Rako Science calculate R0 for New Zealand delta outbreak

Updated: May 16

Last year Rako Science developed a novel epidemiological method called SIR+B which is now a public domain method described in this technical report. We have used this new method to gain insights into the spread of COVID-19 with daily calculations and the results are reported in a mapping tool here. This method has given us many valuable insights into how SARS-CoV-2 variants have spread across the globe in the last year and more recently the transmission of the delta variant.


In this post we apply the SIR+B method to New Zealand for the second outbreak, and the results are displayed in the infographic below.

Figure 1 Infographic of New Zealand delta outbreak starting in August. The graphic has SIR+B calculations of the Effective Reproduction Number, RO, (black squares) with 75% Confidence Intervals (dark grey) and 95% Confidence Intervals (light grey) as a time series. The critical line of R0 = 1 is displayed as a dashed red line. When R0 is above this critical line the disease is increasing and below this line the disease is decreasing. On the right axis is the scale for daily reported positive cases for New Zealand taken from Johns Hopkins University - Center for Systems Science and Engineering which is displayed as blue bars. The commentary is shown in speech bubbles. Red speech bubbles are increases in New Zealand Government COVID-19 Alert Levels. Green speech bubbles are New Zealand Government Alert Level relaxations. Yellow speech bubbles are events that are relevant to the current delta outbreak. Click on the image to expand.


The index case of the current delta outbreak will likely never be known; however, it is most likely that delta infection was introduced into New Zealand by unquarantined, returning travelers prior to the closure of the trans-Tasman travel bubble by the New Zealand Government on 23 July 2021.


The New Zealand Government required returning travelers to have evidence of a pre-departure test on arrival and it was widely reported that only 10% of arrivals were checked for COVID-19 testing status. The timing of the subsequent outbreak, the lack of adequate surveillance testing at the time and the eventual whole genomic sequencing indicated that the current outbreak was a result of this infiltration.


The first delta case was detected in symptomatic testing of a Devonport male on 17 August 2021. The government immediately imposed Alert Level 4 restrictions (see red speech bubbles). It is known that lockdowns and social distancing restrictions rapidly lower the Effective Reproduction Number R0 and this can be seen with R0 decreasing below 1 on 31 August less than 13 days after the detection of the first symptomatic case.


The lockdown was followed by an increase in testing and positive daily cases leading to reports on 24 August that a cluster of 58 positive cases had resulted from a Mangere church service on 15 August.


The aggressive restrictions placed on New Zealand society was slowly lifted in a series of relaxations (see green speech bubbles) on 31 August, 2 September, 7 September, and 25 September with the implementation of border testing and travel restrictions north and south of Auckland. Again, these restrictions were not rigorously enforced and merely having evidence of having a test, rather than a test result confirming COVID-19 negativity, was sufficient to cross the border and travel outside of Auckland.


The testing and travel restrictions imposed by the Government on the Waikato border were not rigorously applied and positive cases travelled across the border first to Taranaki where a symptomatic test of a truck driver detected delta-variant, followed by a series of outbreaks in South Waikato starting 3 October related to the movement of individuals allegedly connected with illegal activity within marginalised communities.


On or about 24 September the R0 increases and becomes greater than 1. About 10 days later the daily case data begins to rise. By 3 October our SIR+B calculations show that R0 was 1.6 (CI 95% 1.4-1.9). The R0 value has continued to rise since 3 October.


The mathematics is clear. The delta variant was circulating at low levels in the Auckland population for a month during the lockdowns from 17 August to about 24 September. The presence of delta variant infections in marginalised communities, which were not complying with public health orders, led to outbreaks in Waikato and the movement across the northern border into Northland.


During this time lockdown fatigue and the “social license” of the general population was eroding. Delta variant infections were being transmitted from marginalised communities and into the general population and the R0 value increased.


Today the Effective Reproduction Number R0 = 1.9 (CI 95% 1.6-2.2).


New Zealand is still without the protection of adequate, diagnostically validated surveillance testing infrastructure required to suppress or eliminate the current outbreak. The longer this is the case the greater risk to lives and livelihoods in Aotearoa New Zealand.


The testing infrastructure required must be highly sensitive and non-invasive, operated without the need of medical professionals who are running at capacity and beyond, with fast turnaround times and deployed on a population scale. With such an infrastructure we can interrupt transmission and “buy more time” to get out vaccination rate to the sought after 90%.



​Stephen Grice is a founder and director of Rako Science. Stephen has a PhD in Physical Chemistry and 30 years of experience working in the high tech, business and science sectors.


Stephen's work with University of Illinois Urbana Champaign on new mathematical methods for the epidemiology led to licensing and development of covidSHIELD in New Zealand and the implementation of the saliva test protocol by accredited New Zealand laboratory IGENZ.

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