# How Mathematical Models are Used to Understand COVID-19

By Samuel Jenness, PhD and Christina Chandra, MPH

Mathematical models have been used in two ways during the COVID-19 pandemic. 1) To understand what has happened and what might happen next. 2) To figure out what to do about it.

One model that you may have heard about is called the “Imperial College model” published early in March 2020. This is an agent-based model that projected the numbers of deaths and hospitalizations related to COVID-19 in the UK and the US.

The model compared these projections against critical care capacity in hospitals in different scenarios. In the “do nothing” scenario (meaning no social distancing or any other preventive steps), the model projected 2.2 million deaths in the US and over 500,000 in the UK.

The model also included scenarios in which public health measures--like social distancing and  isolating people sick with COVID--were implemented. The number of predicted deaths was much lower. This is an example of the second category: what to do about it. The model showed how using these strategies could “flatten the curve.”  After these models were published, the US federal government responded by encouraging social distancing.

The Imperial College model suggests that when social distancing measures are relaxed and countries “reopen” there will be an increase of new cases. (In the graph below, this occurs in September, with an increase in cases in November and December.) The model also assumes that we will not have a vaccine or a treatment at that time.

An update to the Imperial College model was released late in March. This revised model projected around 20,000 deaths in the UK compared to over 500,000 in the earlier model. Some people wondered if this change meant the first model was way off. Probably not. The revised model incorporated the large-scale public health strategies implemented in the UK and other European countries earlier in March to calculate the new estimate. Adherence to social distancing and other preventive measures is estimated to have prevented nearly 60,000 deaths during March.

The Imperial College model is just one of many mathematical models for COVID-19. Several other examples include:

A famous statistician, George Box, once said that “All models are wrong, but some models are useful.” He meant that the world is a complicated place, and it’s hard to describe it precisely with math. This applies to mathematical models for COVID-19, too.

Useful models are informed by good data, which takes time to collect. Models are updated all the time as new data is added, such as the revised Imperial College model discussed earlier. This does not mean that the earlier model was bad. In a practical sense, models are useful in helping us decide the best course of action amid uncertainty, which may in turn change the future epidemic models.

Last Updated: May 19, 2020, 5:00pm ET

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