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Monday, September 15, 2014

Ebola Update #1

April 29, 2015
My latest update regarding the history of the Ebola epidemic can be found here:
Ebola Update #1
The first post in this series provided a projection of the growth of the Ebola epidemic, if the disease is not effectively contained.   Two methods were used to make a mathematical fit to the data and extrapolate the cumulative number of cases.  Extrapolation of the current trend shows that massive numbers of people could become infected in a short period of time.  The cumulative number of cases is doubling every month.  If the epidemic continues to grow at the same mathematical rate, one million people could become infected by April 2015.  Further extrapolation would pass one billion cases in the fall of 2015 to early 2016.
December 17, 2014: 
The exponential growth rate of the Ebola epidemic continued for about two months after my original blog post.  The exponential trend was broken in mid-October, 2014, thanks to global relief efforts and effective public health programs in the affected countries.  Updates to my original charts can be found here:
This post will look at new data and efforts to contain the epidemic.  The World Health Organization (WHO) is monitoring the situation, publishing periodic updates, and developing strategies for containing the epidemic.  Since my first post on this topic, the cumulative number of cases and deaths reported by WHO has generally matched the exponential projections. 
As the epidemic grows and social order breaks down in affected areas, data is likely to become less complete and more uncertain, limiting what can be done with analytical tools.

Extrapolation Method #1: Exponential Regression
A regression through the data is easily performed in Excel.   The data chosen begins on May 23, at a point where about 10 new cases were appearing every day, and the number of cumulative cases showed steady exponential growth.   The original regression through the data resulted in the following formula, counting days from May 23, 2014:
Number of Cases = 285.6e(0.0239 * number of days

A regression including the new data changes the exponent only slightly, to e(0.0248 * number of days), and changes the date for 1 million cases from April 29th to April 17th.
Extrapolation Method #2: Contagion Model
In the original model, each infection is assumed to lead to 1.31 subsequent infections, following a lag of eight days.   New data is still a good fit to this trend.

After some thought and reading, I realized that I neglected the incubation period in defining the contagion model.  A better model would assume that the subsequent infection would occur after about 8 days of the original case diagnosis.   An additional 8 days should be required for the incubation period of subsequent cases.   I changed the model to a 16 day interval between diagnosis of the initial case and subsequent cases, and fit the data by changing Ro from 1.31 to 1.63.   The new model is in close agreement with the first method, an exponential regression to the data.

Containment Efforts
The WHO is coordinating efforts to contain the epidemic.  On the 28th of August, the WHO issued a report as a roadmap to the containment effort.  At the time, 3069 cases of Ebola had been reported in West Africa.  The report acknowledges that in some areas, the actual number of cases may be 2 to 4 times the number of reported cases.

This WHO roadmap outlined procedures for containing the outbreak, defined roles for coordination of relief efforts, defined metrics for success, and specified the budget necessary to perform the work.  A total budget of $490 million was requested.

This report forecast that as many as 20,000 cases might occur, and that six to nine months might be required for eradication of the outbreak.   No processes or programs are identified in the event that the success metrics are not met.

Containment Procedures
The process employed by WHO in West Africa is the same process used successfully to combat previous Ebola outbreaks.   The process is straightforward, but labor-intensive.  Treatment centers are established for confirmed cases of Ebola, and isolation centers are established to evaluate suspected cases.  When cases are confirmed, patients are transferred to the treatment centers.  Patients suspected of having an Ebola infection are interviewed, to determine what other people they might have infected.  All of their contacts are monitored for 21 days.  For the WHO planning document, each patient was assumed to have 10 contacts which need to be monitored.   Further, for each 70 bed hospital, about 200 to 250 staff are required to care for the patients.

Clearly, as the number of Ebola cases rises, the ability to contain the epidemic becomes more strained.  As the disease grows exponentially, the required staffing also grows exponentially.  The current rate of new cases is about 140 new cases daily, as of September 13.   This implies 1400 new contacts, each day, which must be monitored for 21 days.  Over the next few weeks, there will be 30,000 to 45,000 new contacts who must be monitored for signs of the disease.  The September 12th update to the WHO Roadmap acknowledges that the capacity for contact tracing in Guinea, Liberia, and Sierra Leone is under extreme pressure.  The capacity to perform safe burials is also under stress.
Complicating the problem of obtaining sufficient staff to treat the epidemic are the grim statistics for health care workers.  As of September 7th, 301 health care workers had contracted Ebola, and 144 have already died.

I am uncertain of the status of funding for the WHO roadmap.  President Obama requested $88 million from Congress to contribute to the containment effort, but Congressional leaders approved only $40 million.   Philanthropist Bill Gates gave $50 million to various agencies, and his former business partner Paul Allen donated $9 million, in addition to $2.8 million he gave last month.   The US Department of Defense, in a statement pathetically detached from reality, promised to construct a 25-bed field hospital, with no provision for staffing.   A spokesman later defended the offer, saying that it represented the minimum contribution which the Army might make.

As I prepared to publish this post, a new article appeared on Google News.  President Obama will visit the US Centers for Disease Control for a briefing on the Ebola outbreak.  Today, in advance of his visit, the president requested $1 billion from Congress for the US military to fight the epidemic in West Africa.

Limits to Growth
The WHO Roadmap plan seemed to offer the best hope for an early and successful resolution of the crisis, but there are already indications that the plan is failing.   Treatment centers are overwhelmed by as many as 4-times as many patients as capacity and are turning away as many patients as are being admitted.   There is no hope of containing the disease with rising numbers of Ebola carriers returning to their homes to spread the disease.

The window for successfully containing the epidemic is rapidly closing.   At some level of contagion, social order will break down entirely.  At that point, treatment of cases will become difficult or impossible; clear data about the status of the epidemic may disappear.  The problem of the epidemic will be complicated by the refugees fleeing affected areas – and possibly propagating the disease to new places.  A number of senior Liberian government officials have already fled the country.

WHO appears to have no contingency plan in the event that the August 28th Roadmap fails.  If medical intervention fails, we have to consider the natural limits to growth of the disease and the size of the population at risk.  Monrovia, capital of Liberia, is the site of most reports of inadequate medical facilities.  Monrovia has a population of 1 million within an area of 5 square miles.   On a slightly larger scale, Sierra Leone and Liberia, with a combined population of 10 million, have the greatest active transmission of disease.  The nation of Guinea is also considered by WHO as having widespread and intense transmission, bringing the potential population exposure to 21 million.  As the disease has spread along the coast, it is now active in two Liberian counties adjacent to Cote d’Ivoire.  It seems possible that Cote d’Ivoire’s population of 22 million may also be at risk.  

Considering these numbers in combination with the extrapolations above, we can make a few guesses about the future spread of the disease.  A few university scientists in the United States are beginning to talk in terms of hundreds of thousands of possible victims.  By year-end 2014, West Africa may hit a cumulative 100,000 cases, with about 30,000 active cases.  The majority of these can be expected to be in Monrovia, Liberia.  By mid-February 2015, the countries of Liberia, Guinea, Sierra Leone, and possibly Cote d’Ivoire may experience a cumulative 430,000 cases, or 1% of the total population, with over 100,000 active cases.  These are the locations, the dates, and the numbers that should be used for planning the next steps in the epidemic response.  If the epidemic grows to these numbers, new processes and tactics are needed to combat the disease.

The Hot Zone
For those wishing to know more about Ebola, the best-seller “The Hot Zone”, by Richard Preston, is an informative non-fiction account of earlier Ebola outbreaks and research.  The book is tautly well-written in the style of a horror novel.  The symptoms of Ebola are described graphically, and are quite horrific.  It requires a strong stomach to read this book.

Doctors Without Borders
The relief organization “Doctors Without Borders” is one of the leading players in fighting the Ebola epidemic.  I’ve just given them a donation.

In many situations, people give money to relief organizations in response to a disaster, such as a hurricane or an earthquake.  In this situation, timely giving may help limit the scale of the disaster.


WHO Ebola Response Roadmap, August 28, 2014


Inadequacy of Current Response

General Facts and Graphs about Ebola

The Hot Zone
Best-selling, factual book about Ebola
Richard Preston, 1994, The Hot Zone, 300 pp., published by Random House, New York.


  1. It looks like the CDC's worst-case scenario (1.4 million cases by January 20th, 2015) exceeds even your "Extrapolation Method #2: Contagion Model" assessment/estimate. The CDC's best-case scenario assumes "assumes that the dead are buried safely and that 70 percent of patients are treated in settings that reduce the risk of transmission", but their report showed "the proportion of patients now in such settings as about 18 percent in Liberia and 40 percent in Sierra Leone".

    I wonder if they have a secret "don't show the public who would stupidly panic" report with an estimate of the probability that this Ebola virus strain evolves a way to be transmitted through the air.

  2. Hi Steve -- The CDC's worst-case scenario does exceed my Extrapolation Method #2, with Ro = 1.63. The CDC acknowledges unreported cases, and assumes that there are 1.5x unreported cases for every reported case. Further, they extrapolate to 550,000 reported cases by January 20, while my most aggressive analysis shows 200,000 cases by January 20. So the CDC numbers get very large, very quickly. My next post will put some geography to these numbers, to see where and when populations will be at risk. At some point, populations will become saturated, and the rate of transmission must drop. On the other hand, as long as the epidemic can spread to new populations, without containment, it will grow.

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