Projecting the path of Ebola is not a simple task. There is a lack of historical data to accurately model an outbreak as large as the current one in West Africa meaning all predictions and projections should be treated as speculative. The data used to model any prediction is based off official statistics and does not generally take into consideration under reporting or incorrect data.
The simplest of models use basic but unfortunately inaccurate mathematics to calculate the number of cases at a point in time by adding the growth rate daily. This is simple mathematics and a good way to get a quick idea of the potential number of cases but a virus does not always continue to spread in an exponential fashion. Several factors can change the growth rate including geography, intervention, weather and human behavior.
More accurate models will attempt to factor in the doubling rate of the virus and perhaps include basic limits around populations of an affected area. These models provide more realistic data to work with but still do not provide an accurate model.
The following projections forecast the Ebola outbreak and potential case count for October as follows:
20000 Variable Transmission
11000 Exponential Smoothing
15000 Exponential Cumulative
It is very likely that we will see more than 15000 cases by the end of October 2014 based on current reporting. The CDC report which predicted between 550000 and 1.4 million case by early next year factored in under reporting. Adjusting the 15000 by a factor of 2.5 to reach 37500 potential cases of Ebola within the next 30 days with as many as 26000 dead.
Predictions around the spread of Ebola in the USA are impossible at this stage. It is possible that the first case of Ebola in the USA will have a first wave of infections based on reports that the patient was infectious for as many as 4 days and further reports indicating that he was in contact with family members including children. It is likely that 3-12 cases could have been generated based on the current information available.
Several commentators have already predicted that there could be at least 500000 cases of Ebola by January 2015 however Bloomberg is reporting that the CDC is on the verge of releasing a report confirming the possibility. The report confirms a “worst case” scenario where no successful intervention is possible in the coming months resulting in the uncontrolled spread of the virus culminating in 550000 cases of the deadly disease by January.
To reach these numbers in a very simplistic manner we can apply a bit of thought to what we already know. The official confirmed case number is 5357 at the moment which is considered by most experts to be deflated number. Taking a simple view that the number is 2-3 times larger than reported, and assuming a doubling rate of 21 days which the current trend reflects, you can easily reach the numbers predicted. It is noteworthy that the doubling rate seems to be increasing or at the very least has not been accurately measured yet. The WHO has reported doubling rates between 2 weeks and 3 weeks.
With predictions as terrifying as these it is important to remember that they are mathematical models that often assume exponential growth will continue which is unlikely once you consider geography, intervention, blockades and of course the potential to improve treatments and education on the prevention of the disease. It is worth acknowledging that so far intervention in the affected regions has not slowed the spread of the disease and predictions like these have a role to play in understanding the potential scenario if intervention continues to fail.
The CDC report cited which is believed to contain these figures has not yet been finalized or released to the general public. However, Bloomberg is a credible news source and there are at least 2 ways to reach the same predictions for January mathematically by adjusting the case total for accuracy as shown or by lowering the doubling rate.
The next 3 weeks are crucial in the fight against Ebola according to the Fred Hutchinson Cancer Research Center which is predicting 10000 cases by the end of September 2014. Several doctors and experts have contributed to their research which paints a bleak picture.
Data from WHO
Several other organizations have modeled the outbreak and although the numbers are not consistent the message is clear, without significant intervention the virus could spiral out of control and the results would be catastrophic.
Another model predicts more than 12000 cases by the end of September using an R0 of 2. R0 is a basic reproduction number of an infection that is simply thought of as the number of infections created by a single infection. Influenza typically exhibits a R0 of between 2 and 3 as an airborne virus. Ebola R0 values are typically between 1 and 4. The 1995 outbreak in the Democratic Republic of Congo had an estimated R0 of 1.83.
Some quick and simple models using exponential curves based on current World Health Organisation data indicate 8000 cases by the end of September while the WHO itself has indicated that it expects more than 20000 cases before containing the epidemic.
Alessandro Vespignani from Northeastern University reached similar numbers predicting between 6000 and 10000 cases by the end of the month. He was quick to remind everyone that statistical predictions are not 100% accurate and unfolding events could change the results.
Scientific and statistical models are not without flaws and it is important to remember that these are typically “worst case” scenarios often modeled without GIS data or Regression and at best based on limited and possibly inaccurate data currently available.
These models are invaluable since they not only provide data for authorities to base decisions off of but also provide a comparison to previous Ebola outbreaks which form a large part of the modelling process.