With an outbreak developing rapidly in Guinea, many have been wondering: is there a chance that #Ebola2014 will spread to the United States? Maia Majumder combines elements of mobility, epidemiology, and probability to tackle this global health question.
Quick Answer: Don’t worry yet. As of 4/20/2014, 203 cases have been reported by the WHO – confirmed and suspected – out of Guinea’s population of about 10000000. Here’s what the model derived below spits out:
P(Ebola Spreads to the USA) = [(1)(203/10000000)(8/19)]/(21/38) = ~.0015%
7.29.2014 – The probability of actually getting on an airplane after contracting Ebola is not considered in this initial calculation.
3.25.2014 – While Ebola is exceptionally rare, the fact that it’s currently erupting in West Africa changes our own chances of contracting the disease. So, just how likely is it that #Ebola2014 will make it to the United States? Though we don’t yet know how far the virus has managed to spread outside of Guinea, we do know is that it’s both highly contagious and can exhibit long incubation periods, making it a prime candidate for contagion. It’s quite possible for individuals who are infectious to feel healthy enough to travel, and traversing long distances has become easier than ever thanks to the advent of commercial airplanes. At its very core, this question sits at the crux of globalization, infectious disease epidemiology, and conditional probability. In this post, we’ll try to address this problem by using crude human mobility analytics and an approximation of Bayes’ Theory.
As a refresher, Bayes’ Theory helps us find the probability of Event A given that Event B has already occurred – AKA, P(A|B). To take this approach, we need to have an intelligible idea of what the probabilities of Event A and Event B – AKA, P(A) and P(B). We also need to know what the probability of Event B is given that Event A has already occurred – AKA, P(B|A). So, without further ado, let’s define our events:
Event B: Ebolavirus outbreak occurs in Africa in 2014Event A: Ebolavirus spreads to the United States from Guinea in 2014
According to Bayes’ Theory, we find P(A|B) as follows: P(A|B) = [P(B|A)P(A)]/P(B)
So, this is what we know off the bat:
P(B|A) = 1
…Because if Ebola spreads to the USA from Guinea, there’s a 100% chance that there’s Ebola currently active somewhere in Africa.
P(B) = 21/38
…Because there have been 21 outbreaks in Africa since 1976, when Ebola was first identified and recorded.
P(A) = …This is where things get a little interesting.
Here are a few assumptions I’m going to make this more feasible for solving:
1. The disease can only spread to the United States by air travel out of Guinea. Thus, infected individuals can only transmit the disease via Conakry International Airport. The prevalence of disease among air travelers is consistent with that of the general Guinean population.
2. JFK International Airport in New York City is the only point of entry into the USA used by infected individuals traveling from Guinea into the States.
3. Because there is no direct flight from Canokry International Airport to JFK, individuals use one of the following common flight routes: [Conakry – Dakar – Dubai – NYC]; [Conakry – Casablanca – NYC]; or [Conakry – Paris – NYC]. The probability that an air traveler out of Conakry chooses any of the above routes is determined solely by availability.
4. Flights that do not travel from Conakry to Dakar, Casablanca, or Paris do not impact the likelihood of Ebolavirus arriving in the USA.
5. As long as a person who is infected with Ebola is on any given flight from Conakry to Dakar, Casablanca, or Paris, we can expect it to transmit all the way to NYC – whether the individual carrying the virus goes to NYC or not. We make this assumption because of the highly contagious nature of the disease; combined with the fact that an airplane is an enclosed space, this makes for an ideal transmission setting. Basically, we theorize that the disease will on average spread to at least one of the individuals on the plane who are taking the route all the way through to NYC. While highly imperfect, this statement helps us solve the equation as fully as possible.
So, how does this list of assumptions help us define Event A? Because we state that the only way the disease will end up in USA is via air travel from Conakry, what we really need to know is how likely it is that an air traveler flying out of Conakry is: (1) infected with Ebolavirus and (2) flying through Dakar, Casablanca, or Paris. Event A happens at the intersection of these two smaller events, (1) and (2). As set theory would have it, by multiplying (1) and (2) together, we’ll get P(A). Because we assume that an air traveler out of Conakry is just as likely to have Ebolavirus as the rest of the population, we can solve the first half as follows: (Prevalence of Ebolavirus in Guinea) = # Cases / # Total Population = 87/9982000
For the second half, we need to figure out how likely it is that any given air traveler that is flying out of Conakry will be on a plane that goes to Dakar, Casablanca, or Paris. We can do a quick and dirty estimation based off of which airlines fly out of Conakry and the destinations they serve. Six airlines fly to Dakar; one airline flies to Casablanca; and one airline flies to Paris. A total of nine airlines fly out of Conakry, serving 19 locations, 12 of which are unique. Thus, the likelihood that any given flight leaving Conakry will go through Dakar, Casablanca, or Paris is 8/19.
Thus, we can conclude:
P(A) = (87/9982000) x (8/19)
Now, it’s just a matter of plugging in all the different values into Bayes’ model:
P(A|B) = [P(B|A)P(A)]/P(B) = [(1)(87/9982000)(8/19)]/(21/38) = ~.0007%
That is a teeny, tiny number – thankfully! However, as the number of cases increases, the value of P(A) will also go up. To give you a sense of how the number of cases identified in Guinea would effect our own likelihood seeing Ebola in the USA, here’s a chart based off of the above model:
This of course assumes that no travel ban will be instated, which is highly unlikely if case numbers continue growing. However, not adjusting for this is at least in part mediated by the fact that as the number of cases in Guinea grow, the likelihood of transmitting Ebola to other countries also increases. If Ebola spreads further in Guinea’s neighboring countries, the probability of seeing it in the USA will also increase because there will be more opportunities for the virus to travel aerially.
As we learn more about #Ebola2014, I’ll be making adjustments to the model developed here so that it better represents how the disease is proliferating. While we’ll need to see much steeper prevalence in West Africa before our own risk even enters the single digit percentages, this application Bayes’ Theory to #Ebola2014 crystallizes just how significantly the capacity of disease transmission has changed due to globalization. #Ebola2014 may not yet be an immediate threat to those of us living in the United States, but without question – the 4,000 miles between New York City and Conakry is not as large a distance as it appears.