If this rate continues how many total infections should there be by day 100?

Question

Data shown below.

Number of days since total # of infections

first infection reported.

0 1

10 6

20 12

30 15

40 69

50 1029

58 9415

Answer 1

The average change in the log is .270 from day 40 to day 50 and .277 from day 50 to day 58, so it appears to be stabilizing. The rate was actually much lower before this. We con't really have enough information to justify a more complicated model like the logistic model. A continuation of the day 50 to 58 growth rate would lead to 9415 * (9415/1029)^(42/8) = 1,050,016,950

(there are 42 days from day 58 to day 100).

An alternative view which would lead to a much lower estimate would be to use the entire timeframe from day 0 to day 58.

Then, on day 100, there would be 9415*(9415/1)^(42/58) or, simplifying the formula,

9415^(100/58) = 7,102,551.