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Why mathematical modelling matters so much in fighting Covid-19

The health workers and contact tracers are out on the front lines, but in the backrooms teams of mathematicians are running scenarios to figure out exactly what needs to be done, and how bad things could get. 

In big picture terms, fighting a pandemic is a numbers game, but with real world consequences. To succeed, you need to make sure that any outbreak of cases is contained, so that the number of people with the virus gets smaller by the day.

It’s often called the R number, or reproduction number. When the R number is 1, that means the average person with the virus is passing it on to an estimated one other person. If the R number is lower than 1, then you can be sure that the number of cases will diminish over time. And if it’s higher than 1 – even if it is only 1.1 – that means big trouble could be on the way.

We know that lockdowns and social distancing work to prevent high R numbers of Covid-19, because all of those actions help break the chains of transmission that allow the virus to spread. But we also knew that before this particular virus came along. How? A combination of following epidemiological evidence and mathematical modelling.

To explain why the second one matters so much for the fight against Covid-19, The Spinoff spoke to Professor Michael Plank from the School of Mathematics and Statistics at the University of Canterbury in New Zealand. He and his team got straight back to work when new cases of community transmission were announced last night, to try and figure out what else might be out there, and what comes next.

The Spinoff: When it comes to actually “firing up the model”, as one of your colleagues put it, what does that actually involve?

Professor Michael Plank: So this was my colleague Dr Alex James, late in the evening. She ran the model to try and get a handle on the likelihood that there are more cases than the four that were detected yesterday. When they were detected, it was immediately apparent that they didn’t have a link to international travel, or someone working in quarantine at the border. And so that raises the question – what’s the source of infection? And so the modelling was run to go through chains of transmission to end up with these four cases now, and get to what the likelihood that there are more cases. And that’s part of the reason why we’ve gone so quickly into this alert level, because the concern is that there could be a lot more cases out there.

Just to go back slightly, can you explain on a really simple level of what running a mathematical model actually involves? 

On a basic level, an analogy I use is to imagine five million ping pong balls in a cement mixer. They’re all bouncing around and coming into contact with others. Then if you chuck in a couple of infected cases, each time one of them comes into contact with someone else, there’s a chance they pass the virus on. It’s not guaranteed, but we simulate it to work out how many other people a case might have come into contact with, and make estimations of probability. We can simulate that in a computer, and run that forward through time and work out how many new cases you get each day.

So the usefulness of that is that it gives you a clearer picture of not just the future, but also potentially how many cases are currently undetected? 

Yes, so we’ll be trying to make some estimates on that, because at the moment we don’t really have good data on how many cases are there. So we need to do some model simulations to get a handle on that. An important point I’d make [is that] there’s a lot of luck with these outbreaks in the early stages. If you get lucky, then a lot of people might not pass the virus on, but if you get unlucky you might have a super-spreader. What the model tries to do is work out the probabilities of those different outcomes.

How much would the model itself change if new cases were announced? Or would it be more a case of just adding new data into the existing model?

It would be new data to feed in. Every new bit of data reduces the uncertainty we have. It’s designed to deal with that uncertainty, but at the moment there’s a lot.

University of Canterbury professor Michael Plank (Supplied)

When you build these models, do you factor in the experience of outbreaks in other countries? For example, has it changed based on what we’ve seen recently in Victoria?

For sure, it takes that into account. Not necessarily specifically what has happened in Victoria, but it has loomed large in our thinking over the last few weeks, and it has fed into some work we did recently assessing the risk of a case coming in from the border.

It has been gradually refined, rather than radically changed. These models are fairly well established already, they’re well used and understood ways of modelling epidemic spread within population. In the early stages of the Covid outbreak there was uncertainty in some of the parameters. The average reproduction number – in the early stages we didn’t have any good data for what that would be in New Zealand, and that’s obviously a really crucial parameter for the model.

Does your model have a standard sort of number for how many people someone is going to be in contact with over a given period of time? 

We model that, but there’s a lot of variation between people based on factors like age. We can work out the average number of contacts someone has with different age groups, that sort of thing, and then that translates into a probability of passing the virus on.

When you look at the model right now, what’s the best case scenario that we’re looking at? And what’s the worst? 

The best case scenario would be that there’s a short chain of transmission between the border, and the cases that were found yesterday. So that might be, for example, a casual contact, and that’s the route of transmission, and there may only be two or three other cases that we don’t know about.

But the worst case scenario is that it has potentially gone through quite a few steps in the chain, and we’ve maybe had a super-spreading event. Then there could be many more cases out in the community, and potentially spread to different parts of the country as well. So there’s a big difference between the best and worst case scenario, and it really won’t be until contact tracing investigations – which are underway at the moment – start to produce some results that we’ll really know which scenario we’re closer to. They’ll be working flat out, but it will take a few days.

On a personal level, do you ever reflect on the maths you’re doing being applied to a real world unfolding scenario like this?

Do I reflect on it? Yes. It’s fair to say it’s on our minds all the time. I mean, we’re very conscious of the importance of getting these decisions right. Lives depend on it, and it’s something that’s always with you.



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