COVID Odyssey: NZ New Year Fear 22 Post #949~ COVID-19 simulation: COVID-19 spread using a formula instead of Goal Seek

We develop the previous post and create a formula to use instead of using Goal Seek in Excel. Our formula when r = 1.4 (daily increase in case numbers of 1.4) is:

R = SQRT( (10 x 1.4^10)/10 – 3/4 ) – 1/2

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.

:

See:

https://towardsdatascience.com/how-bad-will-the-coronavirus-outbreak-get-predicting-the-outbreak-figures-f0b8e8b61991

We have:

We develop a formula by completing the square:

10R^2 + 10R + 10
= 10 x 1.4^10

R^2 + R + 1
= (10 x 1.4^10)/10

(R+ 1/2)^2 + 3/4
= (10 x 1.4^10)/10

(R+ 1/2)^2
= (10 x 1.4^10)/10 – 3/4

R + 1/2
= SQRT( (10 x 1.4^10)/10 – 3/4 )

R = SQRT( (10 x 1.4^10)/10 – 3/4 ) – 1/2

This is our formula.

For r = 1.4 we get R = 4.808056659

We created 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 used 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.

Also see:

See:

COVID Odyssey: NZ New Year Fear 21 Post #948~ COVID-19 simulation: COVID-19 spread with Excel Goal Seek

Welcome

Shared Posts (Pingbacks)