This session is our first foray into applied maths. Our lives have been enormously affected by the current pandemic; indeed you wouldn't be taking this course if it wasn't going on. This session aims at modelling the spread of a disease in a population, and looks at some of the techniques employed. You'll get to play with some of the models and try to fit them to the publicly available data.
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).
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.