̽��ֱ�� of Cambridge - mathematical model

New Cambridge-developed resources help students learn how maths can help tackle infectious diseases

sc604 — Mon, 19 Feb 2024 07:00:00 +0000

From measles and flu to SARS and COVID, mathematicians help us understand and predict the epidemics that can spread through our communities, and to help us look at strategies that we may be able to use to contain them.

̽��ֱ��project, called Contagious Maths, was led by Professor Julia Gog from Cambridge’s Department of Applied Mathematics and Theoretical Physics (DAMTP), and was supported by a Rosalind Franklin Award from the Royal Society.

̽��ֱ��curriculum-linked resources will give students between the ages 11 and 14 the opportunity to join researchers on the mathematical frontline to learn more about infectious disease spread, along with interactive tools to try mathematical modelling for themselves. Teachers receive full lesson plans, backed up by Cambridge research.

“I’ve always loved maths. I was lucky enough to have amazing teachers at sixth form who challenged me and were 100% behind me pursuing maths at the highest level, but maths as it’s taught in school can be highly abstract, so students often wonder what the point of maths even is,” said Gog, who is also Director of the Millennium Maths Project. “This is something I’m trying to help with now: to offer a glimpse from school to the research world to see the role mathematics can play in tackling important real-world problems.”

̽��ֱ��Contagious Maths project introduces mathematical modelling; explores how mathematicians can model the spread of disease through a population and the type of questions we might think about when looking at models; and gives an insight into what mathematics researchers working on these real-life problems actually do.

“I’ve been engaged in outreach for many years at Cambridge, and the Contagious Maths project grew out of discussions with colleagues who have expertise in reaching school-age children,” said Gog. “ ̽��ֱ��11-14 age group we are targeting is a real crunch point for retaining girls in maths, and future female mathematicians. What exactly happens is complex and multifaceted, but this is a period when people form their views on how they fit with maths and science.

“Many of them disengage, as it can seem that maths at school is utterly disconnected from the real world. It can also be a time when maths appears very starkly right or wrong, whereas any research mathematician can tell you it’s always so much more subtle than that, and therefore so much more interesting!”

Gog hopes the Contagious Maths resources might be able to help, as they are designed to be used in regular school lessons, and cover a topic with clear real-world importance.

“ ̽��ֱ��maths is never black and white in this field: there are always ways to challenge and develop the models, and some tricky thinking to be done about how the real epidemics and the simulations are really related to each other,” she said. “I suspect some students will find this frustrating, and just want maths to be algorithmic exercises. But some will be intrigued, and they are the ones we are trying to reach and expose to this larger world of applied maths research.”

Contagious Maths also provides teachers with all the ideas and tools they need, so they have at their fingertips all they need to deliver these lessons, even if they have no experience with research mathematics. “We hope this project will help these teachers to bring in the wider view of mathematics, and we hope it inspires them too,” said Gog. “It’s been really fun developing these resources, teaming up with both NRICH and Plus to make the most of our combined expertise.”

Maths teachers can attend a free online event on 20 March to learn more about the project.

In addition to the school resources, Gog and her colleagues have designed another version of Contagious Maths for a more general self-guided audience, which will work for students older than 14 or anyone, of any age, who is interested in learning about mathematical modelling.

“ ̽��ֱ��paradox between the cleanness and precision of mathematics, and the utter hot mess of anything that involves biological dynamics across populations – like an outbreak of an infectious disease, is what intrigued me to stay in mathematics beyond my degree, and to move into research in mathematical biology,” said Gog. “Elegant theoretical ideas can tell us something valuable and universal about mitigating the devastating effects of disease on human and animal populations. Super abstract equations can hold fundamental truths about real-world problems - I don't think I will ever tire of thinking about that.”

Adapted from a Royal Society interview with Professor Julia Gog.

Cambridge mathematicians have developed a set of resources for students and teachers that will help them understand how maths can help tackle infectious diseases.

Orbon Alija via Getty Images

Aerial view of crowd connected by lines

̽��ֱ��text in this work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Images, including our videos, are Copyright © ̽��ֱ�� of Cambridge and licensors/contributors as identified. All rights reserved. We make our image and video content available in a number of ways – on our main website under its Terms and conditions, and on a range of channels including social media that permit your use and sharing of our content under their respective Terms.

Yes

Swarming cicadas, stock traders, and the wisdom of the crowd

sc604 — Thu, 01 Feb 2024 14:36:51 +0000

Pick almost any location in the eastern United States – say, Columbus Ohio. Every 13 or 17 years, as the soil warms in springtime, vast swarms of cicadas emerge from their underground burrows singing their deafening song, take flight and mate, producing offspring for the next cycle.

This noisy phenomenon repeats all over the eastern and southeastern US as 17 distinct broods emerge in staggered years. In spring 2024, billions of cicadas are expected as two different broods – one that appears every 13 years and another that appears every 17 years – emerge simultaneously.

Previous research has suggested that cicadas emerge once the soil temperature reaches 18°C, but even within a small geographical area, differences in sun exposure, foliage cover or humidity can lead to variations in temperature.

Now, in a paper published in the journal Physical Review E, researchers from the ̽��ֱ�� of Cambridge have discovered how such synchronous cicada swarms can emerge despite these temperature differences.

̽��ֱ��researchers developed a mathematical model for decision-making in an environment with variations in temperature and found that communication between cicada nymphs allows the group to come to a consensus about the local average temperature that then leads to large-scale swarms. ̽��ֱ��model is closely related to one that has been used to describe ‘avalanches’ in decision-making like those among stock market traders, leading to crashes.

Mathematicians have been captivated by the appearance of 17- and 13-year cycles in various species of cicadas, and have previously developed mathematical models that showed how the appearance of such large prime numbers is a consequence of evolutionary pressures to avoid predation. However, the mechanism by which swarms emerge coherently in a given year has not been understood.

In developing their model, the Cambridge team was inspired by previous research on decision-making that represents each member of a group by a ‘spin’ like that in a magnet, but instead of pointing up or down, the two states represent the decision to ‘remain’ or ‘emerge’.

̽��ֱ��local temperature experienced by the cicadas is then like a magnetic field that tends to align the spins and varies slowly from place to place on the scale of hundreds of metres, from sunny hilltops to shaded valleys in a forest. Communication between nearby nymphs is represented by an interaction between the spins that leads to local agreement of neighbours.

̽��ֱ��researchers showed that in the presence of such interactions the swarms are large and space-filling, involving every member of the population in a range of local temperature environments, unlike the case without communication in which every nymph is on its own, responding to every subtle variation in microclimate.

̽��ֱ��research was carried out Professor Raymond E Goldstein, the Alan Turing Professor of Complex Physical Systems in the Department of Applied Mathematics and Theoretical Physics (DAMTP), Professor Robert L Jack of DAMTP and the Yusuf Hamied Department of Chemistry, and Dr Adriana I Pesci, a Senior Research Associate in DAMTP.

“As an applied mathematician, there is nothing more interesting than finding a model capable of explaining the behaviour of living beings, even in the simplest of cases,” said Pesci.

̽��ֱ��researchers say that while their model does not require any particular means of communication between underground nymphs, acoustical signalling is a likely candidate, given the ear-splitting sounds that the swarms make once they emerge from underground.

̽��ֱ��researchers hope that their conjecture regarding the role of communication will stimulate field research to test the hypothesis.

“If our conjecture that communication between nymphs plays a role in swarm emergence is confirmed, it would provide a striking example of how Darwinian evolution can act for the benefit of the group, not just the individual,” said Goldstein.

This work was supported in part by the Complex Physical Systems Fund.

Reference:
R E Goldstein, R L Jack, and A I Pesci. ‘How Cicadas Emerge Together: Thermophysical Aspects of their Collective Decision-Making.’ Physical Review E (2024). DOI: 10.1103/PhysRevE.109.L022401

̽��ֱ��springtime emergence of vast swarms of cicadas can be explained by a mathematical model of collective decision-making with similarities to models describing stock market crashes.

Ed Reschke via Getty Images

Adult Periodical Cicada

Yes

For the brain, context is key to new theory of movement and memory

Anonymous — Wed, 24 Nov 2021 16:00:00 +0000

How is it that a chef can control their knife to fillet a fish or peel a grape and can wield a cleaver just as efficiently as a paring knife? Even those of us less proficient in the kitchen learn to skilfully handle an astonishing number of different objects throughout our lives, from shoelaces to tennis rackets.

This ability to continuously acquire new skills, without forgetting or degrading old ones, comes naturally to humans but is a major challenge even for today’s most advanced artificial intelligence systems.

Now, scientists from the ̽��ֱ�� of Cambridge and Columbia ̽��ֱ�� (USA) have developed and experimentally verified a new mathematical theory that explains how the human brain achieves this feat. Called the COntextual INference (COIN) model, it suggests that identifying the current context is key to learning how to move our bodies.

̽��ֱ��model describes a mechanism in the brain that is constantly trying to figure out the current context. ̽��ֱ��theory suggests that these continuously changing beliefs about context determine how to use existing memories — and whether to form new ones. ̽��ֱ��results are reported in the journal Nature.

“Imagine playing tennis with a different racket than usual or switching from tennis to squash,” said co-senior author Dr Daniel Wolpert from Columbia ̽��ֱ��. “Our theory explores how your brain adjusts to these situations and whether to treat them as distinct contexts.”

According to the COIN model, the brain maintains a repertoire of motor memories, each associated with the context in which it was created, such as playing squash versus tennis. Even for a single swing of the racket, the brain can draw upon many memories, each in proportion to how much the brain believes it is currently in the context in which that memory was created.

This goes against the traditional view that only one memory is used at a time. To improve performance on the next swing, the brain also updates all memories, once again depending on its belief about the current context. When the context of the movement is judged to be new (the first time we play squash after years of tennis, for example), the brain automatically creates a new memory for that context. This ensures that we do not overwrite previously established memories, such as the memory for playing tennis.

This research may lead to better physical therapy strategies to help people with injuries use their bodies again. Often the improvements seen in the setting of a physical therapist's office do not transfer to improvements in the real world.

“With a better understanding of how context affects motor learning, you can think about how to nudge the brain to generalise what it learns to contexts outside of the physical therapy session,” said first author Dr James Heald. “A better understanding of the basic mechanisms that underlie the context dependence of memory and learning could have therapeutic consequences in this area.”

“What I find exciting is that the principles of the COIN model may also generalise to many other forms of learning and memory, not just memories underlying our movement,” said co-senior author Professor Máté Lengyel from Cambridge’s Department of Engineering. “For example, the spontaneous recurrence of seemingly forgotten memories, often triggered by a change in our surroundings, has been observed both in motor learning and in post-traumatic stress disorder.”

COINing a new model

Practice with a tennis racket, and the brain forms motor memories of how you moved your arm and the rest of your body that improve your serve over time. But learning isn’t as simple as just making better memories to make movements more precise, the researchers said. Otherwise, a tennis player’s serves might improve to the point at which they never hit a ball out of bounds. ̽��ֱ��real world and our nervous systems are complex, and the brain has to deal with a lot of variability.

How does the brain distinguish this noise — these random fluctuations — from new situations? And how does it understand that a slightly lighter tennis racket can still be operated using previous tennis racket memories? But that a table tennis paddle is an entirely different kind of object that requires starting from scratch?

̽��ֱ��answer, according to the COIN model, may be Bayesian inference, a mathematical technique used to deal with uncertainty. This method statistically weighs new evidence in light of prior experience in order to update one's beliefs in a changeable world. In the COIN model, a context is a simplifying assumption that, in a given set of circumstances, certain actions are more likely to lead to some consequences than others. ̽��ֱ��new theory's acceptance of the role that uncertainty plays in motor learning is similar to how quantum physics views the universe in terms of probabilities instead of certainties, the scientists noted.

Getting a handle on the theory

̽��ֱ��researchers put the COIN model to the test on data from previous experiments, as well as new experiments, in which volunteers interacted with a robotic handle. Participants learned to manipulate the handle to reach a target while the handle pushed back in different ways.

Volunteers who spent time learning to operate the handle as it pushed to the left, for instance, had more trouble operating the handle when it changed behaviour and pushed to the right, as compared to volunteers who started with a handle pushing to the right. ̽��ֱ��COIN model explained this effect, called anterograde interference.

“ ̽��ֱ��longer you learn one task, the less likely you are to move into a new context with the second task,” said Wolpert. “You’re still forming a motor memory of the second task, but you’re not using it yet because your brain is still stuck back in the first context.”

̽��ֱ��model also predicted that a learned skill can re-emerge even after subsequent training seems to have erased it. Called spontaneous recovery, this re-emergence is seen in many other forms of learning besides motor learning. For example, spontaneous recovery has been linked with challenges in treating post-traumatic stress disorder, where contexts can trigger traumatic memories to spontaneously recur.

Scientists usually explain spontaneous recovery by invoking two different learning mechanisms. In one, memories learned quickly are forgotten quickly, and in the other, memories learned slowly are forgotten slowly, and can thus reappear. In contrast, the COIN model suggests there is just one mechanism for learning instead of two separate ones, and that memories that apparently vanished may be ready to pop back with the right trigger: the belief that the context has re-emerged. ̽��ֱ��researchers confirmed this in their lab with new experiments.

Máté Lengyel is a Fellow of Churchill College. ̽��ֱ��research was supported by the European Research Council, the Wellcome Trust, the Royal Society, the National Institutes of Health, and the Engineering and Physical Sciences Research Council.

Reference:
James B Heald, Máté Lengyel and Daniel M Wolpert. ‘Contextual inference underlies the learning of sensorimotor repertoires.’ Nature (2021). DOI: 10.1038/s41586-021-04129-3

Adapted from a Columbia ̽��ֱ�� press release.

Mathematical model could help in physical therapy and shed light on learning more generally.

̽��ֱ��COIN model may also generalise to many other forms of learning and memory, not just memories underlying our movement

Máté Lengyel

Chino Rocha via Unsplash

Tennis match

̽��ֱ��text in this work is licensed under a Creative Commons Attribution 4.0 International License. Images, including our videos, are Copyright © ̽��ֱ�� of Cambridge and licensors/contributors as identified. All rights reserved. We make our image and video content available in a number of ways – as here, on our main website under its Terms and conditions, and on a range of channels including social media that permit your use and sharing of our content under their respective Terms.

Yes

Study suggests R rate for tracking pandemic should be dropped in favour of ‘nowcasts’

cg566 — Tue, 28 Sep 2021 23:26:07 +0000

̽��ֱ��study, published in the Journal of the Royal Society Interface and led by researchers from the ̽��ֱ�� of Cambridge, is based on time-series models developed using classical statistical methods. ̽��ֱ��models produce 'nowcasts' and forecasts of the daily number of new cases and deaths that have already proved successful in predicting new COVID-19 waves and spikes in Germany, Florida in the USA, and several states in India.

̽��ֱ��study is co-authored by Andrew Harvey and Paul Kattuman, whose time-series model reflecting epidemic trajectories, known as the Harvey-Kattuman model, was introduced last year in a paper published in Harvard Data Science Review.

“ ̽��ֱ��basic R rate quickly wanes in usefulness as soon as a pandemic begins,” said Kattuman, from Cambridge Judge Business School. “ ̽��ֱ��basic R rate looks at the number of infections expected to result from a single infectious person in a completely susceptible population, and this changes as immunity builds up and measures such as social distancing are imposed.”

In later stages of a pandemic, the researchers conclude that use of the effective R rate which takes these factors into account is also not the best route: the focus should be not on contagiousness, but rather on the growth rate of new cases and deaths, examined alongside their predicted time path so a trajectory can be forecasted.

“These are the numbers that really help guide policymakers in making the crucial decisions that will hopefully save lives and prevent overcrowded hospitals as a pandemic plays out – which, as we have seen with COVID-19, can occur over months and even years,” said Kattuman. “ ̽��ֱ��data generated through this time-series model has already proved accurate and effective in countries around the world.”

̽��ֱ��study examines waves and spikes in tracking an epidemic, noting that after an epidemic has peaked, daily cases begin to fall as policymakers seek to prevent new spikes morphing into waves. ̽��ֱ��monitoring of waves and spikes raises different issues, primarily because a wave applies to a whole nation or a relatively large geographical area, whereas a spike is localised.

Therefore, a localised outbreak in a country with low national infection numbers can result in a jump in the national R rate, as occurred in the Westphalia area of Germany in June 2020 after an outbreak at a meat processing factory. However, this sort of jump does not indicate that there has been a sudden change in the way the infection spreads and so has few implications for overall policy.

̽��ֱ��Harvey-Kattuman model has been adapted into two trackers. ̽��ֱ��two Cambridge academics worked with the National Institute of Economic and Social Research to produce a UK tracker which is published biweekly by the National Institute of Economic and Social Research. In addition, they produce an India tracker which is published by the Centre for Health Leadership and Excellence at Cambridge Judge Business School. District-level pandemic trajectory forecasts using the model are used by public health policymakers in three states in India – Punjab, Tamil Nadu and Kerala – to identify regions at high risk and to frame containment and relaxation policies.

Reference:
Andrew Harvey and Paul Kattuman. ‘A Farewell to R: Time Series Models for Tracking and Forecasting Epidemics.’ Journal of the Royal Society Interface (2021). DOI: 10.1098/rsif.2021.0179

When the COVID-19 pandemic emerged in 2020, the R rate became well-known shorthand for the reproduction of the disease. Yet a new study suggests it’s time for ‘a farewell to R’ in favour of a different approach based on the growth rate of infection rather than contagiousness.

These are the numbers that help guide policymakers in making the decisions that will save lives and prevent overcrowded hospitals as a pandemic plays out

Paul Kattuman

Image by torstensimon from Pixabay

Covid-19 vaccine

Yes

Mathematical model predicts best way to build muscle

sc604 — Mon, 23 Aug 2021 04:28:37 +0000

̽��ֱ��researchers, from the ̽��ֱ�� of Cambridge, used methods of theoretical biophysics to construct the model, which can tell how much a specific amount of exertion will cause a muscle to grow and how long it will take. ̽��ֱ��model could form the basis of a software product, where users could optimise their exercise regimes by entering a few details of their individual physiology.

̽��ֱ��model is based on earlier work by the same team, which found that a component of muscle called titin is responsible for generating the chemical signals which affect muscle growth.

̽��ֱ��results, reported in the Biophysical Journal, suggest that there is an optimal weight at which to do resistance training for each person and each muscle growth target. Muscles can only be near their maximal load for a very short time, and it is the load integrated over time which activates the cell signalling pathway that leads to synthesis of new muscle proteins. But below a certain value, the load is insufficient to cause much signalling, and exercise time would have to increase exponentially to compensate. ̽��ֱ��value of this critical load is likely to depend on the particular physiology of the individual.

We all know that exercise builds muscle. Or do we? “Surprisingly, not very much is known about why or how exercise builds muscles: there’s a lot of anecdotal knowledge and acquired wisdom, but very little in the way of hard or proven data,” said Professor Eugene Terentjev from Cambridge’s Cavendish Laboratory, one of the paper’s authors.

When exercising, the higher the load, the more repetitions or the greater the frequency, then the greater the increase in muscle size. However, even when looking at the whole muscle, why or how much this happens isn’t known. ̽��ֱ��answers to both questions get even trickier as the focus goes down to a single muscle or its individual fibres.

Muscles are made up of individual filaments, which are only 2 micrometres long and less than a micrometre across, smaller than the size of the muscle cell. “Because of this, part of the explanation for muscle growth must be at the molecular scale,” said co-author Neil Ibata. “ ̽��ֱ��interactions between the main structural molecules in muscle were only pieced together around 50 years ago. How the smaller, accessory proteins fit into the picture is still not fully clear.”

This is because the data is very difficult to obtain: people differ greatly in their physiology and behaviour, making it almost impossible to conduct a controlled experiment on muscle size changes in a real person. “You can extract muscle cells and look at those individually, but that then ignores other problems like oxygen and glucose levels during exercise,” said Terentjev. “It’s very hard to look at it all together.”

Terentjev and his colleagues started looking at the mechanisms of mechanosensing – the ability of cells to sense mechanical cues in their environment – several years ago. ̽��ֱ��research was noticed by the English Institute of Sport, who were interested in whether it might relate to their observations in muscle rehabilitation. Together, they found that muscle hyper/atrophy was directly linked to the Cambridge work.

In 2018, the Cambridge researchers started a project on how the proteins in muscle filaments change under force. They found that main muscle constituents, actin and myosin, lack binding sites for signalling molecules, so it had to be the third-most abundant muscle component – titin – that was responsible for signalling the changes in applied force.

Whenever part of a molecule is under tension for a sufficiently long time, it toggles into a different state, exposing a previously hidden region. If this region can then bind to a small molecule involved in cell signalling, it activates that molecule, generating a chemical signal chain. Titin is a giant protein, a large part of which is extended when a muscle is stretched, but a small part of the molecule is also under tension during muscle contraction. This part of titin contains the so-called titin kinase domain, which is the one that generates the chemical signal that affects muscle growth.

̽��ֱ��molecule will be more likely to open if it is under more force, or when kept under the same force for longer. Both conditions will increase the number of activated signalling molecules. These molecules then induce the synthesis of more messenger RNA, leading to production of new muscle proteins, and the cross-section of the muscle cell increases.

This realisation led to the current work, started by Ibata, himself a keen athlete. “I was excited to gain a better understanding of both the why and how of muscle growth,” he said. “So much time and resources could be saved in avoiding low-productivity exercise regimes, and maximising athletes’ potential with regular higher value sessions, given a specific volume that the athlete is capable of achieving.”

Terentjev and Ibata set out to constrict a mathematical model that could give quantitative predictions on muscle growth. They started with a simple model that kept track of titin molecules opening under force and starting the signalling cascade. They used microscopy data to determine the force-dependent probability that a titin kinase unit would open or close under force and activate a signalling molecule.

They then made the model more complex by including additional information, such as metabolic energy exchange, as well as repetition length and recovery. ̽��ֱ��model was validated using past long-term studies on muscle hypertrophy.

“While there is experimental data showing similar muscle growth with loads as little as 30% of maximum load, our model suggests that loads of 70% are a more efficient method of stimulating growth,” said Terentjev, who is a Fellow of Queens' College. “Below that, the opening rate of titin kinase drops precipitously and precludes mechanosensitive signalling from taking place. Above that, rapid exhaustion prevents a good outcome, which our model has quantitatively predicted.”

“One of the challenges in preparing elite athletes is the common requirement for maximising adaptations while balancing associated trade-offs like energy costs,” said Fionn MacPartlin, Senior Strength & Conditioning Coach at the English Institute of Sport. “This work gives us more insight into the potential mechanisms of how muscles sense and respond to load, which can help us more specifically design interventions to meet these goals.”

̽��ֱ��model also addresses the problem of muscle atrophy, which occurs during long periods of bed rest or for astronauts in microgravity, showing both how long can a muscle afford to remain inactive before starting to deteriorate, and what the optimal recovery regime could be.

Eventually, the researchers hope to produce a user-friendly software-based application that could give individualised exercise regimes for specific goals. ̽��ֱ��researchers also hope to improve their model by extending their analysis with detailed data for both men and women, as many exercise studies are heavily biased towards male athletes.

Reference:
Neil Ibata and Eugene M. Terentjev. ‘Why exercise builds muscles: Titin mechanosensing controls skeletal muscle growth under load.’ Biophysical Journal (2021). DOI: 10.1016/j.bpj.2021.07.023

Researchers have developed a mathematical model that can predict the optimum exercise regime for building muscle.

Surprisingly, not very much is known about why or how exercise builds muscles: there’s a lot of anecdotal knowledge and acquired wisdom, but very little in the way of hard or proven data

Eugene Terentjev

John Arano on Unsplash

Woman lifting weights

Yes

How accurate were early expert predictions on COVID-19, and how did they compare to the public?

sc604 — Wed, 05 May 2021 18:00:00 +0000

Researchers from the Winton Centre for Risk and Evidence Communication surveyed 140 UK experts and 2,086 UK laypersons in April 2020 and asked them to make four quantitative predictions about the impact of COVID-19 by the end of 2020. Participants were also asked to indicate confidence in their predictions by providing upper and lower bounds of where they were 75% sure that the true answer would fall - for example, a participant would say they were 75% sure that the total number of infections would be between 300,000 and 800,000.

̽��ֱ��results, published in the journal PLOS ONE, demonstrate the difficulty in predicting the course of the pandemic, especially in its early days. While only 44% of predictions from the expert group fell within their own 75% confidence ranges, the non-expert group fared far worse, with only 12% of predictions falling within their ranges. Even when the non-expert group was restricted to those with high numeracy scores, only 16% of predictions fell within the ranges of values that they were 75% sure would contain the true outcomes.

“Experts perhaps didn’t predict as accurately as we hoped they might, but the fact that they were far more accurate than the non-expert group reminds us that they have expertise that’s worth listening to,” said Dr Gabriel Recchia from the Winton Centre for Risk and Evidence Communication, the paper’s lead author. “Predicting the course of a brand-new disease like COVID-19 just a few months after it had first been identified is incredibly difficult, but the important thing is for experts to be able to acknowledge uncertainty and adapt their predictions as more data become available.”

Throughout the COVID-19 pandemic, social and traditional media have disseminated predictions from experts and non-experts about its expected magnitude.

Expert opinion is undoubtedly important in informing and advising those making individual and policy-level decisions. However, as the quality of expert intuition can vary drastically depending on the field of expertise and the type of judgment required, it is important to conduct domain-specific research to establish how good expert predictions really are, particularly in cases where they have the potential to shape public opinion or government policy.

“People mean different things by ‘expert’: these are not necessarily people working on COVID-19 or developing the models to inform the response,” said Recchia. “Many of the people approached to provide comment or make predictions have relevant expertise, but not necessarily the most relevant.” He noted that in the early COVID-19 pandemic, clinicians, epidemiologists, statisticians, and other individuals seen as experts by the media and the general public, were frequently asked to give off-the-cuff answers to questions about how bad the pandemic might get. “We wanted to test how accurate some of these predictions from people with this kind of expertise were, and importantly, see how they compared to the public.”

For the survey, participants were asked to predict how many people living in their country would have died and would have been infected by the end of 2020; they were also asked to predict infection fatality rates both for their country and worldwide.

Both the expert group and the non-expert group underestimated the total number of deaths and infections in the UK. ̽��ֱ��official UK death toll at 31 December was 75,346. ̽��ֱ��median prediction of the expert group was 30,000, while the median prediction for the non-expert group was 25,000.

For infection fatality rates, the median expert prediction was that 10 out of every 1,000 people with the virus worldwide would die from it, and 9.5 out of 1,000 people with the virus in the UK would die from it. ̽��ֱ��median non-expert response to the same questions was 50 out of 1,000 and 40 out of 1,000. ̽��ֱ��real infection fatality rate at the end of 2020—as best the researchers could determine, given the fact that the true number of infections remains difficult to estimate—was closer to 4.55 out of 1,000 worldwide and 11.8 out of 1,000 in the UK.

“There’s a temptation to look at any results that says experts are less accurate than we might hope and say we shouldn’t listen to them, but the fact that non-experts did so much worse shows that it remains important to listen to experts, as long as we keep in mind that what happens in the real world can surprise you,” said Recchia.

̽��ֱ��researchers caution that it is important to differentiate between research evaluating the forecasts of ‘experts’—individuals holding occupations or roles in subject-relevant fields, such as epidemiologists and statisticians—and research evaluating specific epidemiological models, although expert forecasts may well be informed by epidemiological models. Many COVID-19 models have been found to be reasonably accurate over the short term, but get less accurate as they try to predict outcomes further into the future.

Reference:
Gabriel Recchia, Alexandra L.J. Freeman, David Spiegelhalter. ‘How well did experts and laypeople forecast the size of the COVID-19 pandemic?’ PLOS ONE (2021). DOI: 10.1371/journal.pone.0250935

Who made more accurate predictions about the course of the COVID-19 pandemic – experts or the public? A study from the ̽��ֱ�� of Cambridge has found that experts such as epidemiologists and statisticians made far more accurate predictions than the public, but both groups substantially underestimated the true extent of the pandemic.

Predicting the course of a brand-new disease like COVID-19 just a few months after it had first been identified is incredibly difficult, but the important thing is for experts to be able to acknowledge uncertainty and adapt their predictions as more data become available.

Gabriel Recchia

NIH Image Gallery

Novel Coronavirus SARS-Cov-2

Yes

Licence type:

Public Domain

New national modelling group to provide faster, more rigorous COVID-19 predictions

sc604 — Thu, 18 Feb 2021 16:47:30 +0000

̽��ֱ��JUNIPER consortium (‘Joint UNIversities Pandemic and Epidemiological Research’) brings together leading mathematical and statistical modellers from seven UK universities and has received £3 million in funding from UK Research and Innovation (UKRI).

JUNIPER is developing and using customised models to provide predictions and estimates on key questions about the COVID-19 pandemic. These results feed regularly into SPI-M, the modelling group that provides evidence to the Scientific Advisory Group for Emergencies (SAGE) and the wider UK government.

Examples of modelling JUNIPER provides to government includes:

Understanding how new variants are spreading across the UK and developing statistical models to determine whether new variants are causing more hospitalisations or deaths.
Forecasting and providing real-time estimates of the R-value, using data from sources such as Pillar 1 and 2 testing, hospital data and mobility data. They are currently providing eight of 12 models contributing real-time R estimates that go from SPI-M to SAGE each week.
Modelling the effectiveness of different testing strategies on virus transmission and suppression, and modelling the effect of vaccinations and predicting outcomes from different scenarios of how to ease lockdown restrictions.

Professor Julia Gog, co-lead of the consortium from Cambridge’s Department of Applied Mathematics and Theoretical Physics, said: “By bringing research groups together from our seven universities we can provide predictions and estimates about the pandemic to address questions from the government with unprecedented speed. By combining the right expertise together swiftly across research teams we can now respond to questions in less than 24 hours, which might have taken a week for one team working alone. And further, being able to call upon specialist expertise combinations across multiple research groups means we can provide more robust outputs.

“In this unprecedented pandemic, modelling has been hugely important to provide evidence-based predictions and estimates at great speed. Our insights from transmission modelling are fully integrated with scientific evidence from other disciplines and feed into government decision-making.”

Professor Matt Keeling, co-lead of the consortium from the ̽��ֱ�� of Warwick, said: “We’re generating about half the models for the nowcasting that goes into SPI-M and SAGE every week. This consortium allows us to not only boost our speed and capacity, but also to continue to advance the accuracy of our models using the new data and growing knowledge from the pandemic.

“Standard epidemiological modelling tools have worked well so far, but the future with COVID-19 now demands a suite of new tools to deal with the upcoming complexities of the pandemic, such as localised regional outbreaks, growing understanding of socioeconomic differences with this disease, complexities of imperfect vaccines and the growing problem ahead with new variants. Having several teams using different models working on the same problem helps us to verify our results and makes the consortium much bigger than the sum of its parts.”

̽��ֱ��consortium is funded as part of UKRI’s COVID-19 Agile Call, which has so far invested more than £150M in over 400 projects to address the impacts of the COVID-19 pandemic.

Professor Charlotte Deane, COVID-19 Response Director at UKRI, said: “This consortium enables disease modellers to pool their expertise nationally to increase the scale, speed and quality of their models of policy options and predictions for the pandemic. They’ll provide cutting-edge evidence about the pandemic into the UK government’s decision-making.”

̽��ֱ��consortium will also proactively generate new model-based predictions and develop the necessary methodology as part of a horizon-scanning process.

̽��ֱ��consortium plan to make their models open-source, so scientists worldwide can access them and benefit.

̽��ֱ��seven universities involved in JUNIPER are Cambridge, Warwick, Exeter, Oxford, Bristol, Manchester and Lancaster Universities.

They will work closely with other organisations and research teams active on COVID-19 research including the Alan Turing Institute, the Royal Statistical Society, Health Data Research UK, Public Health England, the Royal Society’s ‘RAMP’ initiative, and the Isaac Newton Institute for Mathematical Sciences.

A new national consortium, co-led by the ̽��ֱ�� of Cambridge, will bring together mathematical modellers to produce faster, more rigorous predictions for the COVID-19 pandemic and advise UK government bodies.

Gordon Johnson from Pixabay

Connections

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̽��ֱ��cosmologist modelling the Universe with maths

cg605 — Thu, 18 Feb 2021 13:11:42 +0000

Dr Tobias Baldauf likes nothing better than seeing an equation ‘cross reality’. His work is helping us to answer some of the remaining questions about the Universe.