In 2020, We found that in New Zealand given a a 10-day infectious period, and a daily increase in COVID-19 infections of r = 1.4, one person with COVID-19 may infect on average 4.14 other people and for a 15-day infectious period, one infected person may infect around 6 other people.
We extend our previous results to show values for Ro (or Re) between 3.5 and 7.5.
Since early calculations (e.g. by WHO) assumed a value for Ro of between 1.4 and 2.5, our results are a significant increase over the original estimates and most current Ro values. See:
In this post we consider again the formula developed last year during simulations for the spread of COVID-19 in New Zealand to calculate (Ro) the number of people one person with COVID-19 may infect on average during the initial outbreak in early 2020 (without quarantine or self-isolation) and consider Re, the effective reproduction rate with quarantine and self-isolation.
We assume a homogeneous population where the spread within the population is similar throughout the population.
New Zealand is relatively isolated and therefore is suitable for estimating the spread of COVID-19 in general in the world.
By definition we let:
- r denote the effective Reproduction rate of COVID-19 for one day
- Ro (R0; R-Zero; R-Nought) denote the Reproduction number for COVID-19 without any quarantine or isolation
- Re denote the effective Reproduction number for COVID-19
(Re assumes isolation/quarantine is happening)
- a case be defined as a person diagnosed as having COVID-19
Note that Ro and Re are numbers (not rates), the number of people one person with COVID-19 may infect on average without quarantine or isolation (Ro) and with quarantine or isolation (Re).
We assume a person may be infectious for n days once they become symptomatic (show symptoms). A person may be infectious for at least two days prior to becoming symptomatic.
We assume a 5-day cycle where the incubation period is one cycle long (until symptoms appear) and the infectious period is two cycles long.
In New Zealand we have found a daily rate of increase of r ~ 1.4 (40% increase per day) in March and assume a 10-day infectious period (when a case can infect others).
We assume a daily increase of r (e.g. r = 1.4) and a daily decay in infectivity of 1/r over a 10-day infectious period for each case. We also consider r = SQRT(2) [~1.4142]
Our findings produced the formula in the table below to calculate Ro, where n is the number of days a person is infectious. We show values for Ro (or Re) between 3.5 and 7.5.