The Math Of An Ebola Epidemic, And Why The Administration’s Isn’t Adding Up

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Most students either love or hate math. I fall in the former category, because love it or hate it, it is one of those subjects that is absolute. While there are many wrong answers there only one correct one. Math is not subject to interpretation and does not bend to the winds of political correctness. Numbers do not regard race, religion, gender, or sexual preference.

Math also doesn’t care about the politics of Ebola, where it started, who catches or spreads it, and ultimately how large of problem it will be. But there are certain mathematical attributes of Ebola, which we collectively ignore at our peril. Math doesn’t lie.

The first is the reproduction rate. In other words, now many new cases develop from the initial index case. The best estimates of the reproduction rate during the current outbreak in Sierra Leone, Guinea, and Liberia range from 1.5 to 2.5. Let’s use an average of 2.0. This means that one case will lead to two more cases, and those two lead to four cases, and so on.

We see this playing out in real time. Thomas Duncan, index case, led to two additional cases, Nina Pham, a nurse in Dallas, and as recently reported, Amber Vinson, a second nurse, both of whom cared for Mr. Duncan when he was sick. Who did these nurses come in contact with? Friends, family, coworkers? The CDC is now busy tracking everyone on the flight from Cleveland to Dallas taken by Ms. Vinson before she became ill. How did she get to Cleveland? Who was she with in Cleveland? It seems plausible that these two nurses could transmit an infection to four (or more) others.

The second is exponential growth. At a reproduction rate of two, the number of cases doubles with each generation of transmission. Two, four, eight, sixteen, and so on. Still small numbers. There is an old science question involving folding a piece of paper in half over and over again. Each time it doubles in thickness. And the numbers add up quickly, “It only takes 42 foldings of a paper to get from the Earth to the Moon, and only about 94 foldings of a paper to make something the size of the entire visible Universe.” If it takes two to three weeks to manifest Ebola infection, it won’t take that long for an exponential growth rate of Ebola to reach the moon.

The third mathematical notion can be called “hyper-exponential growth.” Amber Vinson, the second infected Dallas nurse flew on a commercial flight from Cleveland to Dallas. Interestingly, the CDC, “told her it was okay to fly.” This is based on the CDC assertion; “A person infected with Ebola is not contagious until symptoms appear.” Despite also telling the CDC that she had a fever. So then why is the CDC checking 132 travelers who were on the plane with her? If she was asymptomatic, she was not contagious, according to the CDC. The hyper-exponential growth here is that one infected individual leads to monitoring of over 100 other persons. What about those standing on a TSA line with Ms. Vinson? Or those handling her luggage? Or bringing her to or from the airport? The point is that a single infected individual leads to scrutiny of hundreds or thousands of other potentially exposed persons, clearly straining the resources of the CDC.

The fourth bit of math is viral load. “At the peak of illness, an Ebola patient can have 10 billion viral particles in one-fifth of a teaspoon of blood.” Compare that to 100,000 viral particles in active HIV infection or up to 20 million in Hepatitis C. How many viral particles does it take to create infection? Not sure anyone knows. But the math tells us that there 100,000 times as many Ebola than HIV virus particles in a droplet of blood. So which would be easier to catch if you were in close proximity to or exposed to bodily fluids an infected individual?

The fifth math item is hospital beds. If any of what I describe above comes to pass, where will these new Ebola cases be hospitalized and treated? Currently there are, “Only four hospitals equipped with special containment units and experienced Ebola workers” according to the CDC. Emory University in Atlanta, the NIH in Bethesda, University of Nebraska Medical Center, and St. Patrick Hospital in Missoula, Montana. This is out of 5700 hospitals in the U.S. Further crunching the numbers, “These four units have a combined total of just 19 available beds suited for Ebola patients.” There are recommendations to treat new Ebola cases only at these specialized hospitals with the most recent Dallas nurse being transferred to Emory.

Remember exponential growth? 2-4-8-16-32-etc? After two or three more transmission cycles, those 19 beds will be full and where will patients then be sent? Even large hospitals such as Texas Health Presbyterian Hospital Dallas, “a respected, renowned hospital” was unable to properly contain the index case despite their best efforts following CDC protocols. What happens when other Thomas Duncans find their way into the U.S. from West Africa, infected with Ebola and needing treatment? What about the thousands of U.S. military personal in West Africa, some of which are bound to become infected? How will 19 beds service hundreds or thousands of infected individuals?

Finally there is the math of dollars. The announcement of a second infected nurse dropped the Dow Jones Industrial Average 460 points. Fortunately it partially recovered, losing only 176 points (1 percent) for the day. What will happen with more cases? What if the public decides air travel is too risky given the risk and scrutiny applied to the 132 passengers on Amber Vinson’s flight? Expect the Dow to drop by thousands, not just hundreds of points. Math doesn’t lie.

Government officials can say what they want, reassuring us and telling us not to panic. Math, however, is unemotional. The numbers march on, regardless of elections, polls, political agendas, and fears. Even those who hated math in school understand basic arithmetic enough to know that the Ebola numbers coming from the administration and its various agencies don’t add up.

Dr. Joondeph is a retina surgeon at Colorado Retina Associates and serves on the faculty of Rocky Vista University School of Medicine. Twitter @retinaldoctor.