In October 2014 using the cumulative death figures from the terrible West African Ebola outbreak, I fitted a four parameter logistics function to the data using Excel. This is straightforward to do using Excel's 'Solver' functionality, you set up the squared residuals, sum them, and use the solver to adjust the parameters to set the sum of squares to zero.
The resulting fit indicated an eventual cumulative total death toll of 9,216 people. The logistics function assumes that the response to growth is proportional to that growth in the end, and that is a good basic description of the growth of bacterial colonies and so on. In the case of the Ebola outbreak, the death toll is no doubt reduced by the fact that preventative measures are taken, and this is also in some measure related to the rate of growth, so the logisitcs function can describe this system.
I have included in the image information on how to set up the necessary formulae to create this ultra simple model. If you follow the link in the image below you will reach a larger version of the image.
This was done in October 2014, approximately 7 months ago. The current total death toll, according to this CDC site is 10,980, so the prediction was not catastrophically wrong. Basically, the logistics function says that the tail off after the maximum increase is seen will be similar to the ramp up when the disease first gets a foothold.
I like the logistics function! See the following links:
Companies and Bateria
Company Growth