I hope you're right. The formula I'm using is Cases ^ (((DTR-1) * DaysOut) + 1).
Let's do an example, based on the actual data:
On 6/1/14 there were 383 reported cases. 101 days later, on 9/10/14 there were 4,845 cases. This gives a DTR of 1.004224155. Let's see how that DTR would project from June 1 to June 30 (29 days later).
If you use the formula, you will get:
383^(((1.004224155 - 1) * 29) + 1)
383^((.004224155 * 101) + 1)
383^(0.426639655 + 1)
383^1.426639655 = 794
The actual number of cases on June 30 was 759. So it's about 5% high in this instance. But let's do it again using June's DTR to project what the number of cases were at the end July. June's DTR was 1.00396518542771.
383^(((1.00396518542771 - 1) * 60) + 1)
383^((.00396518542771 * 60) + 1)
383^(0.219111856626 + 1)
383^1.219111856626 = 1,410
But at the end of July (actually, July 30) there were, in fact, 1440 cases. So the model is pretty close, but comes in 2% low.
Keep in mind that the model will improve over time as the actual numbers are incorporated.
Your math is not making sense to me.
First a DTR (Daily Transmission Rate) of 1.004 is way too low.
And I’m not sure what you are doing putting both the DTR and the DaysOut in the exponent. That might work in your formula, but I don’t think the formula makes logical sense.
Work it through one day at a time and see if you get the same result.
Start with 100 cases and let’s do just 3 days.
If you have 100 cases on day 0 and the DTR is 1.004 then you would have 100*1.004 = 100.4 on day 1, and 100.4x 1.004 = 100.8 on day 2, and 101.2 on day 3.
But if you plug it into your formula for 3 days, then you get:
100^(((1.004-1)*3)+1=
100^(.004*3)+1 =
100^(.012+1) =
100^1.012 = 105.6, but it should equal the same result that we walked through day by day. So either your formula is wrong, or I don’t understand exactly what you are doing.