You're not far off. Not an epidemiologist, but I think these sorts of things generally follow a logistic (S-shaped or sigmoid) curve (1/1+e^-x). Initial growth is approximately exponential, then you hit a point of saturation, growth slows, and eventually levels off.

The key question is how long does it take for it to level of?

Right now it its infecting 1.7 persons per infected person (avg) so it is still growing, however it is also in the slums of the poorest area on earth.