Coronavirus: The maths of Covid-19 - and how you can change it

A statistical model widely used in epidemics can help health officials track and limit the spread of Covid-19. Professors Michael Plank and Shaun Hendy, of Te Pūnaha Matatini, New Zealand's Centre of Research Excellence in Complex Systems and Data Analytics, explain to science reporter Jamie Morton how it works, and what Kiwis can do themselves.

Epidemiologists are using what's called an SIR model. What does that mean and how does it work?

SIR models allow us to simulate what happens when someone in the community catches a disease, like Covid-19 or the measles.

"SIR" is an acronym. The "S" stands for the people who are susceptible to the disease (everyone who hasn't had it yet), "I" are people who are currently infectious, and "R" represents the people who are recovered, meaning they've had the disease but are no longer infectious and now have some immunity.

After someone catches the disease, they move from "S" to "I" and can now pass the disease to those who are susceptible, but not those who have recovered. Once they recover they move from "I" to "R". The model tells us how an infection spreads across a population.

One of the key parameters in an SIR model is called "R0". This is the basic reproduction number: the average number of people that will catch the disease from an infected person.

If R0 equals 2, then before they recover one infected person will likely infect two more people, who will each infect two more people and so on.

If R0 equals 3, then one infected person will likely to infect three more people and so on.

Data from overseas suggests that Covid-19 has an R0 of between 2 to 3 or so before it is brought under control, so each person that catches the virus will, on average, pass it on to two to three other people.

This is not as high as a disease like the measles, which has an R0 of 12 to 18, but it is enough to create an epidemic that can spread to a large fraction of the population.

How might it be applied to this pandemic? How does it project spread?

The SIR model allows us to anticipate scenarios where Covid-19 might start spreading in New Zealand.

We can use data from how it has spread overseas, to estimate how many cases we might have here in New Zealand and when these might occur.

This is really important for understanding how busy our hospitals might become as well as investigating ways that we might stop the spread.

There are other types of models that can be used but an SIR model is relatively simple and doesn't require many parameters.

Early on, the SIR model shows that the numbers of infected people grows exponentially, which is exactly what has been seen overseas.

But eventually the curve flattens, as more people recover and become immune to further infection.

Eventually the chances of an infected person meeting a person who is still susceptible falls and the epidemic dies down.

What happens to this model if we succeed in "flattening the curve"? Or put another way, what impact comes from infecting even one less person?

The SIR models, and others like it, show that we can flatten the curve by reducing the number of people who will catch the disease from each infected person.

This #FlattenTheCurve graph surged to prominence this week. But it didn't say why it is so bad when medical treatment capacity is overwhelmed -> mortality rate rises. So, here is a small animation that shows the value of early containment and double dividend of delay. #Covid19 pic.twitter.com/YlMPZOpydp

— Alexander Radtke is declustering crises (@alxrdk) March 9, 2020

If each infected person only passes the virus on to two, rather than three people then this slows down the epidemic: fewer people will get infected and the load on the healthcare system over a longer period of time.

If we can flatten the curve, a hospital might have to deal with only 50 severe cases per week for 16 weeks instead of 100 per week for 12 weeks.

So what are the best ways to flatten that curve – or reducing R0?

There are two things we can all do. Firstly, think about how to reduce the number of people you come into close contact with every day.

Stay at home if you feel unwell, avoid large crowds, and hold meetings online rather than day-to-day.

Secondly, try to reduce the chance of catching it or giving it to others when you do meet people.

Wash your hands regularly, avoid touching your face or shared surfaces like tables, and reduce physical contact by giving up handshakes, hugs, or hongi.

By doing these things, we should be able to get R0 below one, at which point we will have brought the epidemic under control. This is what we have seen happen in China and South Korea.

Why is it critical that we have experts in New Zealand who can undertake this modelling?

It is really important to project disease spread ahead of time so that the healthcare system can plan for the expected demand for beds and staff, and so that the Government can implement effective policies to contain the epidemic.

For example, a big question is whether we should close schools and universities.

Models can help answer these sorts of questions because they can compare the expected outcomes from different scenarios. Models can also help us understand that all of us have a responsibility to help flatten the curve.

This is why it is disappointing that experts in SIR models like Professor Mick Roberts at Massey University are currently facing the loss of their jobs.