In February 2020 we looked at the animation below. if 5 people with new coronavirus can impact 2.6 others, then 5 people could be sick after 1 Cycle, 18 people after 2 Cycles, 52 people after 3 Cycles and so on.
We create this table (see Total infected):
We use a five day cycle. Historically cycles up to seven days have been used, usually with an incubation period of one cycle and an infectious period of two cycles.
We look at New Zealand data in early 2020 (the initial outbreak). We choose a five day cycle to match the actual case numbers. Since the value for Re is based on a single five day cycle, we expect the value to be low for low values of r.
We use Goal Seek in Excel (under Data, What-If Analysis in Excel 2010). We want to set E4 to zero by changing D6.
We see the actual case numbers are close to our estimates when there is a daily increase of r = 1.4.
We also look at r = SQRT(2) and r = SQRT(3).
i.e. r = 1.41421 and r = 1.73205.
We may look further in another post. Also see: