How many travelers need to be checked in order to prevent one case of Ebola in the United States?

Note (added on Oct 12th): several of my colleagues think that my analysis is too optimistic. Specifically, they think that the epidemic is currently larger than the reported numbers and they think that the epidemic will keep on growing. 

I was planning to spend this week’s class entirely on discussing a polio outbreak in Hispaniola in 2000, but the students asked whether we could spend a little more time on Ebola. Of course I was happy to comply.

I decided to ask the students to work in groups of three to estimate how many travelers would have to be screened at American airports to prevent one case of Ebola in the United States. The goal was to get a ballpark answer. I hoped that the exercise would give my students a feeling for the numbers in the Ebola epidemic. The answers they came up with varied widely. I think that for each Ebola patient that may be found by airport screenings, we’d need to screen at least 26,000 travelers. But if the epidemic grows much bigger than it is now, this number will go down.

Here is a description of how this number could be calculated.

How many people currently have Ebola, but are not yet too sick to travel?

(Note that those that have died cannot travel and let’s assume for now that those that have recovered don’t travel either)

In the last couple of weeks there have been approximately 900 new Ebola cases per week, or 129 per day (link Wikipedia).

“West Africa Ebola 2014 Reported Cases per Week Total” by Malanoqa – Own work.

The average incubation period of Ebola is 8 to 10 days (link CDC), so I’ll use 9 days for now. Each of the patients who get infected will therefore, on average, be asymptomatic for 9 days, meaning that on any given day, 129 x 9 = 1161 patients are infected but asymptomatic. After the incubation time, patients may show symptoms, such as fever, but may still be able to travel. I haven’t found any good information on how long this period lasts on average. In the case of Thomas Duncan, I understand that he went to the hospital for the first time on September 25th, and by September 28th he was vomiting all over the ambulance. I’d assume that he may have gotten a fever one or two days before the 25th, which means that he may have had symptoms for 5 days before he became too sick to travel.

In the case of the Spanish nurse Theresa Romero Ramos, it seems that there were seven days between the moment she started feeling ill and the day that she was so sick she called an ambulance (link CNN). So, if we take the average from those two cases, it means that patients may feel sick and have a fever for six days before they become too sick to travel. This means that at any one point in time, 129 x 6 = 774 patients may have a fever because of Ebola, but could still travel.

I therefore estimate the total number of people with Ebola, but still able to travel to be around 1161 + 774 = 1935.

How does this number of infected people compare to the number of people in the affected countries?

OK, so I now have a rough idea of how many people have Ebola at any one time, with or without symptoms, who could still travel. Next, let’s see how these numbers compare to the total number of people who live in the countries that are affected (Sierra Leone, Liberia, Guinea). From Wikipedia I learned that there are approximately 20 million people in the three countries combined. This means that, if you’d pick a person at random from one of the three countries, the probability that they have Ebola is around 1935/20,000,000 = 0.0001 (one in 10,000). The probability that they have Ebola with no symptoms would be 1161/20,000,000 = 0.00006 (one in 17 thousand) and with symptoms 774/20,000,000 = 0.00004 (one in 26 thousand).

How many infected people could fly from West Africa to the United States?

The next step is to look at how many people travel to the United States from the three affected countries. Several news outlets reported that around 150 or 160 people travel to the US from the three countries every day. If one in 10,000 people in infected, then we may expect that one infected person would travel to the US in the time that 10,000 people in total travel to the US. With 160 travelers per day, 10,000 people travel to the US in 10,000/160 = 62.5 days, or roughly two months. In other words, we should expect about one traveler with Ebola to arrive in the US every two months.

If we split this up again in asymptomatic and symptomatic Ebola patients, we find that we should expect an asymptomatic patient (like Thomas Duncan) every 17000/160 = 106 days (3.5 months) and a symptomatic patient every 26000/160 = 161 days (5.5 months) arriving in a US airport.

If the airports in the United States would check every traveler from West Africa for Ebola symptoms, I’d expect them to find one such patient every 5.5 months, in the time they screen 26,000 travelers. During that time it is quite likely that an asymptomatically infected person enters the US, because we should expect one every 3.5 months.

It seems to me that a screening for fever or Ebola symptoms at US airports is not very useful. In fact, I assumed in my calculations that everyone is equally likely to travel, whether they have a fever or not, unless they become too sick to travel. This is probably not true, especially because everyone is already screened at the airport when they leave one of the affected countries. If someone already has a fever, they will not be allowed to board a plane. This means that the screenings at the US airports are even less likely to find Ebola patients.

My conclusion: simply screening for fever and other symptoms is not useful

Screening may be useful for other reasons though. For example, it may the a good opportunity to provide information to travelers who have arrived from West Africa.

The effect of the size of the epidemic

I’ve assumed that the epidemic will stay at the size it is now (900 cases per week). I am not an epidemiologist and know little about Ebola, but there have been a steady 900 cases per week since four weeks, so I think it could stay this way. However, if the epidemic still grows, then there will also be more infected people traveling. However, no matter how big the epidemic gets, I think it will always be more likely that asymptomatically infected people arrive at an airport than then symptomatically infected people. There are two reasons for this: first, once symptoms start, people get quite sick quite quickly and may be unlikely to travel, secondly, everyone is already checked at the African airports.

Checks at the airports of the African countries

According to the New York Times, already more than 36,000 people have been screened as they left West Africa in the last two months. 77 of these people were not allowed to fly, but none of them turned out to have Ebola.

Because everyone is already checked in West Africa before boarding the flight and, possibly again when they have a lay-over in Europe, it becomes even more unlikely than I initially calculated that someone with symptoms arrives in the USA.

Comparison of my calculations with data

If 36,000 people have left the three affected countries by air in the last two months (I am not sure if this number is accurate as I have only seen it in the NYT, but let’s assume), then my calculations suggest that the expected number of patients among them would have been 3.6 (of course there can never be 3.6 patients, rather an integer number fairly close to it. I assume here that the epidemic was the same size over the last two months, even though it was a bit smaller in the first month). If we assume that only asymptomatic people travel, then the expected number of exported cases would be 2.1.

As far as I know, there have been only two cases of people taking the virus with them on a plane: Thomas Duncan and the patient who took Ebola to Nigeria (link Wikipedia). Two is not significantly lower than the expected 3.6, and really close to 2.1. Wow, I did all this handwaving and made a ton of assumptions, and the real number is not too different from my calculated prediction! 

The reasonable fit between reality (2 cases) and the prediction (3.6 or 2.1) suggests that the data we have on the epidemic may be quite accurate. For example, if the epidemic really would be much bigger than reported because of unreported cases, then we should have seen more exported cases of Ebola. Of course, it is also possible that the epidemic really is much bigger, but one of my assumptions is not correct. For example, it may be that people who are infected with Ebola are not as likely to travel as other people.

Corrections?

Please let me know if you find any mistakes in this post.