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Finding a way out of lockdown

"Supporting the fight against COVID-19 is extremely important. We feel that if we have a certain expertise to contribute, then the work we normally do should take a backseat and we should try to do whatever we can."

See here for all our coverage of the COVID-19 pandemic.

That's Ronojoy Adhikari talking, a mathematician at the University of Cambridge whose normal work has nothing to do with diseases. He is a member of the Soft Matter Group which studies materials such as emulsions, foams, powders and liquids. Recently, though, his group joined the Rapid Assistance in Modelling the Pandemic (RAMP) initiative coordinated by the Royal Society.

The involvement of the Soft Matter Group may seem surprising at first, but there is a mathematical bridge between what the group normally does and modelling a pandemic: soft matter physics involves modelling chemical processes that see molecules meeting and reacting with each other, while epidemiology involves modelling what happens when people meet and potentially infect each other. Similar mathematics can be used to model both situations, which is why everyone in the Soft Matter Group, from PhD student to Professor, is now busy contributing to the fight against COVID-19.

So what are they doing and how is their work being used?

Hitting the sweet spot

One way of modelling how a disease will spread is to represent all the individuals in a population in the model and then simulate what happens as individuals meet and potentially pass the disease on. The particular characteristics of the disease — such as how infectious people are and how long for, and the length of time they need to recover — can be represented mathematically and built into the model. In addition, the model needs to accurately reflect the demographics of a particular population. "Every individual has attributes such as gender, age, where someone lives, where someone works or goes to school, etc," explains Adhikari. "It's a humongous amount of information"

Shibuya crossing

Agent based models are used widely in simulating systems in biology, sociology, economics and even management – including modelling the movement of people. Photo: Andrew Eland, CC BY-SA 2.0.

Such agent based models, as they are called, give you the highest resolution you could possibly ask for, but they are also unwieldy. Because of their large size they don't submit to classical pen-and-paper analysis but instead need to be simulated on a computer, which turns them into a bit of a black box. "You dial in some rules, you code it up, and [then get some output]," explains Adhikari. "These models are difficult to analyse mathematically and it's difficult to do inference on the data." (You can find our more about agent based models here.)

At the other end of the spectrum are models that do not resolve a population down to the individual, but instead divide it into broad classes, based on people's disease status: whether they are susceptible, infected, or recovered, for example. The characteristics of the disease are reflected in the parameters of equations which describe how people pass from one class into the other (find out more here). "This approach is much simpler, but completely washes out all details of the individual other than their epidemiological state." says Adhikari.

"[The problem with] a disease like COVID-19 is that the effect is strongly age-dependent. When the disease is introduced into a population the effect will depend on the age structure of the population. So to understand exactly how much load is going to be placed on a medical system you need to resolve that age structure."

This is why researchers of the Soft Matter Group have developed models that lie between the agent-based approach and the simplest SIR approach: they don't resolve the population all the way down to the individual, but they do come with compartments representing the various age groups. "These models hit a sweet spot because they keep a sufficient amount of detail while at the same time [being tractable]," says Adhikari.

Adhikari had already developed such a model back in March specifically for the population of India. "Then we heard about the RAMP collaboration and everybody [in our group] decided to pitch in. We now have about twenty people working on the model and we made a lot of progress in one month." The result is a refined modelling tool that can make a range of predictions, ranging from the number of deaths we can expect to the likely load placed on the health care system.

Exiting lockdown

One crucial question this research can help with is how to exit the lockdown. "The lifting of the lockdown has to be sensitive, not only to economic and other considerations, but also to the age structure of the population," says Adhikari. Nation-wide lockdowns have large economic costs and it may be possible to design localised lockdown scenarios which balance the various costs of non-pharmaceutical interventions. These localised lockdowns would come into effect when infections exceed a certain threshold in an area.

Lockdown exit sign

The modelling tools developed by the Soft Matter Group can forecast when these thresholds would be exceeded in a way that is sensitive to the age structure of the population. The predictions mean that people can be forewarned of a coming lockdown, which would give them time to prepare and avoid reactive behaviour such as panic buying.

One of hardest challenges scientists are currently facing is that this is a live pandemic unfolding in front of our eyes, which comes with a lot of uncertainty. An important feature of the model built by the Soft Matter Group is that it contains the smallest number of parameters for a given accuracy of prediction compared to other models. This minimises uncertainty because parameter values need to be estimated, so the fewer parameters there are the less estimation has to take place. Through this mathematical simplicity the models embody Occam's famous razor.

Uncertainties aside, another challenge facing scientists in a dynamic situation such as this one, where the policy questions and directives are changing rapidly, is that one needs to be able to quickly modify a model or add features to it, to adapt to the revised situation. This is why the Soft Matter Group have not only built a mathematical model, but also a software platform for mathematical models. "Our platform has provided very agile, as we can rapidly provide an answer to policy questions," says Adhikari.

The Soft Matter Group has quickly turned a rudimentary model into a functioning tool used by other researchers. As Adhikari points out, it's not only down to mathematical expertise, but also to the group's diversity: members from around the world have been able to access information from a range of countries in their own language. "[Our colleagues] are amazed at how much we have achieved in a month's time," says Adhikari. "It's because twenty people from around the world have been working so hard on this collective effort."

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