B. SIR model

Modelling (and ultimately control) of infectious disease spread is a hot topic these days.

There's a lot of more or less fancy models, and most of them are based on a very simple compartment model introduced in a 1927 paper:

Kermack m.fl. 1927. A contribution to the mathematical theory of epidemics Links to an external site.. Proceedings of the Royal Society of London. 115(772), 700-721

The model is referred to as the SIR model, or the Susceptible, Infectious, Removed model. Removed refers to either recovered and immune or diseased.

You will find a Matlab implementation of the SIR model here: NyTeknik Links to an external site..

Read up a bit on SIR model. Start out with the links below, then conduct your own literature search.

Now you too can be a hobby epidemiologist! Implement the SIR model from the link and use it to simulate an epidemic.

Things to investigate in this project:

Understand and explain the parameters N, r, Re, gamma, and lambda in the code.
What is the interpretation of S(1), I(1), R(1)?
Assume you have the power to change people's behaviour, but only for one week. Extend the code so that Re is decreased by a factor 2 during one week. Try to introduce your intervention at different time points. When is it most efficient?
There is no flow from the R state to the S state. This can be interpreted as everyone who recovers becomes immune forever. But what if this is not true? Change the model so that you can simulate scenarios where immunity fades after some time, and see what happens.
Everyone (?) is talking about herd immunity. Can you explain the concept using the parameters of the SIR model? Illustrate using a simulation example! Hint Links to an external site.

There are scheduled sessions on zoom where a group can discuss their questions with Kristian, you can book a time here.