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Showing posts with label Ebola charts. Show all posts
Showing posts with label Ebola charts. Show all posts

Friday, November 7, 2014

Charting the 2014 Ebola Epidemic; March 11th Update

The following charts are updates to previous posts about the Ebola epidemic in West Africa. 
I will update these charts as new data becomes available.
Additional resources may be found at StopEbola.uk:

April 29, 2015
My latest update regarding the history of the Ebola epidemic can be found here:
http://dougrobbins.blogspot.com/2015/04/ro-and-history-of-ebola-epidemic-in.html
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March 11, 2015
Data from the World Health Organization is complete through March 8.

The exponential rate of growth observed in the initial months of the epidemic was broken in mid-October, 2014.   The rate of disease transmission fell from early December, 2014 to mid-January, 2015.  Since that time, the rate of transmission has remained fairly constant at about 50 new cases per day.  The most recent data indicates a slight increase in the rate of transmission.  The geographic dispersion of new cases is also a serious concern.

The Ro history for the epidemic has been calculated, and appears at the bottom of this update. Ro represents the rate of new disease transmission, with the number representing the number of new cases generated by each case of Ebola.  An Ro value greater than 1 means the epidemic is growing, and a value less than 1 means the epidemic is diminishing.  Ro approached 1.3 during the period of most rapid growth, and has been approximately 0.9 while epidemic declined.  A recent rise in Ro is noted, and is of some concern.

The most important chart of the Ebola epidemic is now the chart of daily new cases.  Daily new cases have been falling since early December, after peaking around 160 new cases per day. New cases fell to about 50 cases per day in the second week of January.  Since that time, the rate of transmission has stalled at about 50 new cases per day, with a slight uptick in the rate of transmission seen in the latest data.

The current rate of 50 new cases per day was last seen in early August, 2014.  This rate of disease transmission is still a tragedy, and still dangerous.  Ebola is a disease capable of explosive growth, and cannot be considered contained until it is eradicated.

The locus of disease transmission in West Africa has shifted westward, from Liberia to Sierra Leone and western Guinea.  The dispersion of new cases is also a concern.  In the last two weeks, new cases have appeared in four provinces of Guinea which border Senegal, Mali, and Cote d'Ivoire.  Intervention efforts must remain flexible to meet the disease wherever it appears.


Sierra Leone remains the most active area of Ebola transmission.
The chart of cumulative cases has taken on the S-shaped curve, indicating decline in the rate of transmission, but has not approached a zero rate of transmission.

Ro is the parameter which indicates the rate of transmission for an epidemic.  The number Ro indicates the number of subsequent new cases, on average, generated by each case.  Thus, an Ro value larger than 1 indicates a growing epidemic; an Ro value less than one indicates the epidemic is shrinking.  
I applied a 3rd-degree polynomial regression to three parts of the cumulative case chart.  (The entire case history was too complicated to represent well with a single expression, and contains some large data revisions in the middle of the epidemic.)   I used the regressions to smooth the data, and calculate the daily new cases, and the rate of Ebola transmission, assuming an average 8-day lag between infections.  
From these regressions, I calculated Ro for the history of the epidemic.
The epidemic grew quite rapidly during the period when Ro exceeded 1.2, in part due to the extremely rapid course of the disease.  Ro fell below 1 in late September, and the growth of the epidemic declined substantially.  New cases in Liberia are approaching zero, but the main locus of transmission has shifted westward, into Sierra Leone.  In the fall of 2014, the World Health Organization set a goal of placing 70 percent of patients in isolation, after which WHO anticipated ending the epidemic by January 2015.   Clearly, the desired level of disease transmission was not achieved, and the epidemic did not end.

Ro approached 0.9, at its lowest point.  While the number of new cases is still declining, Ro has begun rising again, which is a matter of serious concern.
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My previous posts on the Ebola topic can be viewed here:

Previous Posts
Discusses the exponential rate of growth of the epidemic, and likely future changes to the pathogen.
Discusses the inadequacy of the medical response in terms of a linear response to an exponentially growing problem.
Discusses the geographic distribution of populations corresponding to points on the exponential extrapolation.

References
http://www.who.int/csr/disease/ebola/situation-reports/en/

Infighting among health authorities fighting the Ebola epidemic.

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Obsolete Updates
February 13, 2015
Data from the World Health Organization is complete through February 8.

The exponential rate of growth observed in the initial months of the epidemic was broken in mid-October, 2014.   The rate of disease transmission fell from early December, 2014 to mid-January, 2015.  Since that time, the rate of transmission has remained fairly constant at about 50 new cases per day.  The most recent data indicates a slight increase in the rate of transmission.  The geographic dispersion of new cases is also a serious concern.

The most important chart of the Ebola epidemic is now the chart of daily new cases.  Daily new cases have been falling since early December, after peaking around 160 new cases per day. New cases fell to about 50 cases per day in the second week of January.  Since that time, the rate of transmission has stalled at about 50 new cases per day, with a slight uptick in the rate of transmission seen in the latest data.

The current rate of 50 new cases per day was last seen in early August, 2014.  This rate of disease transmission is still a tragedy, and still dangerous.  Ebola is a disease capable of explosive growth, and cannot be considered contained until it is eradicated.


The locus of disease transmission in West Africa has shifted westward, from Liberia to Sierra Leone and western Guinea.  The dispersion of new cases is also a concern.  In the last two weeks, new cases have appeared in four provinces of Guinea which border Senegal, Mali, and Cote d'Ivoire.  Intervention efforts must remain flexible to meet the disease wherever it appears.



The following charts are updates to the original extrapolations made on this blog in early August.  
The Ebola Response Roadmap issued by the World Health Organization on August 28, acknowledged that the aggregate case load could exceed 20,000 cases, which I considered unrealistically optimistic at the time.  The reduction in the rate of growth to date, remarkably, appears to meet the projections of the WHO roadmap.  It is a credit to the all of the organizations working to end the epidemic to see the progress made to date.  But the job is not complete, and the situation remains dangerous, as long as the disease continues to spread in Sierra Leone, or any other locality.


January 15, 2015
Data from the World Health Organization is complete through February 1.  Case numbers from Liberia continue to lag data from Sierra Leone and Guinea.

The exponential rate of growth observed in the initial months of the epidemic was broken in mid-October, 2014.   The rate of disease transmission has been falling since early December, 2014.

The most important chart of the Ebola epidemic is now the chart of daily new cases.  Daily new cases have been falling since early December, after peaking around 160 new cases per day. New cases fell to about 100 cases per day in early January, and are now trending downward at about 50 new cases per day.   

The current rate of 50 new cases per day was last seen in early August, 2014.  This rate of disease transmission is still a tragedy, and still dangerous.  The locus of disease transmission in West Africa has shifted westward, from Liberia to Sierra Leone and western Guinea.  Intervention efforts must remain flexible to meet the disease wherever it appears.

December 24, 2014
Data from the World Health Organization is complete through December 20.  Case numbers from Liberia continue to lag data from Sierra Leone and Guinea.

The exponential rate of growth observed in the initial months of the epidemic was broken in mid-October, 2014.  If the original rate of growth had continued, cumulative cases would number about 45,000, rather than the current figure of 19,400.  A tragic number of new cases are still occurring.   Over 100 people are still falling ill with Ebola every day.

The rate of daily new cases is falling, but erratically.  The number of daily new cases is persistently high, and not far below the peak number of cases seen in October and November.
December 1, 2014
Data released on December 1 2014 by the World Health Organization shows that the epidemic set a new record in the number of daily new cases, exceeding 200 new cases per day.  The interpolated and smoothed chart below also shows a new record of 161 new cases per day.

The daily number of new cases had been declining from early November through November 17, raising hopes that the epidemic was coming under control.  However, the latest case numbers from Liberia and Sierra Leone have sharply reversed that trend.  These numbers are insufficient to draw clear conclusions, as we have only a few data points.  But the reversal of the declining trend and the new record of daily new cases are extremely troubling.

As progress is made against the epidemic, the most dangerous opponent may be complacency.
November 29, 2014
The growth rate of reported Ebola cases has stabilized when considering the entire epidemic.   There has been a sharp reduction in the rate of transmission in Liberia.  However, gains in Liberia are offset by a continuing high rate of transmission in Sierra Leone, as seen in the following charts of cumulative cases by country, on linear and logarithmic scales.  The epidemic continues to grow at a nearly exponential rate in Sierra Leone, with only slight improvement noted in the past two weeks.

The following charts are updates to the original extrapolations made on this blog in early August.
  
The Ebola Response Roadmap issued by the World Health Organization on August 28, acknowledged that the aggregate case load could exceed 20,000 cases, which I considered unrealistically optimistic at the time.  The reduction in the rate of growth to date, remarkably, appears to meet the projections of the WHO roadmap.  It is a credit to the all of the organizations working to end the epidemic to see the progress made to date.  But the job is not complete, and the situation remains dangerous, as long as the disease continues to spread in Sierra Leone, or any other locality.



November 21, 2014
Figures from the World Health Organization show a continuing trend of improvement in the cumulative number of Ebola Cases.  Rates of transmission are falling in Guinea and Liberia, although the daily number of new cases is still rising in Sierra Leone.  The falling rate of transmission in Liberia indicates success in educating the public about the disease and implementing basic public health measures.   At this time, only 18 of 53 planned Ebola treatment centers are open.  The epidemic is diminishing due to success in changing behaviors which contributed to the spread of the disease.

Six cases have now been reported in Mali, which borders Guinea to the north.  Contacts from these cases are being traces.  Still new infections in Mali represent a troubling extension of the disease into the interior of Africa, and outside the countries with intensive efforts to quell the epidemic.

Like firefighters working to control a wildfire, efforts to quell the epidemic must continue unabated as long a sparks remain. The official number of daily new cases is now about 150, down from 170 about two weeks ago.  There is good reason to be hopeful, but the fire is still burning.

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The following chart is the number of reported daily new cases of Ebola, interpolated and smoothed with a nine-day rolling average.  The exponential rate of growth was broken in mid-September.   Recent data is distorted by data revisions, but appears to have settled around 150 new cases per day. There are hopeful signs of a decline in new cases over the past two weeks, but there are still great doubts about the accuracy of the official case numbers.  Dr. Hans Rosling, epidemiologist acting as consultant to Liberia's Health Ministry, stated on November 5, "We are absolutely sure that we cannot be sure about the data."

Death rates calculated from reported cases continue to fall.  While a decline in death rates is expected, the magnitude of decline seems improbable.  WHO also reports substantial under-reporting of Ebola deaths.  This should be of concern to health authorities, because it means that many burials are not being conducted according to safety protocols.


November 14, 2014

The latest figures from the World Health Organization show a continuing trend of improvement in the cumulative number of Ebola Cases.  Rates of transmission are falling in Guinea and Liberia, although the number of cases is now rising sharply in Sierra Leone.  The falling rate of transmission in Liberia indicates success in educating the public about the disease and implementing basic public health measures.   At this time, only 17 of 53 planned Ebola treatment centers are open.  The epidemic is diminishing due to success in changing behaviors which contributed to the spread of the disease.

Four cases have been reported in Mali, which borders Guinea to the north.  The three new cases are unrelated to the previously reported case, and represent a troubling extension of the disease into the interior of Africa, and outside the countries with intensive efforts to quell the epidemic.

Like firefighters working to control a wildfire, efforts to quell the epidemic must continue unabated as long a sparks remain.  The epidemic is still growing at a rate of about 160 new cases a day.  By comparison, in July of this year, the rate of transmission was about 20 cases a day.  The world was unable to control the epidemic at that level.

There is good reason to be hopeful, but the fire is still burning.

November 7, 2014

There are definite indications that the Ebola epidemic in Liberia is easing.  Anecdotal reports indicate there are beds available in treatment centers, and burial teams are collecting fewer bodies from the city.  Official numbers are unfortunately still highly questionable, with recent changes dominated by revisions, rather than by new cases.  Following a large upward revision on October 25, there has been an almost unbelievably low of number of reported new cases.   Recent case numbers in Sierra 
Leone are also dominated by revisions to previous estimates, but large numbers of new cases are still being reported. 

Avoidance of official treatment centers is still a problem, due to fear and cultural objections to the approved safe burial practices and/or cremation. 



The following charts were prepared from case numbers issued by the World Health Organizations.  Case numbers are subject to study and subsequent revision.  Reporting from the affected countries has been somewhat erratic, and at irregular intervals.  I interpolated the cumulative number of cases in certain countries to obtain discrete reporting dates for the entire epidemic.



The exponential extrapolation is the original extrapolation, created by an exponential regression to the data from May 23 to August 26, with days beginning on May 23.  Despite the recent positive reports from West Africa, data continues to fall near the line of the original extrapolation.

Sunday, October 12, 2014

Forecasting the 2014 Ebola Outbreak; Update #2

April 29, 2015
My latest update regarding the history of the Ebola epidemic can be found here:
http://dougrobbins.blogspot.com/2015/04/ro-and-history-of-ebola-epidemic-in.html
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December 17, 2014: 
The exponential growth rate of the Ebola epidemic continued for about two months after my original blog post in August, 2014.  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:
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There is no clear end-point to the Ebola outbreak in West Africa.  The Ebola outbreak in West Africa, now involves about 9000 reported cases, with the likelihood of an equal number of unreported cases (10/17 update).   Like ripples from a stone thrown into the water, the epidemic has the potential to infect heavily populated areas of west Africa, to spread across porous borders by people fleeing the epidemic, and to jump from large cities to other large cities. The following figure shows a timeline extrapolated from the exponential growth of the disease, and marked by points representing populations at risk.  Africa is impoverished and lacks the resources to maintain a stringent defense against the epidemic.  There are no firebreaks, and the world will be able to do very little to stop a general pandemic if the case numbers continue to grow well into the coming year.

Reports from the World Health Organization (WHO) are increasingly bleak.  The WHO October 8th situation report states:

” …the situation in Guinea, Liberia, and Sierra Leone continues to deteriorate, with widespread and persistent transmission of EVD [Ebola Virus Disease]….the reported fall in the number of new cases in Liberia over the past three weeks is unlikely to be genuine.  Rather, it reflects a deterioration in the ability of overwhelmed responders to record accurate epidemiological data….There is no evidence that the EVD epidemic in West Africa is being brought under control….”

The international community is increasing support to the affected countries.  New teams and equipment are being sent from the United States, Great Britain, Cuba and Nigeria, among others.  However, the scale and speed of the intervention appears too little and too late.   At this point, we have to ask where this epidemic is going, and when will it get there.

This is the third post on the topic of Ebola on this blog.  The first two are here:
Course of the Epidemic
We can consider the future course of the epidemic by linking our charts of case numbers to the geographical distribution of actual populations.  Here is a map of Africa showing population density. 

The colored outlines show populations which might be at risk if the epidemic spreads across Africa.   For illustrative purposes, these populations are linked to the extrapolation of the cumulative number of cases, using a contagion model with Ro = 1.63.   In this model, each case of Ebola infects (on average) 1.63 new victims after a transmission and incubation period of 16 days.  This model fits the reported exponential growth of the disease to date.
A number of cases can be expected in developed countries as a result of infected individuals traveling to new countries.  The United States and Spain have already seen such cases and subsequent secondary infections.  However, rich countries with well-developed medical systems should be able to easily quell the epidemic, given only a few points of infection.  

The Ebola epidemic is much more likely to spread through the impoverished nations of Sub-Saharan Africa.   By the numbers, at the established rate of growth would spread the epidemic to every individual in Guinea, Sierra Leone, and Liberia, totaling 21 million people, by the mid-year 2015.  The epidemic could spread to every individual in West Africa, 412 million people, by autumn 2015.  By year-end 2015, the epidemic could spread to nearly a billion people in Sub-Saharan Africa by year-end 2015, showing the astonishing power of exponential growth.

Of course, the epidemic will not unfold as a neat mathematical formula.  There are factors which will impede the growth of the disease.  And there are factors which may accelerate the spread of the disease.  As the rate of infection rises in a population, several things may happen.  Some of these things will reduce the transmission of disease, and some things will increase the transmission of disease.  In affected populations, intense public health campaigns are being conducted, which should reduce risky behaviors and reduce the rate of infection.  Also, as the infected population approaches saturation, the rate of new infections should decline.  On the other hand, high infection rates will strain the fabric of society, overwhelm treatment facilities, and reduce the number of qualified professionals working to contain the epidemic.  And perhaps worst for the rest of the world, at some point large numbers of Ebola refugees will flee infected countries and carry the disease to new places.

Liberia Case Count
Recent data reported by the World Health Organization seem to show a slower rate of growth than in the earlier history of the epidemic.  However, there is serious doubt about the accuracy of recent reports, particularly from Liberia.  The October 8th report from WHO bluntly states “Evidence obtained from responders and laboratory staff in the country indicates beyond doubt that there is widespread under-reporting of new cases, and that the situation in Liberia, and in Monrovia in particular, continues to deteriorate from week to week.”

The number of new cases appears to be declining; but this is unlikely to be true considering other evidence.

Since early September, reports from the Liberian Ministry of Health have been late, contradictory, and inconsistent.  The most recent reports from Monrovia and Freetown still indicate that all isolation units and hospitals are full, and that patients are turned away to transmit the disease at home or in the streets.  Although we can hope that public health measures are reducing the rate of transmission, we are in a state of uncertainty, without reliable numbers to support that conclusion.   

Adequate medical facilities are necessary to measuring the development of the epidemic.  If families of Ebola patients believe that they will receive treatment, patients will be brought to medical facilities, and data gathered about the progress of the disease.  If patients are consistently turned away from treatment facilities, there is no point to bringing stricken people to the clinics.   For the past two months, the number of beds in Ebola clinics in Liberia has been only about 20 % to 25 % of the number needed.   Some 75% to 80% of Ebola patients have been turned away, or left to suffer in the streets.  In this environment, it is understandable that families do not seek official care, but instead choose to care for loved ones at home.  This means that official figures no longer have any validity in measuring the epidemic, and virtually guarantees the spread of the disease. 

Ebola Clinic Beds
Specialized treatment centers are necessary for Ebola patients.  Without proper equipment and training, medical personnel are at tremendous risk of contracting the disease.  [As of October 8th, 416 healthcare workers have contracted the disease, and 233 have died.]  But throughout the epidemic, the number of beds in proper treatment centers has lagged far behind the need.   According to WHO, throughout the months of September and October, the number of beds available to patients has been about 25% of the number needed.

In the 8th October report, WHO indicates that there are about 1100 beds available to Ebola patients in qualified treatment centers.  The current need is for over 4300 patients, a shortfall of 3200 beds.   There is adequate care for only 25% of the patients.

The United States and Britain have mobilized military resources to fight the epidemic.   The United States will build and staff treatment centers containing 1700 beds in Liberia, while the British army will build and staff treatment centers containing 700 beds in Sierra Leone.  Both programs will require about 60 days for implementation. This effort will still leave a shortfall of 800 beds, according to current needs.  It is likely that other organizations will also contribute new beds, and perhaps bring the total number of beds to 4300 by the end of November.  

The problem is the human tendency for linear thinking, whereas problems in nature are generally exponential.  By my estimates, the Ebola epidemic is doubling about every twenty-nine days.  (The CDC calculates the epidemic is doubling every 20 days, by assuming a large number of unreported cases).   In 60 days, the epidemic will have grown four-fold.   In mid-September, when the US Army intervention was announced, about 1800 new beds were needed, for a total of 2425 beds.  If the epidemic continues to grow exponentially, by mid-November about 10,000 beds will be needed. 

Death Rate
In my first post, I noted that diseases evolve quickly, and that evolution causes the disease to become more contagious, and less deadly.  Living patients propagate the virus better than dead patients.  As expected, the mortality rate for Ebola patients appears to be falling, from about 70 percent to about 55 percent.
The chart shows cumulative reported deaths as a fraction of cumulative reported cases, with a lag of eight days.  I would like to calculate a daily death rate (an instantaneous function), but the official figures are reported too sporadically for a meaningful chart. 

Future Course of the Epidemic
The equation used by epidemiologists to forecast an epidemic looks like this:
Cumulative Cases = ((Ro/1+d)t)t
The term “d” is a decay parameter, which reduces the rate of transmission over time.  This could represent effective medical intervention, or a public awareness campaign, or disease saturation within the population at risk.  We might hope that the declining number of reported new cases in Liberia reflects a real decline in new infections, but all other evidence indicates that the people of Liberia increasingly distrust the official treatment centers, and no longer bring patients to be counted.

We might also consider a parameter which increases the rate of transmission over time.  Such a parameter might represent breakdown of social order, growing distrust of medical facilities, or dispersion of the population fleeing the epidemic.  In any event, the data quantifying the epidemic are now uncertain, and there is little basis for assigning values to parameters which may reduce or increase the rate of transmission. 

While we must make every effort to stop Ebola within the current area of active transmission, we should also realistically consider what will happen if those efforts fail.  It is likely that neighboring nations will receive refugees through porous borders, and some of those refugees will carry the virus.   Ebola can be expected to spread along the West African coast through coastal communities, and jump from infected large cities to other large cities.  Like ripples from a stone thrown in the water, Ebola has the potential to expand through heavily populated West Africa, and ultimately affect the entire continent.  At some point, perhaps at 20,000 active cases, or 100,000 active cases, the disease will not be stoppable with the procedures that ended previous epidemics.   According to the rate of growth and the distribution of African population, the 2nd half of 2015 may be a very bad time for Africa.

Some people do survive Ebola, and they are surviving in increasing numbers.  This shows that the human organism can mount an effective immune response to Ebola.  Medical science has developed vaccines for other deadly viruses.  It is inevitable that an effective vaccine will ultimately be developed and produced on a large scale.  The question is how soon the vaccine can be produced and brought to protect the people at risk.

In considering the impact of the Ebola epidemic, I am strangely reminded of something a colleague said to me on the morning of 9/11/2001.  The second plane had just struck the World Trade Center.   Being quicker and brighter than me, she turned and said, “You realize, nothing will ever be the same again”.  Of course, I had not realized the impact of the event, and didn’t fully understand until several years later.  In the same way, something with global impact has happened in West Africa.  The world does not yet realize that everything has changed, and nothing will ever be the same again. 
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*  Cumulative Cases = ((Ro/1+d)t)t
 I used a simpler exponential function for my first model, and a simple rolling formula in Excel to create my contagion model with Ro.  In the equation shown, one “t” must represent the time between initial and subsequent infection, and the second “t” must indicate the life of the epidemic.  I will update this post after I have some time to play with the equation.
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Obsolete as of November 7, 2014, see latest post

Chart Updates to my original post, using the original extrapolations.
In the October 29 report, WHO presents revised figures that add about 3700 cases to the previous total.  These cases were recognized through study of patient databases, and occurred throughout the epidemic period, and not only since October 22.  The additional cases return the cumulative case number to my original exponential extrapolation, first presented on August 26th.

It is uncertain whether the apparent flattening of the cumulative cases, observed through the month of October, is real or the result of under-reporting.  Case reporting is increasingly late, and WHO cites data missing for a number of dates. 

I have now seen two anecdotal reports that give a more optimistic appraisal of the situation in Monrovia, indicating fewer patients are reporting to Ebola clinics, and fewer bodies are being collected from the city outside the clinics.  Authorities disagree on whether the drop in patients shows a real decline in the epidemic, or avoidance of the clinics.
New Cases (yellow circles) as of WHO Roadmap update, 10/25/2014.   Reporting dates by country are variable.
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References:
WHO Situation Reports, Ebola Response Roadmap

Ebola disease outbreak news

Population, Landscape, and Climate Estimates, v3: Population Density 2010, Africa
National Aggregates of Geospatial Data Collection

It = ((Ro/1+d)t)t   where is scaled in generation time, with Rthe basic reproductive number, and d a “control parameter” that causes incidence to decay. 



October 12, 2014
Personal report by Drew Hinshaw, WSJ, on awful situation in Monrovia.   Patients now told to stay at home; families told to leave patients alone.  Increasing numbers of patients on street, as compared to several weeks ago.   Mobs of people moving on streets; people trying to leave.

US military intervention to fight Ebola; commitment of 3000 soldiers and 1700 beds.

UK commits to building five treatment facilities with 700 beds in Sierra Leone.  Estimated to allow treatment of 8800 patients over six months.

Lots of facts about Ebola.

Lots of numbers and graphics showing that the global response will never catch up with the epidemic.

Infographic showing the rate of increase in cases over two months, and the number of beds available for treatment.   Also shows the US commitment to build additional beds over the next two months, which will provide about 1.5% of the needed beds in November.

Public education programs to convince population that Ebola is real; overflowing clinics; people touching and praying over Ebola patient.

Ebola is transmitted even under stringent conditions of containment.



Monday, September 15, 2014

Ebola Update #1

April 29, 2015
My latest update regarding the history of the Ebola epidemic can be found here:
http://dougrobbins.blogspot.com/2015/04/ro-and-history-of-ebola-epidemic-in.html
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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.
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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:
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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.

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References

WHO Ebola Response Roadmap, August 28, 2014

Financing

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.