We have assumed that case numbers increase at a daily rate of r and infectivity decreases daily at a rate of 1/r.
This simplifies the formula. However it is possible that infectivity decreases daily at a different rate.
Below is a graph showing various rates:
Below is data for the graph.
Note: values have been scaled so that the total is 1 in each column.
This means that we can consider each value a probability.
It is possible that for a daily rate of increase of r = SQRT(2), we could have a daily decline of infectivity of 1/2.
However a daily decline of infectivity of 1/SQRT(2) gives us a lower estimate for Ro since fewer cases occur earlier on and hence there is a slower spread.
Prior to scaling, we obtained these values:
We also obtained cumulative values:
This enabled the use of random numbers in simulations and the use of lookup tables to estimate the day a case was infected.
We have used the table and formula below to estimate Ro.