# COVID-19 NZ: Is Ro < 3? Is Ro = 5.4 feasible?

We continue investigating the value of R0 and Re in New Zealand and overseas.

We will look at [excerpts from] this article: taaa021 (Click to view PDF):
The reproductive number of COVID-19 is higher compared to SARS coronavirus
published 13 February 2020, obtained from here:
(Journal of Travel Medicine, Volume 27, Issue 2, March 2020)

For background to Ro and Re, please look at:
https://www.cebm.net/covid-19/when-will-it-be-over-an-introduction-to-viral-reproduction-numbers-r0-and-re/

In the last post, we found two ways to generate a curve that closely matched actual case values from when there were a total of only 8 actual cases (Day 18; 16 March; 10 cases estimated) until the day after New Zealand went into Lockdown Level 4 at 11.49 pm on 25 March (Day 28; 26 March; 283 actual cases total; 289 estimated total). See:
https://aaamazingphoenix.wordpress.com/2020/05/25/covid-19-nz-using-a-fibonacci-sequence-to-estimate-total-case-numbers-v/

The same curve was calculated using these formulae:
(where C[18] = 10, C[19] = 14, and C[20] = 19.6 )

C[D] = 1.4 * C[D-1] for D > 18

C[D] = 1.14333333 * ( C[D-2] + C[D-3] ) for D > 20

where C[D] is the estimated number of case numbers on Day D.

The right had sides must be equal so

1.4*C[D-1] = 1.14333333 * ( C[D-2] + C[D-3] )

or after renumbering D, we obtain

C[D] = 1.14333333 * ( C[D-1] + C[D-2] )/1.4

or

C[D] = 0.816666667 * ( C[D-1] + C[D-2] ) for D > 19

Any of the above formulae can be used to calculate the same value C[D].

Coming back to Ro, in the above article in China we have a graph showing various values for Ro in China:

There is an interesting table in the article (heading below) that is worthwhile to read:

Below are the conclusions:

In previous posts, we have estimated the value of Re (and hence Ro) at up to 2.9 for New Zealand and also considered 2.7 as well.

In the conclusions above we see a median of 2.79 which is close to the average and median of our two estimates.

Our previous posts helped to confirm an incubation period of one cycle (5 days) and an infections period of two cycles (10 days).

We conclude that Ro for New Zealand may be at least as high as 2.9
i.e. a person infected with COVID-19 may infect on average close to three other people.

New Zealand went from 8 actual cases (Day 18; 16 March; 10 cases estimated) until the day after New Zealand went into Lockdown Level 4 at 11.49 pm on 25 March (Day 28; 26 March; 283 actual cases total; 289 estimated total).

New Zealand went from 8 cases to 283 cases in 10 days.

This is similar to 1 case going to 36 (283/8 = 35.373) in two more cycles.

Our estimates go from 10 cases to 289 cases over the same period.

This is similar to 1 case going to almost 30.

This suggests Ro is close to 5; a tree structure with 5 branches at each level produces the sequence 1, 5, 25 giving a total of 31 cases.

Ro = 5 maybe therefore feasible.

In the post below we considered R = 5.3782 too high:
https://aaamazingphoenix.wordpress.com/2020/05/23/covid-19-nz-can-one-person-infect-2-7-to-2-8-others/

Maybe a value for Ro close to 5.3782 (5.4?) is correct after all?

We will explore this in the next post.

A value for Ro of 5.3782 presently appears unrealistic.

See the table below:
(model starts with a total of 10 cases- extra numbers backfilled)

Cases and cases estimates are shown in the graph below
(the red curve can be produced by any of the formula at the top of this post):

My other COVID-19 posts can be found here:
https://aaamazingphoenix.wordpress.com/tag/coronavirus/

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