Updating a model of a modern Ebola epidemic...

Professor David Fisman, University of Toronto, Canada published one of the excellent recent models designed to estimate where Ebola virus disease case numbers might be heading.[1] He has updated his model using the latest World Health Organization EVD data that includes up to 13-Sept.

This morning I awoke to find the fruits of his labour generously presented to the world via Twitter.

I'm constantly impressed by how much info can and is being provided for everyone to share, discuss and  constructively mull over. This is just the latest fantastic effort.


Prof Fisman's (@DavidFisman) model has provided a very close estimate when compared to the real figures on which it is, of course, based (Figure 1.). His estimates have not changed with the latest data. He calculates an overall R0 of 1.75, and 'd' (a value that can indicate the level of control; when d is zero, you have uncontrolled exponential growth) is at 0.0078. The d values for different countries in the outbreak, differ.

Figure 1. Showing that the model (black line) fits extremely well
to actual reported case numbers (red bars) to date

The projected end date is November 2016 with a final size of approximately 480,000 cases. (Figure 2) This is just based on current numbers and without knowing what interventions are coming not how successful they will be. Prof Fisman says his model currently predicts an epidemic peak in June-2015 at which time there could be 227,000 cases. By Jan-2015, projected case counts reach 28,450.

Figure 2. Extending the model into 2017.
Red curve (right y-axis): incidence by 15-day generation.
Blue curve (left y-axis): cumulative cases.

Keeping in mind that these numbers do not include deaths. The proportion of fatal cases (PFC) requires some further mathematical wizardry in order to account for the time between when cases present to a treatment facility, and when they die. 

Figure 3. Ebola virus disease cumulative curve for Nigeria.
The proportion of fatal cases is markedly lower than for
 the more overwhelmed countries. This does
not appear to be an artefact as most cases have
been laboratory confirmed.

It's not a simple division of deaths and total cases at the same time point (these are the crude percentages I report on VDU and which the WHO report-this reporting may change in the future). 

The addition of that calculation spikes the PFC to >80% at times (see the post by @maiamajumder post on HealthMap), but seems to vary to lower figures depending on country and population for example, in Nigeria (Figure 3). But whatever way you look at it, many people will die from Ebola virus infection, as well as all the other diseases and medical care needs that going with sufficient attention.

References..

1. Early Epidemic Dynamics of the West African 2014 Ebola Outbreak: Estimates Derived with a Simple Two-Parameter Model
   http://currents.plos.org/outbreaks/article/obk-14-0036-early-epidemic-dynamics-of-the-west-african-2014-ebola-outbreak-estimates-derived-with-a-simple-two-parameter-model/

Ebolavirus disease (EVD) cases, clusters and outbreaks mapped out...

The West African region outbreak (top map) and the totals from past Ebola outbreaks and the few imported monkey cases (the US & Philippines; hence zero human cases) plotted by total numbers and country (bottom map)

These maps are best viewed alongside my Ebola numbers page found here.

The WHO have commenced creating multi-page Situation Reports.[2] They contain more granular data than is publicly available. They will be reported at least once per week.

If I become impatient, I'll cobble together the individual country's numbers via reliefweb.int, then update that once WHO data are available (which may result in a drop in totals as WHO numbers may have been collected a littler earlier).

This is a static page - it will be updated with new numbers but the website address will remain the same.

Latest data taken from: http://apps.who.int/iris/bitstream/10665/135029/1/roadmapupdate26sept14_eng.pdf?ua=1
Date of DON: 26-Sept
Dates covered: 23-Sept

Learn About Tableau

A note about the proportion of fatal cases (PFC): 
On these graphs, my PFC calculations for West African countries and the DRC are based on dividing the total number of suspect/probable/confirmed deaths by the number of total suspect/probable/confirmed cases for the same date. This is crude and may be a sizable underestimate of the true PFC.

It may be better to use the deaths at the most recent date divided by the total cases from 9-14-days  earlier (this number is not precisely known) to better account for the lag in time between presenting to a treatment facility and dying (for those who do not recover). 

Some estimates suggest the true PFC may be closer to 80%. I don't have enough data (or smarts) to be able to calculate that for now so please be aware the PFC above is likely an underestimate

Reminders:

• The chart above, as with all on VDU, is made for general interest only. It is also freely available for anyone's use, just cite the page and me please. It may be that I have misinterpreted the language in the reports (sometimes a little tricky to wade through) or miscalculated some totals based on the way data have been presented. 
• Sometimes there are very country-specific differences in what gets presented to/via the World WHO DONs/SitReps which make this process less clear than it could be. I recommend you have a read and compare the data from each of the countries for yourself to understand these issues. 
• As I've talked about previously,[1] these numbers are all volatile for a variety of reasons, some Ebola-specific, so regard this chart for its trends only.
• I am only able to plot what is publicly available. To date, this does not include granular data with dates of onset, or daily data of any kind. The WHO have these data and you will see them become more available through their Situation Reports found here http://www.who.int/csr/disease/ebola/situation-reports/en/

References... 

1. Ebola virus disease and lab testing...
   http://virologydownunder.blogspot.com.au/2014/04/ebola-virus-disease-and-lab-testing.html
2. Ebolavirus outbreak Situation Reports
    http://www.who.int/csr/disease/ebola/situation-reports/en/