modelling coronavirus

1. Preliminary videos

Watch this video to get a flavour for some of the modelling that mathematical biologists do. Then watch this longer video, and make notes on the key points . In the next few sections we will expand on some of these ideas and delve a bit more deeply into looking at the numbers. 

2. Exponential growth model

Watch the video below, and then answer these questions. Solutions here.

3. The SIR model

Work through section 1 of this notebook.

You will need a Google account; on mobile devices you can copy the link to your browser rather than using the Google Drive app. You'll need to choose 'open with' and the 'connect more apps' to use Colaboratory, and it's probably easiest to make a copy in your own Drive.

(Optional) Watch this video and try making your own SIR model in Geogebra (download geogebra classic for this task).

4. Refining the model: adding randomness

Work through section 2 of this notebook, then answer these questions.

5. Further refinements

The model we've used here is certainly useful in making a start on predicting how a virus may spread, but it makes certain assumptions about how the population is distributed and how members of that population behave. The key assumption is that all members of the population are mixing randomly and have the same chance of infecting/becoming infected. Of course this isn't the case in real life; individuals tend to be clustered: in households, in neighbourhoods, in towns and cities. Individuals are just that, and no two people behave in exactly the same way. Governments intervene - by introducing social distancing measures, by insisting on isolation for those exhibiting symptoms, by 'track and trace', etc. In the case of Covid19, there is evidence of symptom-free individuals, whose behaviour will be very different from someone who has to be hospitalised. These are factors that can be introduced to our model; indeed the whole idea of mathematical modelling is to go through a cycle of continual refinement when the numbers no longer fit what's observed in real life.

Watch this video to get an idea of some other possible refinements to the model.