When Maths Meets Life and Death: Modelling the COVID-19 Pandemic

Modelling has played a key role in informing our response to the COVID-19 pandemic. Predictive modelling can be used to give us an idea of how the disease might spread with and without various preventative measures such as social distancing. Based on this information, governments will make decisions that will ultimately save or cost lives.

At the most basic level, modelling takes into account the number of disease carriers, the probability of transmitting the infection, and the duration of the illness. Based on movement of the population, the model then attempts to predict how new cases develop over time.

As individuals recover, an increasing proportion of the population becomes resistant, making it harder for the virus to spread. This concept, known as herd immunity, is also taken into account in predictive models. The following video provides an excellent visual representation of these concepts, and how different characteristics of the disease influence its spread.

The key takeaways are as follows:

• The number of daily interactions, duration of the disease, and the likelihood of transmission strongly affect the growth rate.
• When efforts are made to isolate cases, a small number of cases that escape testing has a disproportionately large effect on the number of infections
• Social distancing slows the spread of disease, but small imperfections in social distancing also greatly prolongs the pandemic.
• Restricting movement too late into the pandemic has little effect.
• Shared central locations like shops drastically accelerate the spread.

Of course, these predictions are not perfect. “All models are wrong, but some are useful,” a quote attributed to statistician George Box, seems pertinent here. Most models rely on a number of basic assumptions, differences in which can lead to drastically different results. Our understanding of how Sars-Cov-2 spread also continues to evolve, leading to significant revisions of earlier models. Imperial College, for example, significantly revised their model on the 16 of March, concluding that even a reduced peak would fill twice as many intensive care beds as estimated previously. This lead to the UK government adopting strict movement limitations a few days later.

Since small differences in the attributes of the virus can have large effects on infection rates, it is vital that these models continue to be updated based on current research.