COVID Odyssey: NZ New Year Fear 15 Post #942~ COVID-19: Estimating Case numbers

In the previous post we created a table to estimate Ro (the average number of people one person may infect without isolation over a 10-day infectious period), by estimating (projecting) the number of people each case may infect if the case had not been isolated.

We extend the table.

We look at the case numbers for Day 10 (with start day Day 0).

Let Ce be the number of cases on Day 10 with isolation.

Let Co be the number of cases on Day 10 without isolation.

Let r be the daily increase in case numbers for Ce.

We first estimated Co by calculating

Co = Ce * r * r
(multiply Ce by r squared)

We found that it was better to estimate Ce using the formula

Ce = Co / r /r
(divide Co by r squared)

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Note:
Except from the table, the original value for r will not be known for the division above.

The easiest way to solve this is to copy the Co values into a new first column on the Excel spreadsheet used to create the table below and use HLOOKUP in Excel to look up values in any column (based on values for Co for Day 10).

The spreadsheet could be extended to cope with smaller of larger values for Co.

Otherwise if the original value for r was somehow estimated in another way, we could proceed as below.

Update: Alternatively use Goal Seek. See:

COVID Odyssey: NZ New Year Fear 16 Post #943~ COVID-19: Using goal seek to estimate Case numbers

Ce provides a useful upper bound for the theoretical number of cases with isolation on Day 10 when the value calculated for r (based on Ce) is less than 1.7.

Truncate (round when r > 1.77) to two decimal places the value for r calculated from Ce as estimated to get the correct value for r from which the Day 10  theoretical Case total can be calculated.

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For background see:

COVID Odyssey: NZ New Year Fear 14 Post #941~ COVID-19: A table comparing Ro and Re

https://aaamazingphoenix.wordpress.com/?s=new+year+fear

Below is the new table:

The PDF version may be easier to read:
CasesReRorr

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