Appendix: Additional Results and Technical Notes for the EbolaResponse Modeling Tool

Additional Results

Numbers of Ebola virus disease cases (hereafter referred to as Ebola) and daily number of beds in use in Liberia and Sierra Leone alone (Figure 1) and in Liberia and Sierra Leone combined (Figure 2) were estimated using the EbolaResponse modeling tool. The outcome of potential interventions on number of cases and beds in use in the two countries combined was simulated (Figure 3).

EbolaResponse Model Overview

CDC has created a spreadsheet-based modeling tool called EbolaResponse that allows users to estimate the number of Ebola cases in a community (available at http://dx.doi.org/10.15620/cdc.24900). The model tracks patients through the following states: susceptible, infected, incubating, infectious, and recovered (an SIIR model). EbolaResponse is, in effect, a Markov chain model and is similar to an Ebola model built in 2004 (1).

Probabilities drawn from reports of previous Ebola outbreaks are used to model the daily change in patients' status between and within the SIIR states. For example, to estimate the duration of the incubating state, data were adapted from a previous study (2) that indicate the likelihood that an incubation period will last a certain number of days, up to a maximum of 25. A patient can only progress forward through the states and can never regress (e.g., go from the incubating state back to susceptible) or skip a state (e.g., go from the incubating to the recovered state, skipping the infectious state). All infected persons were assumed to eventually become symptomatic. That is, the state of being infected but not becoming symptomatic at any period was not considered.

Assumed Population Size and Numbers Initially Infected

Community sizes equal to the populations of either Liberia or Sierra Leone were assumed and used. The community size can be readily altered. Numbers used in the model as initially infected were chosen to match the number of cases first recorded (2).

Liberia

• Population: 4,294,000 (3)
• Initially infected: Nine

Sierra Leone

• Population: 6,092,000 (3)
• Initially infected: 30

Incubation State

Data from two sources (2,4) were used to construct a lognormal probability distribution of being in the incubation state (Figure 4, Table 1). The mean incubation period derived from this calculation is 6.3 days (standard deviation [SD]: 3.31 days), with a median of 5.5 days and a 99th percentile at 21 days.

In one study, data from a 1995 outbreak in the Democratic Republic of the Congo (DRC, formerly Zaire) and a 2000 outbreak in Uganda were used to estimate mean incubation periods of 5.30 days (SD: 0.23 days) and 3.35 days (SD: 0.49 days), respectively (1). These are lower than other published estimates (2,4). Some of the differences might be attributable to different subtypes of the virus (4).

The incubation distribution can be changed, with an upper limit of 25 days of incubation. Users of the EbolaResponse modeling tool can change the incubation distribution by selecting from two alternative, preprogrammed distributions available from the drop-down menu in the appropriate page in EbolaResponse. The two alternative distributions were based on previously published studies (2,4). As yet another alternative, users can enter their own distribution.

Infectious State

Average Number of Days

An average infectious state of 6 days was assumed in the model, which includes any time taken for a traditional burial. In comparison, data from a 1995 outbreak in DRC and a 2000 outbreak in Uganda (the latter caused by the Sudan strain of Ebola) (5) were used to calculate estimated mean infectious periods of 5.6 and 3.50 days, respectively (1). Data from the 1995 Ebola outbreak in the Congo also were used to calculate an estimated mean infectious period of approximately 6 days (6). Repeated testing of patients with Ebola has demonstrated that the amount of virus present increases until death or approximately 6–10 days after initial infection (7). The EbolaResponse modeling tool can be used to adjust this period from 1 day to a maximum of 15 days.

The risk for onward transmission of infection to a person in the susceptible state was assumed to be equal throughout the 6 days. No data were found regarding whether risk for onward transmission changes over the duration of fulminant illness. However, the possibility exists that the risk does change as a patient becomes more ill and requires more care.

Burial Practices

Traditional burial of the body of a person who has died from Ebola could involve contact with body fluids, posing a risk for infection. For example, in northern Uganda, the body is prepared for burial by the paternal aunt (or if no paternal aunt exists, by an older woman on the paternal side of the family). After removing clothes from the body, the woman washes and dresses it. Funeral rituals include all family members washing their hands in a common bowl and touching the face of the deceased person in the open casket, referred to as a love touch. A white cloth is used to wrap the body, and the body is buried (8). Although this burial ritual is an example from Uganda, researchers have mentioned that similar practices occur throughout Africa (9). Because cultural practices regarding burial might vary by region, users might want to change the period of infectiousness in the model.

Population Governor

Although an exposed state is not included in the model, a population governor is included that prevents the model from calculating more cases than the input population. This overestimation is possible if a user of the model assumes that most of the patients remain home with no effective isolation, the patient category that has the highest risk for onward disease transmission (Table 1).

The governor was programmed by reducing the daily estimate of persons newly infected proportionate to the cumulative reduction in the susceptible population as follows:

Factor to reduce estimate of newly infected at
Day t = [Model population – Cumulative total of newly infected up to Day (t-1)] / Model population

This governor reduces, on a daily basis, the estimated number of persons infected, which effectively lowers the risk for transmission (Table 1). In most instances, this governor is unlikely to affect the calculations from large populations. The governor only begins to appreciably reduce estimates when approximately 40%–50% of the population has become infected. The EbolaResponse governor also is programmed so that the minimum value of the calculated factor cannot be less than 0, preventing the possibility of negative cases.

Distribution Over Time of Patients by Patient Category

Patients were categorized by three types of patient. These three categories have different levels of isolation: 1) hospitalized, 2) home or in a community setting such that there is a reduced risk for disease transmission (including safe burial when needed), and 3) home with no effective isolation.

• Hospitalized patients are in facilities such as Ebola treatment units (ETUs) where medical care is provided. Ideally, such facilities have infection-control protocols that prevent additional disease transmission. However, this is not always the case, and health-care workers in medical care facilities have been infected after contact with Ebola patients (10). Therefore, the average daily risk for transmission is greater than zero in these facilities (i.e., transmission occurs), but the risk is fewer than one person infected per infectious patient (Table 1).
• A patient who is at home or in a community setting such that there is a reduced risk for disease transmission (including safe burial when needed) is being attended to with the overall goal of reducing transmission to other members of the household. If the patient dies, safe burial practices are used. Risk is fewer than one person infected per infectious patient (Table 1).
• A patient who is at home with no effective isolation is being attended to at home but with no specific infection-control measures in place. In addition, if the patient dies, no measures are in place to limit transmission. This patient category has the greatest risk for onward transmission (Table 1).

These three categories have varying risk for onward Ebola virus transmission over time (Figure 5). The estimated values were calculated by altering these values with the risk for onward transmission (Table 1) as well as the number of imported cases or cases in patients with no known contacts (Table 2). All of these values were altered until the estimates of cases produced by the model closely matched (i.e., fit) the reported cases to date (see also Goodness of Fit section).

The distribution of patients into the three patient categories influences the overall progress of the epidemic. For example, the more patients who are hospitalized and at home or in a community setting such that there is a reduced risk for disease transmission, the slower the progress of the epidemic because these two categories are calculated to have transmission rates of fewer than one person infected per infectious person (Table 1). A certain proportion of patients who were home or in a community setting such that there is a reduced risk for disease transmission and home with no effective isolation was assumed to eventually become hospitalized in ETUs (Table 3). However, they were assumed to be hospitalized so late in the progression of the disease that the average risk for onward transmission was unchanged.

Risk for Onward Transmission

The risk for onward transmission from an Ebola patient in the infectious state to persons in the susceptible state varies by patient category (Table 1). The estimated values were calculated by altering these values along with the distribution of patients by category of patient (Figure 5) as well as the number of imported cases or cases in patients with no known contacts (Table 2). All of these values were altered until the estimates of cases produced by the model closely matched (i.e., fit) the reported cases to date (see also Goodness of Fit section).

Allowing for Imported Cases or Cases in Persons With No Known Contacts

The ability to add imported cases (whole numbers) every 10 days was built into the EbolaResponse modeling tool. These persons are entered into the model as infected and then go through incubation before becoming infectious. Imported cases represent 1) Ebola cases in persons who travel into the community undetected from another outbreak-affected area or 2) cases in persons whose infection cannot be readily explained by contact tracing (i.e., apparently no known contact with a previously ill patient). The values shown (Table 2) were used to calculate the estimated cases presented in the main report.

The estimated number of imported cases per each 10-day time step were calculated by altering these numbers along with the distribution of patients by category of patient (Figure 5) as well as the risk for onward transmission (Table 1). All of these numbers were altered until the estimates of cases produced by the model closely matched (i.e., fit) the reported cases to date (see also Goodness of Fit section).

Likelihood of Being Hospitalized and Duration of Hospital Stay

To estimate daily hospital admissions and daily number of beds in use, both the likelihood of a patient being hospitalized and the number of days that a patient in each patient category would spend in the hospital had to be assumed (Table 3).

Correcting for Potential Underreporting

Substantial underreporting of cases might be occurring both in Liberia and Sierra Leone (11). To adjust for such a possibility, the calculated daily number of hospital beds in use was compared with expert opinion of number of beds in use. A correction factor of approximately 2.5 was calculated for Liberia (Table 4). Therefore, to obtain an estimate of actual cases, the reported cases are multiplied by 2.5. After a corrected number of cases was calculated, the model was refitted (see Goodness of Fit section).

Goodness of Fit

The following three variables were altered so that the estimates from the model more closely matched (i.e., fit) the actual reported cases:

• Percentage of patients in each of the three patient categories, with percentages changing over time in increments of 30 days (Figure 5)
• Daily risk for transmission of Ebola by patient category (Table 1)
• Addition of imported cases (Table 2)

For both the Sierra Leone and Liberian data, these three numbers were altered until the estimates of cases for either Sierra Leone or Liberia produced by the model fit the reported cases to date (Table 5, Figure 6) (12). Visual inspection was used to validate the fit of the model-predicted cases to the actual reported cases (Figure 6).

Interventions

Controlling the Epidemic

The EbolaResponse modeling tool was used to construct a scenario to illustrate how control and prevention interventions can slow and eventually stop the Ebola epidemic in Liberia. Control is achieved by moving patients who are being attended to at home with no effective isolation to either the hospitalized category or at home or in a community setting such that there is a reduced risk for disease transmission (including safe burial when needed) category (see also Distribution Over Time of Patients by Patient Category). The more patients who are hospitalized or being attended to at home or in a community setting such that there is a reduced risk for disease transmission, the slower the progress of the epidemic because these two categories are calculated to have transmission rates of fewer than one person infected per infectious person (Table 1). The interventions affect the cumulative numbers of cases of Ebola and daily beds in use (Figure 3, Figure 7).

Methods

Applying Interventions and Distribution of Patients into Categories

As described previously, in the EbolaResponse modeling tool, Ebola patients are categorized by three levels that result in different levels of isolation: 1) hospitalized, 2) home or in a community setting such that there is a reduced risk for disease transmission (including safe burial when needed), and 3) home with no effective isolation. These three categories affect the risk for onward Ebola virus transmission; the highest risk for transmission occurs among patients who are in the third category (Table 1). In the absence of a universal preventive intervention (e.g., vaccine), control of the epidemic consists of having as many patients as possible in either the hospitalized category or at home or in a community setting such that there is a reduced risk for disease transmission category.

To illustrate how increasing the percentage of patients in these two categories can control and eventually end the epidemic in Liberia, the following circumstances were assumed. Starting on August 24, 2014 (day 151 in the model), the percentage of patients hospitalized in ETUs was assumed to increase from 10% of all patients to 17%. In the subsequent 30 days (starting September 21, 2014), the percentage was increased to 25% and stayed at that level for the remainder of the simulation (Figure 8). In addition, starting on August 24, 2014, the percentage of patients at home or in a community setting such that there is a reduced risk for disease transmission (including safe burial when needed) was increased from 8% of all patients to 20%. This percentage was increased to 30% for the following 30 days (starting September 21, 2014). This percentage was then increased to 35% for the 30 days starting October 23, 2015, followed by increases to 40% and 45% on November 22, 2014, and December 22, 2014, respectively (Figure 7).

With the described increases of patients, by December 22, 2014, a total of 70% of patients (25% hospitalized in ETUs and 45% at home or in a community setting such that there is a reduced risk for disease transmission) are estimated to be in the two categories that are known to reduce Ebola transmission.

Fitting the Model and Goodness of Fit

As described previously, to estimate the potential impact of interventions, the input values of the distribution of patients, the risk for onward transmission, and the number of imported cases or cases with no known contacts were altered in the EbolaResponse modeling tool. The interventions are assumed to start after the date of the last reported case. Therefore, the input values for imported cases are the same as those shown for Liberia (both uncorrected and corrected) (Table 2). Similarly, the same values were used for the daily risk for transmission (Table 1). Because the interventions start after the date of the last reported case, the originally calculated input values (Table 1, Table 2, and Table 3) and the resulting goodness of fit for the Liberian data (Table 5 and Figure 6) are all valid for the intervention scenario.

Cost of Delay

To illustrate the cost of delay, in terms of additional cases and the resulting need for additional resources to end the epidemic, in starting to increase interventions that can control and eventually stop the epidemic, a separate control-and-stop scenario was first constructed as follows. Starting on September 23, 2014, and for the next 30 days, the percentage of all patients in ETUs was increased from 10% to 13%. This percentage was again increased on October 23, 2014, to 25%, on November 22, 2014, to 40%, and finally on December 22, 2014, to 70% (Figure 9) (i.e., it takes 90 days for the percentage of patients in ETUs to reach 70% of all patients). The percentage of patients at home or in a community setting such that there is a reduced risk for disease transmission was kept at 8% from September 23, 2014, through the remainder of the period covered by the model. The impact of delay of starting the increase in interventions was then estimated by twice repeating the above scenario but setting the start day on either October 23, 2014, or November 22, 2014.

Starting an intervention on September 23, 2014, such that initially the percentage of all patients in ETUs are increased from 10% to 13% and thereafter including continual increases until 70% of all patients are in an ETU by December 22, 2014, results in a peak of 1,335 daily cases (3,408 cases estimated using corrected data) and <300 daily cases by January 20, 2015 (Figure 10). Delaying the start of the intervention, until October 23, 2014, results in the peak increasing to 4,178 daily cases (10,646 cases estimated using corrected data). Delaying the start further, until November 22, results in 10,184 daily cases (25,847 estimated using corrected data) by January 20, 2015, which is the last date included in the model (Figure 10).

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