The usage of the RATE function is:
RATE(nper, pmt, pv, fv)
There are 41 days between 8/28/14 and 10/5/14, and we won't be making any "payments". The "present value" is the number of cases on the first day of the period in question, and the "future value" is the number of cases on the last day of the period. It is expressed as a negative. So putting in your values we have:
RATE(41, 0, 3053, -8033), which gives a daily percentage increase of 2.3877%.
So to get to 7.125 billion, it will actually take 580 days, 10 hours, and 1 minute.
So either way, at the current rate, we will all be infected in less than 2 years. Nice!
My 2 month, 3-country database shows slowly rising new daily confirmed cases of 125-150/day averaging a 2% daily increase over the previous day’s total case numbers (150/8000 = 1.9%), which roughly doubles my total in 35 days. The bad news is the ministry of health numbers I use are probably just 50% to as low as 33% of the actual daily numbers, as hundreds of victims never get to a care center or are turned away from hospitals and return home, unrecorded as new cases, and later as deaths.
The assumptions that can be made regarding the effect of unreported new case numbers are unclear and subjective for me: if there are actually, say, 300 new cases/day and one assumes the real total now to be 16,000 cases, the growth is still 1.9%: does that roughly indicate a 22 MIL case total in 365 days assuming EVD goes worldwide and grows 2%/day, or maybe I have wandered off the mathematical reservation?
I’m more interested in looking for large infection rate changes indicated by the relationship of 5 and 10 day smoothed moving averages of the daily new case MOH numbers, incomplete, poorly reported and understated as they may be.
YMMV (your math)
You’re right, thanks! I double checked and must’ve fat fingered the calculator.
I was using a different equation, though, from calculus which models exponential growth and get a number closer to yours but still different (2.36%, 621 days). I’ll probably repost this tomorrow for grins. Maybe update the numbers w/new ones, only if the rate stays high, of course.
Bottom line, nothing to fret. Using this model presumes all get infected which won’t be the case. The simple, linear, exponential model is really more suited to the rate of exposure - numbers we don’t have. Not everyone exposed necessarily gets infected. It’s not like everyone got smallpox, the spanish flu, or the plague. Also, the rate (percentage) will likely decrease over time as controls are implemented.
Of course, I could be wrong about that and we’re all screwed.
Anyway, here’s my math:
With f(n) = number infected at day n
f(0) = day zero count (starting from Aug)
EXP = exponential function
LN = natural log function
k = rate of increase
The equation I use is:
f(n) = f(0)*EXP(k*n)
Solve for k with
f(41) = f(0)*EXP(k*41)
8033 = 3052*EXP(k*41)
k = (LN(8033/3052))/41 = .023604 (used excel this time)
Now we want to know when it increases to 7.15 billion, using same equation with our value for k.
7.15*10^9 = 3.052*10^3*EXP(.023604*n)
n = (LN(7.15*10^6/3.052))/.023604 = 621.3723