Rome Didn't Fall in A Day.









Objective Truth Exists, and is Accessible to Everyone.

All Human Problems can be Solved with Enough Knowledge, Wealth, Social Cooperation and Time.


Photo: Rusty Peak, Anchorage, Alaska


Translate

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
------------------------------------
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.
---------------------------------------------------------------------------------------------------------------------
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.

----

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.

----
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.

13 comments:

  1. Thank you for your updates!

    ReplyDelete
  2. Hi Doug,

    Thank you for your detailed analysis. I have read all your updated articles so far and your predictions are very impressive. I am also working on a similar project to predict mortality rates in Africa and would love to have a discussion with you. My email id is: katatonia121@gmail.com.

    Hope to hear from you.

    ReplyDelete
    Replies
    1. Thanks for your attention! Yes, I will write, and I would be interesting in learning about your project. Regards, Doug

      Delete
  3. I have been following your data since August. I think you are spot-on. The recent "down trend" from the predicted numbers is because of poor data gathering in Liberia and Guinea. The rural locations of these countries prevents accurate numbers.
    On another interesting note…I have heard of hospitals NOT testing possible cases for fear of driving away customers (lesson learned from Dallas Hospital). I spoke with a critical care physician that has taken care of patients that he wanted tested, but the hospital refused to allow it.
    Just something to think about….

    ReplyDelete
    Replies
    1. Thanks for your attention to my articles! We're in agreement. I'm afraid of transmission into rural and poorly monitored areas where the epidemic might grow undetected. The epidemic may have passed into a stage where the information is incomplete and inaccurate. Authorities may become overconfident, because of success in some places, while the disease spreads unchecked in other places.
      Your comment about hospitals' reluctance to test possible Ebola cases is truly horrifying. It is exactly this sort of denial that puts all of us at greater risk. Thanks for commenting.
      Regards-- Doug

      Delete
  4. I follow EBOLA INTERNATIONAL SOS and GLOBAL INCIDENT MAP for my information. What sites do you review?

    ReplyDelete
  5. Those look like interesting sites! Thanks for the reference; I hadn't seen them before. I'll spend some time looking at them.
    I'm getting most of my information from the World Health Organization situation reports. The most recent update can be found here:
    http://www.who.int/csr/disease/ebola/situation-reports/en/

    The archive of situation reports to late August is found here:
    http://www.who.int/csr/disease/ebola/situation-reports/archive/en/
    These are updates to the WHO Ebola response roadmap.

    Earlier reports are found here:
    http://www.who.int/csr/don/archive/disease/ebola/en/

    I've also relied on various news reports, and the CDC Ebola webpage.
    http://www.cdc.gov/vhf/Ebola/outbreaks/2014-west-africa/index.html

    Doctors Without Borders also has periodic briefings over the internet.

    Regards--
    Doug

    ReplyDelete
  6. Hi Doug,

    Thank you for a fantastic site and fantastic posts. I am a risk manager leading a team of freelancers here in London, UK pushing the UK government to lead in Europe to deal with the situation in Sierra Leone (the British Army is doing a lot, but more needs to be done). Our website is stopebola.uk
    We are employing a professional designer to create an inforgraphic about what is necessary to bring down R0 in Sierra Leone and stop a catastrophe.

    It would be great to be in touch with you. My email is sjstretton@gmail.com. In particular, do you have a dataset that I can send to the designer?
    (About me: I work in finance and I am funding -with others- and directing our campaign, although not day-to-day in charge. I'm the quantitative one in our team, but rather short of time because of my day job.)

    Thanks again for great posts.

    Regards
    Stephen

    ReplyDelete
    Replies
    1. I have a number of Excel spreadsheets, that I update when WHO publishes new information. I interpolate by country in order to obtain a common reporting date for my charts. I'm happy to share my spreadsheets if you need them. WHO is now also publishing data that might include their revisions of previous numbers. These might be more authoritative than my charts. I'll contact you; thanks for your comments!
      regards--
      Doug

      Delete
  7. I was wondering what your current RO number may me. It appears that all three countries have a similar growth rate since adjustments in October.
    Thanks

    ReplyDelete
  8. Excuse me for the long delay! I just completed a calculation of Ro for the history of the epidemic. It is included in my March 11 update to this post. Ro declined to 0.91 for several weeks. It is now growing very slightly, but is still below Ro = 1.
    Ro never approached the level of 0.7 targeted by the World Health Organization.

    ReplyDelete
  9. more,that is still you may do something to expand on it.yhanks for sharing with us.I think I am going the clearness in your post is simple spectacular and I can take for granted you are an expert on the field.Well with your permission.Like your way of seeing this things. i'll be checking in on a regularly now....keep up the good work.

    Toshiba PVT-375BT

    ReplyDelete