I think these models are extremely suspect, with nil predictive value. Where you have sustained exponential growth dynamics, as here, the results are fantastically sensitive to the parameters which go in the exponent, which in this case you can't predict with enough accuracy.

The simplest ODE is something like:

du/dt = k(t) * u(t)

Whose solution locally looks like (for slow-varying k(t))

u(t) ∝ e^{ k(t) * t }

One possibility is k(t) > 0 sustained for 10 effective doubling times. One possibility is k(t) < 0. In this epidemic, either is plausible (?): the difference is only a small difference in some infection control parameters. A small uncertainty that translates into a factor of a thousand uncertainty in the outcome, because it gets blown up by a gigantic e^x.

And the estimates of k(t) seem to hover around the critical value of k(t) ~ 0. In the CDC model (their Excel spreadsheet is open source [0], and FYI won't import into LibreOffice), the shape of the epidemic is purely determined by the shape of their k(t) assumptions. Their defaults parameter exhibit, first, a fast growth phase, assuming k(t) > 0; then they assume a slight reduction to k(t) ~ 0, leading to slower growth; then slightly more reduction to k(t) < 0, causing the epidemic to halt. As far as I can tell k(t) is basically speculative, and completely determines the shape of u(t). So really you predict nothing.

[0] http://stacks.cdc.gov/view/cdc/24900