We want to estimate Ro and COVID-19 spread when the period of infection is over two five day cycles.
We have weights w1 for Cycle 1 and w2 for Cycle 2 where w1 + w2 = 1 or
w2 = 1 – w1.
In the example below, we use 60% of new case numbers in the first cycle and 40% in the next cycle.
i.e. w1 = 0.6 and w2 = 0.4.
Let C be the number of new cases in a five day period (New in Column D ). These new cases are spread over two cycles (two five day periods) with:
- w1*C cases occurring in the current cycle; and
- w2*C cases occurring in the next cycle
The table below uses New Zealand case numbers for the first outbreak in 2020.
We obtain Re ~ 6.
We use Goal Seek in Excel (under Data, What-If Analysis in Excel 2010). We want to set E10 to zero by changing D12.
We see the value obtained for r = 1.4 is close to that for r = SQRT(2) in the table below.
We can also do the reverse and choose a value for R, say 5.8, and find the corresponding weights by changing the weight for cycle 1 (E6):
By changing 289 to 283 we get:
Rounding to R to 5.25 we obtain:
For background see: