “generation” (based on serial intervals, approximated as incubation + 1/2 the duration of infectiousness; we use 15 days for Ebola ^{7} ). *I _{t}* is incident infections in a given generation, and

*d*is a control parameter identified through fitting. Since the denominator is second order, incidence eventually approximates zero and the epidemic ends. As described elsewhere, our approximate end date for the 0

^{th}generation of the epidemic is January 6, 2014, and subsequent generation end dates are calculated at 15 day serial intervals from this date

^{7}. Using this approach based on data available through August 22, 2014 we had previously estimated the global

*R*for the current Ebola epidemic to be approximately 1.7

_{0}^{5}, similar to estimates of other investigators

^{8}

^{,}

^{9}. We updated this model using World Health Organization case reports to October 18, 2014 (generation 19) obtained from a publicly accessible data repository maintained by Caitlin Rivers at the Virginia Tech [https://github.com/cmrivers/ebola]. We assumed the observations were Poisson distributed and used maximum likelihood methods to identify best-fit model parameters (using the

*mle2*function in the

*bbmle*R package

^{18}), and modeled best- and worst-case scenarios based on upper- and lower-bound 95% confidence intervals (calculated using the

*bbmle confint*function

^{18}). Because

*R*and

_{0}*d*estimates are positively correlated

^{5}(i.e., well-fitting models with higher

*R*have higher

_{0}*d*) our worst case scenario was based on lower bound values for both parameters, while our best case scenario was based on upper bound parameter values for both parameters. Model fits were performed in the open source R statistical environment (http://www.r-project.org/).

We estimated time-dependent estimates of *R _{e}* using model-generated projections of per-generation incidence.

*R*at some time

_{e}*t*can be estimated as:

R_{e} = I_{t}/(I_{t-1}) [Eq. 5]

This is simply the ratio of incident case counts in succeeding generations. Based on time-dependent estimates of *R _{e}* we calculated vaccine doses needed to drive

*R*to 0.9 or to 0.5 in January, February, or March 2015 using Equation 2, and based on a population of 22

_{e’}^{10}million persons (the approximate combined population of Guinea, Sierra Leone, and Liberia, where the epidemic has been centered). We assumed a 100% efficacious vaccine with a single dose required for immunity. For purposes of simplicity, we initially modeled the expected impact on epidemic scenarios when available doses could be given instantaneously. However, real-world vaccination programs would require time for implementation, and so we also explored more realistic scenarios with 10 million doses of vaccine administered in a rolling manner, at either 1 or 0.5 million doses per month, and starting in January, February, or March 2015. We also explored the impact of vaccination with vaccine with efficacy < 100%.

## Results

*Model Fits , Projections and Estimated Re*

Maximum likelihood estimates for *R _{0}* and

*d*were 1.79 (95% CI 1.78-1.81) and 0.00922 (95% CI 0.00879-0.00966) respectively, and the model fit well to available data (

**Figure 1**).

When most likely parameters were used to simulate the full course of the epidemic, we projected an epidemic that peaked in April or May 2015 for all scenarios, and ended in August 2016 (July 2016-September 2016 for best and worst case scenarios, respectively), with a final size of approximately 200,000 cases (160,000 – 260,000) (**Figure 2**).

Model derived estimates for R_{e} are presented in **Figure 3**. It can be seen that *R _{e}* is estimated to fall steadily throughout the epidemic, approaching 1 when the epidemic peaks in April or May 2015. As the final size for the epidemic (in terms of recognized cases) is estimated to be approximately 1% of the regions’ population, this magnitude of decline in

*R*could not be accounted for by accumulation of immune individuals, even in the presence of significant under-recognition and under-reporting of cases.

_{e }Based on Eq. 2 above, and assuming an at-risk population of 22 million individuals, we estimated the number of doses of vaccine that (if given instantaneously) would be necessary to reduce Re to 0.9, or to 0.5, by January, February or March 2015 in all three scenarios (**Figure 4)**.

Regardless of timing and scenario, between 3 and 4.9 million doses of a highly effective vaccine would be required to reduce *R _{e}‘* to 0.9; 11.5 to 12.5 million doses would be needed to reduce

*R*to 0.5.

_{e}‘The projected impact of reduction of Re to 0.9 or 0.5 on epidemic contour for our most likely scenario is presented in **Figure 5**.

Qualitatively similar results were seen for best and worst case scenarios (not shown). Vaccination markedly reduced projected epidemic size for all start dates. In all cases earlier vaccination resulted in a more substantial reduction in the final epidemic size than later vaccination. While vaccination sufficient to reduce *R _{e}‘* to 0.5 resulted in smaller epidemics than reducing

*R*to 0.9 for a given start date, it is important to note that earlier immunization (January 2015) to reduce

_{e}‘*R*‘ to 0.9 resulted in a comparable final epidemic size to that achieved by reducing

_{e}*R*‘ to 0.5 in March 2015 (87,800 cases vs. 74,800 cases).

_{e}We performed additional analyses in which *R _{e}‘ *was reduced to 0.9 or 0.5 as late as October 2015 (

**Figure 6**). If vaccination reduces

*R*to 0.9 and is initiated at or after the epidemic peak (April or May 2015), the reduction in total cases becomes negligible, as the epidemic’s

_{e}‘*R*would be reduced below 1 even in the absence of vaccination. With more intensive vaccination to reduce

_{e}*R*to 0.5, there is a wider time-window during which large reductions in epidemic size is possible, but again, after August 2015 even intensive vaccination results in little change in projected final epidemic size.

_{e}‘We performed an additional series of analyses based on our most likely scenario, in which 10 million doses of a hypothetical vaccine were available. Doses were administered either at a rate of 1 million doses per month over a 10-month period, or at a rate of 500,000 doses per month over a 20 month period. This “rolling vaccination” scenario could begin in January, February, or March of 2015 (**Figure 7**). Earlier and more intensive vaccination was most impactful.

As with instantaneous vaccination, earlier start dates resulted in markedly reduced final size; for a given start date more intensive vaccination resulted in more cases prevented (**Figure 8**).

We performed sensitivity analyses with varying vaccine efficacy (**Figure 9**). It can be seen that rolling vaccination strategies initiated as late as March 2015 could still impact the final epidemic size, even with vaccine efficacy substantially < 100%.

## Discussion

While trials of vaccine for Ebola virus are ongoing, and consequently the estimates presented above are imprecise, our analysis offers four important qualitative results regarding vaccination as a tool for the control of the Ebola epidemic that may be helpful to manufacturers, governments, and health organizations:

Like any mathematical model, the model we use is subject to limitations, including data inputs of uncertain quality (e.g., World Health Organization case counts), its descriptive rather than explicitly mechanistic nature, and limited information on the efficacy of candidate vaccines, including the number of doses that can be given per manufactured vial. We do not wish to imply that manufacture of sufficient doses of vaccine is the only barrier to the implementation of a successful vaccine program; other hurdles related to implementation and cold chain are likely to exist; furthermore we note that even in the event that a vaccine is created, other challenges (including accurate and timely case identification, provision of safe and effective medical care, and adequate protection of caregivers and those involved in burial) are likely to remain. Furthermore, apparent successes have been seen in regional control of the epidemic with non-pharmaceutical interventions; notably, ETC beds in heavily populated areas of Liberia have been empty in October 2014, perhaps as a result of implementation of safer burial practices and other interventions ^{20}.

Nonetheless, the epidemic continues to grow in West Africa as a whole, and the qualitative projections presented here are important, as they suggest that the window for effective use of vaccination will close rapidly if vaccine is not deployed. This in turn raises important ethical questions, as a vaccine program deployed in early 2015 would of necessity lack the usual level of certainty about vaccine efficacy and safety 16 . We would argue that the catastrophic nature of the Ebola epidemic may make widespread use of novel and little tested vaccines, with close monitoring, and ideally in the context of stepped-wedge clinical trials 15 , may in fact be the only ethical alternative if sufficient vaccine is available.

**Addendum:** During the time period while this paper has been under review, an additional generation of case counts has become available for incorporation into our analysis (case counts as of November 2, 2014). As incorporation of these data into our model did not change our projections we have presented the analysis based on October 18, 2014 case counts; we anticipate updating our model regularly and will post important changes in projected epidemic contour as comments on this paper.

# Acknowledgements

The authors wish to thank Dr. Robert Malone for his encouragement related to this manuscript.# References

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