Thursday, 18 September 2014

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/