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ScienceAugust 25, 2023

The maths of Covid immunity

a yellow image showing a map of New Zealand + a virus + a vaccine = ...
Image: Tina Tiller

With Covid now endemic, modelling suggests targeted protection will be more effective than blanket measures.

Interventions designed to limit the spread of Covid have been rolled back around the world. In New Zealand, the government removed all remaining public health measures last week.

But although the emergency is over and the disease is rapidly becoming endemic, the risk of new variants remains. Covid is still causing a significant health burden.

Is there more we could be doing to prevent infections?

We lack quality evidence about how effective different interventions are. But simple maths shows that, in the long term, the prevalence of a highly infectious endemic virus like SARS-CoV-2 is quite difficult to budge.

The basic reproduction number

Back in 2020, we heard a lot about the basic reproduction number or R0. This is the average number of people someone infects when the whole population is susceptible to the disease. With a susceptible population, if R0 is above 1 the disease spreads exponentially.

This situation prompted governments around the world to implement intensive response measures, including lockdowns, to prevent health systems from becoming completely overwhelmed.

The situation in 2023 is vastly different. Almost everyone has some form of immunity, acquired either from vaccination, previous infection, or both. However, people will eventually become susceptible again because of waning immunity and new variants.

This in turn means the virus won’t disappear altogether. Instead, the prevalence of infection will eventually reach what mathematicians call an endemic equilibrium. This is a state of balance: the loss of immunity due to its waning (and the cycle of births and deaths) is balanced by new immunity due to infections and vaccinations.

We don’t expect infection rates to be perfectly steady. Prevalence will rise and fall, influenced by seasons, school holidays and new subvariants, but it will always be pulled back towards the equilibrium level.

Controlling the disease

Unlike measles or polio, it’s impossible to eliminate Covid with the tools currently available. But that doesn’t mean we can’t reduce its impacts. Effective control measures should reduce the number of contacts infectious people have, or the risk of infection per contact. And this should lower the level of the endemic equilibrium, meaning there are fewer infections.

That’s certainly true, but how much effect do control measures realistically have for a virus like SARS-CoV-2?

R0 for the Omicron variant has been estimated between 6 and 10. But the effective reproduction number – the average number of people someone infects at the present time – is much closer to 1. In New Zealand, this number has hovered between 0.8 and 1.2 for the past year.

This tells us something about the amount of immunity in the population. If an average person would infect six people in a fully susceptible population, but only infects one person in reality, that means five out of six people must be immune. If R0=10, then nine out of ten people must be immune, and so on.

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The maths of immunity

People may have acquired immunity through vaccination, but the protection vaccines provide against infection with current Omicron variants is relatively low and short-lived.

The majority of immunity comes from previous infections, including infections in vaccinated people. This is called “hybrid immunity” and it provides better protection than infection or vaccination alone. (This doesn’t mean that getting infected to get immunity should ever be a goal, but it is an important side effect).

A consequence of this is that the fraction of the population that is immune at a given point in time is proportional to the number of infections per year. It turns out this allows us to estimate the benefit of interventions.

For example, suppose R0=6 and a control measure, such as isolation of all confirmed cases, reduces infectious contacts by 20%. That’s equivalent to reducing R0 to 4.8, which means the immune fraction is reduced from 83% of the population to 79%. That’s only a 5% relative reduction in the number of yearly infections, even though the transmission rate was reduced by 20%.

If R0=10, the maths is even more dismal: the same control measure only gives a 3% reduction in infections.

This graph shows the relative reduction in infections as a result of a control measure to limit infectious contacts. For highly infectious diseases with a large R0, the curves are relatively flat on the left side of the graph, which means a moderate reduc
This graph shows the relative reduction in infections as a result of a control measure to limit infectious contacts. For highly infectious diseases with a large R0, the curves are relatively flat on the left side of the graph, which means a moderate reduction in infectious contacts has a relatively small effect on disease prevalence.
Author provided, CC BY-SA

What’s the reason for this surprising finding? To begin with, the intervention reduces the number of infections, which is good. But an unfortunate side effect is that fewer people become immune, which means infections start to increase again.

Things eventually balance out at a lower level than without the intervention, but most of the benefit is sucked up by compensating for the lost immunity in the population.

For pathogens that are much less infectious than SARS-CoV-2, the opposite can be true. If R0=1.2, then a 20% reduction in infectious contacts would be enough to set the disease on a trajectory towards total elimination.

Targeted protection

The arguments above come from a mathematical model that captures the processes behind disease transmission in a simple way. Reality is more complicated. The susceptible-immune binary is a simplification because immunity is not black and white but shades of grey.

And populations are highly varied, not homogeneous. Infections will be more frequent in groups with high contact rates, which typically means younger people. Mathematically, that means infection rates will be harder to budge in younger groups and relatively easier to bring down in older groups.

Interventions targeted towards vulnerable groups are likely to be more effective than blanket measures. Importantly, although reducing infection rates in the long term is difficult, vaccines provide direct protection for those who take them and continue to be highly effective at preventing severe disease.

None of this is an argument that we shouldn’t try to reduce the prevalence of endemic diseases like Covid. But it does mean we can’t assume that a reduction in the number of infectious contacts will translate to an equivalent reduction in infection rates.

Decreasing the number of SARS-CoV-2 infections would be highly beneficial. It would reduce the acute health burden, the incidence of long Covid, and the level of risk for vulnerable groups.

But it’s not a goal we can afford to pursue at any cost. There is a range of healthcare needs competing for limited resources, so any measures need to be cost effective. And that means being realistic about the size of the benefits they’re likely to deliver.

Michael Plank, Professor in Applied Mathematics, University of Canterbury; Freya Shearer, Research Fellow, Epidemic Decision Support, The University of Melbourne; James McCaw, Professor in Mathematical Biology, The University of Melbourne, and James Wood, Professor, epidemiological modelling of infectious diseases, UNSW Sydney

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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(Image: Getty, additional design: Archi Banal)
(Image: Getty, additional design: Archi Banal)

ScienceAugust 17, 2023

The science camp helping Māori and Pasifika students to thrive

(Image: Getty, additional design: Archi Banal)
(Image: Getty, additional design: Archi Banal)

Diversity in academia is essential to expanding our knowledge systems and getting better outcomes for communities. Hands-on science programme DiscoveryCamp is helping expose more young people to the possibilities of science.

This story was first published in September 2022.

Raukura Kahukiwa (Ngāti Whakaue, Ngāpuhi, Tainui) is one of those people who knows exactly how she wants her career to play out. When she leaves Rotorua Girls High School at the end of this year she’s going to enter the first year health science programme at the University of Otago. She then hopes to enter the medical school the following year, and ultimately specialise in paediatrics.

But in the short term she’s just excited to cover a wide variety of scientific topics in her first year at university. She’s always been drawn to the way science helps explain how our world functions and interacts. “Science is so multifaceted and intriguing. I love dissecting and learning about how things work, which is essentially what science is all about,” she says.

But as tangata Māori, Kahukiwa’s path into academia and especially science has traditionally been obscured with systemic barriers. Māori and Pacific academics make up less than 5% and 2% respectively across New Zealand’s universities. New research found Māori and Pasifika postgraduate students in science, technology, engineering, and maths (STEM) experienced racism, tokenism, isolation and exploitation.


Applications for Discovery Camp 2024 are open now!


However, programmes designed to create safe spaces to guide Māori and Pasifika students into science and academia and make sure they succeed when they get there are having a real impact on young people like Kahukiwa as they contemplate their future. When asked if she encountered barriers to pursuing science because she was Māori, she explained her experience had in fact been the opposite.

“I frequently attended the Matakokiri Science Camps run by Ngāti Whakaue which were set up to encourage Maori tamariki to pursue STEM in the future. In addition to this, I was also one of the first students to attend Te Rangihakahaka (also under Ngāti Whakaue), which was practically an extension of the science camps. I have always felt supported in my pursuit of a career in science,” she says.

This year she attended the MacDiarmid Institute’s DiscoveryCamp. The annual programme provides a place for Māori and Pasifika high school students to do real research under the guidance of the country’s leading scientists. The four day residential lab experience helped Kahukiwa appreciate the opportunities that exist for her future.

“Having the opportunity to speak to the PhD students, lecturers, and academics who essentially are the top in their fields and actually see the cutting edge work they’re doing was definitely the most important part of the experience to me. It altered my views on possibly pursuing higher education such as a masters or PhD which would have otherwise seemed unfeasible,” she says.

Applications for DiscoveryCamp 2024 for current year 12 and 13 Māori and Pasifika students are open now. Students on the camp complete hands-on investigations into topics like electron microscopy, laser physics and nano-electronics. The camp is designed to inspire Māori and Pasifika secondary students to continue in science, particularly physical sciences. It wants to showcase the role they could have in helping humanity’s future on our planet through studying materials science.

While Awhi Marshall (Ngāti Pikiao, Ngāti Mahuta, Nga Muri Kaitaua) is not exactly sure where they want to take their career, they know their future is a career in engineering and science, and will include some post-grad research. In their final year at Auckland’s Northcote College, Marshall is fascinated by the role of science in the biggest issues our world faces.

“I am excited for the future of humanity, and the role science has to play. We need science for fighting climate change, ensuring the global food supply, and protecting our environment. If I can be a part of that future, and I can help generations to come, then I’m happy,” they say.

A 2022 DiscoveryCamp attendee, Marshall made close connections with the other campers and was inspired by how much fun real life research was in practice. The experience helped reveal what their future in science could look like.

“Being able to talk to students currently engaging in world-leading post-graduate study really opened the door in my mind to that path for me. It seems impossible to undergo any major study, especially post-grad, with the current state of student financial support, but they made us feel that it was possible, and worth it,” Marshall says.

Marshall believes DiscoveryCamp’s focus on creating a path for Māori and Pasifika students is an essential kaupapa to help the sciences expand their own appreciation, understanding and engagement of diverse cultures and knowledge systems. And they see this is a huge opportunity to bring new perspectives to the most important challenges facing the world right now.

“Having more Māori in science allows greater and wider world views than those that usually dominate scientific research and study. Incorporating te ao Māori, and Indigenous cultures and practices worldwide, is key to scientific progress and solving the issues that face humanity as we move forward,” Marshall says.

But to completely break down the barriers to Māori and Pasifika entering science fields will require deep systemic change, says new MacDiarmid Institute associate investigator Dr Taniela Lolohea. Despite recent progress and programmes like DiscoveryCamp, he remains concerned that universities are saying all the right things about diversity but aren’t making the changes required to allow Māori and Pasifika students to succeed and thrive in those spaces.

“Often the organisations are saying all the right things in their Terms of Agreement documents, but whether it’s fruitful or just words is hard to say. It looks like movement but feels like words till things happen.”

Lolohea has been involved in DiscoveryCamp as a mentor for the past six years. He sees it as an essential opportunity to expose young people who are passionate about science to the realities of university but also introducing them to people who have come into that space and succeeded.

“It’s about building their understanding of what university life is like. For a lot of people university is a foreign thing and so a lot of them don’t actually experience it till they actually get on campus,” he says. “And even then, when it’s your first time experiencing it, you don’t get a lot of interaction time with academics or PhD students. And so it’s, it’s allowing that opportunity for them to explore the university on a different and more interactive level, than I think they could ever get even in their first year.”

When Lolohea was a student at university he watched as the contingent of around 50 other Māori and Pasifika students dwindled to just a few by the end of his third year. And from his honours year into his PhD and post doctoral study he was the only one. Now a lecturer in chemistry at Auckland University of Technology (AUT), Lolohea never dreamed of working at a university because he just didn’t think it was possible for someone like him.

“When I was coming through, I never thought I’d be like an academic at all, because I’d never seen a Maori or Pasifika academic when I was in chemistry and science. And so I’ve never thought it was a thing,” he says.

That experience has motivated Lolohea to work with Māori and Pasifika science students to show them that there is a fertile pathway into the field.

“I think it’s important to have representation, particularly in academia, because it’s hard to be what you cannot see yourself. I think the main thing is to be able to see yourself in an environment and to see role models that you can look towards,” he says. ”I take my position quite seriously because I know there are other Māori and Pacific people looking to me, and they’re kind of thinking, ‘if he could do it, then then why can’t I.’”

And by guiding more Māori and Pasifika into science, Lolohea sees the opportunity to diversify the way we understand science and the knowledge and traditions that inform it. With that diversity comes knowledge of different communities and allows research to have access that might otherwise be unavailable and that can equate to real impact.

“Diversity matters because of diversity of thought, diversity of research, but also the diversity of the researchers. A lot of the time, it does take a Māori person or Pacific person to be that bridging person between a university and the community,” he says.

“Trying to draw students into those kinds of research environments is important. A lot of them are interested in their own history and where they come from and how they can actually help their own people.”

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