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ScienceOctober 26, 2021

We built a model that shows how small rule changes can fuel delta’s spread


Members of the Covid-19 modelling team at Te Pūnaha Matatini explain what their research reveals the way a sparsely connected network can very quickly turn into a densely connected one.. 

By Dion O’Neale, Emily Harvey, Steven Turnbull, James Gilmour and Kylie Stewart

As Aotearoa continues to deal with the ongoing impact of an outbreak of the delta variant of Covid-19, the New Zealand government announced on Friday a three-step “roadmap” to begin reconnecting Aucklanders, followed by a Covid traffic light framework. In Auckland, many Early Childhood Centres have reopened, secondary students are returning to school, and two household bubbles are now permitted to gather together outdoors.

With the move in Auckland from an elimination strategy (with clear and strong lockdown guidelines) to one of suppression (“living with the virus”), we now need to collectively consider the consequences of the decisions made by individuals, households, workplaces, and communities. While the easing of restrictions might come as a relief for many who are missing friends and family, and those who are struggling with social isolation, it is important to understand how this shift in strategy could change the nature of transmission across Auckland. As Aotearoa works hard to vaccinate those who remain we must also be cognisant of the individuals, households, workplaces, and communities we are requiring more of.

Simple changes, complex outcomes

While it is easy to say that decreases in alert levels open up additional transmission pathways, there is more to be said about the complex nature of these changes. Complexity science considers the idea that simple changes in a network can result in complex outcomes. One seemingly small policy change which sees the introduction of just one or two new connections between families, could result in a city, region, or country that is far more connected than initially assumed. A common phenomena within these types of complex networks is called the “percolation effect” where the addition of new connections within a network results in a “phase transition”; where a once sparsely connected network can very quickly turn into a densely connected one. Might the percolation effect mean that the gradual addition of community connections results in a vastly more connected Auckland?

Through the Populated Aotearoa Interaction Network, we have created a “synthetic” version of Aotearoa, where every person has an age, sex, ethnicity, place of employment and/or education. These individuals, which are treated as nodes in a network, also interact through community contexts, much like those we will experience when we begin interacting with family members and friends as restrictions ease. The network provides the opportunity to model contagion in a way that might more accurately reflect the experiences of individuals, when compared to less complex models that average out these interaction patterns.

This has allowed us to model the potential trajectory of outbreaks of Covid-19, and predict the impact of different circumstances like changes in alert level policy, rates of vaccination and increased social connection might have on the spread of Covid-19. One important feature of the network we can look at is the “largest connected component”, which tells us the approximate number of people Covid-19 could theoretically spread to via potential transmission pathways, based on the connections people share.

How much more connected might Auckland become?

In a scenario like alert level four, where the vast majority of community connections are removed, we see the New Zealand network broken up into many small disconnected sections. In this case, the largest connected component would contain around 90,000 connected individuals. But for a level of intervention like alert level three, potential community interactions increase through families extending their bubbles, or reconnecting with others outside their household, we see the size of the largest connected component increase drastically. Our modeling of alert level three indicates the size of the largest connected component in the interaction network is expected to increase by a factor of almost 15, to around 1.4 million connected individuals. These numbers are for the optimistic situation of assuming that we can neglect interactions in workplaces on the basis that measures such as masking and good ventilation mean that transmission in workplaces is significantly reduced.

This clearly demonstrates that New Zealand is a highly connected society. Even without the vast majority of the community interactions we are used to, most New Zealanders will still be connected to each other through the interactions that we share. We do argue that this makes the mitigation strategies that we have in place especially important going forward.

One of our team, Dr Dion O’Neale, has put it like this: “The roadmap looks like a significant increase of risk for wider transmission, given that there is still ongoing community transmission with unlinked cases. Preventing the spread of Covid-19 in the community requires two components: minimising the number of interactions and also minimising the chance of transmission for those interactions that do still occur. Even with people only meeting up in pairs, this change moves us to a situation where Auckland is essentially reconnected from a contagion point of view.”

An equity-based response to the ‘pandemic of the unvaccinated’

This move has come at a point where there are still large sections of the community with very low vaccination numbers, in particular Māori and of course younger people for whom vaccination is not yet an option. The average age of Māori in Auckland is 28, so this younger cohort has only been eligible for vaccination for six to seven weeks. The return of children to ECE, with bubbles of up to 10, is also concerning since infants and toddlers cannot currently be vaccinated and high rates of respiratory illness among New Zealand children further compounds the risk of serious illness if they were to contract Covid-19.

“Low vaccination rates are highly likely to be attributable to difficulties accessing the vaccine especially in rural and remote areas, or where a lot of the population work long hours or are carers who find it hard to get away from responsibility,” wrote Dr Janine Paynter, an expert on vaccination at the University of Auckland. “It is imperative we reduce these barriers quickly: taking the vaccines to where people are, opening vaccination clinics or sites for longer, and encouraging employers to specifically ensure their employees are given time to get vaccinated.”

Researcher Tina Ngata (Ngāti Porou) wrote: “The unfairness is stinging – Te Roopu Whakakaupapa Urutā and numerous other Māori and Non-Māori health and health research organisations foresaw this, warned of this, and were sidelined by the government, and we are now being pushed into  an untenable situation: We were hobbled from the outset, forced to play catch up, and are now being told the rest of the nation will not wait for us to catch up anyway. Yet again, we are being told through policy that we are disposable in the interests of everyone else”

New freedoms in Auckland an option, not a target

Our models clearly show that only a small number of additional connections are necessary to sufficiently connect existing bubbles such that a large percent of the population would be reachable if there is uncontrolled spread. The evidence is very clear from this current outbreak, that the virus is finding unvaccinated people. “Most of the cases are among Māori and Pacific people,” said University of Auckland associate professor Collin Tukuitonga. “The overall trend upwards is a concern. The move down to level three and some relaxation of public health measures would have permitted more movement of people (over and above people who break the rules), and increased the spread of Delta”

Most of us can’t directly impact the decisions the government will make; what we can control is the decisions we make ourselves. The best we can do right now is manage our own risk, make sure when the connections are made, the virus can’t spread. There are several steps we can take to ensure that the connections that we are a part of do not turn into uncontrolled clusters of Covid-19. With the exception of those now required to go back to work, it might pay to think of these new freedoms as an option, not a target. Not all of our connections are equal, some have more serious consequences depending on context.

Even if we’re vaccinated, as many of us as possible, should continue to “act like we have the virus”, thinking about our new contacts as potentially being connected to cases of Covid-19 that haven’t been detected yet. If you choose to reconnect with family or friends, keep the total number of new connections you make to a minimum. If meeting people from other households, take every precaution to keep each other safe, stay outside, and always wear a well fitted mask. Make a note of all of your catch ups in your Covid Tracer app, and remember to record the contact name and phone numbers of your connections to make contact tracing as fast and easy as possible should you come into contact with the virus.

Creating large chains by connecting with lots of different bubbles will very quickly result in one large connected chain, increasing the risk of spread, and making contact tracing more difficult. It falls upon all of us to take every step we can to make sure we protect our loved ones, and our community.

Te matatini o te horapa: a population based contagion network for Aotearoa NZ, is a Health Research Council-funded project in response to Covid-19 led by Dr Dion O’Neale (Department of Physics, University of Auckland) and Dr Emily Harvey (Senior Researcher, Market Economics). They are joined by investigators Dr Steven Turnbull (Research Fellow, University of Auckland), Dr James Gilmour (Research Fellow, University of Auckland) and Kylie Stewart (freelance science communicator.) O’Neale, Harvey, Turnbull, and Gilmour are all members of the Te Pūnaha Matatini Covid-19 Modeling team.

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