As the pandemic races towards an unenviable two-year milestone, the Otago Global Health Institute’s Covid-19 Masterclass Series is bringing together a network of experts to discuss key Covid-19 topics. We’ll be running a piece daily until December 5.

Dr Matthew Parry explains what Covid-19 modelling is and how we can expect it to be used in the future

If you are watching Foundation or are a fan of the original series of novels by Isaac Asimov, you will know they are based on the idea that science can be used to predict the future of societies.

It is a very appealing idea. In Asimov’s universe, a branch of science called “psychohistory”, heavily dependent on mathematics, is able to make predictions about the behaviour of large populations of people. This is because all the different individual behaviours in some sense “average out”, allowing psychohistorians to calculate the future trajectory of society as a whole.

Of course, Asimov was smart enough to realise that one-off random events can derail any prediction and – no spoilers! – much of the Foundation series deals with the impact of unforeseen events on the plan to save the galaxy.

Back on Earth, science is routinely used to make predictions. Since Asimov wrote his books, scientists have learned a lot more about complex systems and have a much better idea about the type of predictions that can be made and, importantly, how reliable those predictions might be.

The way scientists make predictions is by constructing models of the world. Such modelling played an important role in initially helping New Zealand pursue an elimination strategy for Covid-19.

For example, before we had vaccination, modelling was used to estimate the burden that would be placed on our healthcare system if an outbreak was not stamped out.

In our subsequent outbreaks, models were used to estimate the size of the outbreak at the time the first case was detected. This helped inform decisions around regional alert levels.

Recently, modelling has been used to understand what different levels of vaccination will mean for the spread of Covid-19 in New Zealand.

So, what is a model? And what is modelling all about?

Modelling is simplifying and translating a real-world scenario into mathematical language. The resulting model has the same relationship to reality as a model toy has to the real thing. This means we don’t expect the model to tell us everything, but we can use it to get a better idea about key aspects of what is going on.

The use of mathematics in models is not an attempt to mystify people or to scare them off from critiquing the model. In many cases, mathematics just turns out to be the most precise language in which to formulate what we know about a complex system.

Just as you would expect a Parisian to speak French, you should expect a modeller to speak mathematics. Another advantage of the use of mathematics is that it can be translated into computer code and modelling often involves running thousands of simulations of the model on a computer.

One reason we might need thousands of simulations of a model is that most epidemic models are stochastic. This means modellers allow random things to happen in their models, just like in the real world. For instance, one person might spread Covid-19 to six people, another person to no one at all.

Each time we run a simulation we get a different outcome. Taking all the simulations together tells us what the average epidemic will look like, but also how much worse – or better – it might be. The range of possible outcomes from these simulations is often categorised as uncertainty.

There are also other sources of uncertainty in model predictions. A model by its very nature makes simplifying assumptions – though a stochastic model can also mitigate some of this effect.

Models also involve parameters. For example, what is the average number of people an infected person will pass Covid-19 on to? Data allows us to estimate such parameters, but we can never know them with perfect precision.

If modellers are up front about the level of uncertainty in model predictions, models can still provide information that is useful in decision-making.

Often modellers can at least outline future scenarios. For example, if we take action ‘X’, then in a month’s time, the number of people hospitalised with Covid-19 is likely to be between ‘Y’ and ‘Z’. Decision makers can then decide what is the best course of action.

Of course, models come with their own built-in check: did their predictions get it right?

Predictions can be scored in terms of how accurate they are and how precise they are. Accuracy is perhaps obvious, but the headline number from a prediction can often turn out to be wrong simply because circumstances change. Predictions are usually couched in terms of certain things staying the same, e.g. “if the country stays in Alert Level 1, then…”.

Precision reflects the range or uncertainty in the model predictions. Unfortunately, this information is often left out of discussions in the media. Although a precise prediction is preferable to an imprecise one, a precise prediction that is inaccurate is highly dangerous.

So, what will happen next?

While we may not have the ability to predict the future of societies as Asimov portrayed it, as New Zealand transitions to a stage with fewer restrictions, modelling will continue to play an important role.

Recently, a network model has been developed for New Zealand by researchers at Te Pūnaha Matatini. This is essentially a model of New Zealand that is based on publicly available census data and various other forms of data, like mobility data. Don’t worry – the data is anonymised – you are not in the model!

By including five million individual people in the model and information on where people live and how people live, if they go to school, work, etc, modellers can run much more detailed simulations of how Covid-19 might spread throughout the country.

One advantage of the network modelling approach is that we see how truly connected we all are.

As we move into the new year, some of the key issues include the ongoing risk of Covid-19 at our borders, the impact of inequities in healthcare and vaccination, appearance of new strains like the recent Delta outbreak, and the effect of seasonal changes and waning immunity.

Modelling the effect of these last two will be of particular importance in light of the recent resurgence of Covid-19 in Europe.

To make the best use of models, it is crucial they are updated with the latest data and that modellers continue to work closely with epidemiologists, public health experts and decision makers.

Dr Matthew Parry, a senior lecturer in the Department of Mathematics and Statistics at the University of Otago.

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