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This content is taken from the UNESCO UNITWIN Complex Systems Digital Campus & The Open University's online course, COVID-19: Pandemics, Modelling, and Policy. Join the course to learn more.
2.3

## UNESCO UNITWIN Complex Systems Digital Campus

The Interactive Kermac-McKendrick Model used in this step.

# Hands-on Modelling SIR Behaviours

In this step you will use an interactive computer program to model the behaviour of the SIR curves for different combinations of population sizes, infection rates, recovery rates, vaccination rates, and values of the reproduction number, R.

The program can be used with most touch screen devices including phones and iPads. Let us know if you have a problem. Even if you can’t use the program keep reading because some interesting findings emerge.

To see the interactive computer program in a new tab or window CTL click here. It should appear as shown above.

The blue curve is the percentage of people in the population who are Susceptible to catching the virus, i.e. those who have not had COVID-19 and have no immunity.

The red curve is the percentage who are currently Infected by the virus.

The green curve is the percentage who have Recovered from the virus.

Let these number be represented by the symbols $$S$$, $$I$$ and $$R$$. Let $$N$$ be the number of people in the population,. Then as you saw last week

$\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; N \; = \; S \; + \; I \; + \; R$

The SIR program should open in a new window similar to that above. The program is very easy to use. You can change the values using the control bar which is shown below.

All but one of these boxes have arrow heads < and > to the left and right. You click on the < arrowhead or the left part of the box to make the number decrease. You click on the > arrowhead or the right part of the box to make the number increase.

It’s interesting to change the numbers by trial and error, but for the moment consider the questions in the following exercises.

Don’t spend too long on these exercises unless you have a lot of time. Five to ten minutes is enough to get a feel for what the model does

### Modelling Exercise 1: Population size

• what happens when the population is increased from 1,000 to 1,000,000 people?

Go to the program now and click on the right of the population box to observe what happens as the population increases from 1,000 to 10,000 to 100,000 to a million. Make a note of what you observe for the discussion below.

### Modelling Exercise 2: Numbers of infected people at the beginning

A virus can enter a country in different ways. A single traveller can begin an epidemic in a country, or many individual travellers may seed the epidemic in different places. It is possible that an aeroplane to Italy with travellers from Wuhan started the severe epidemic experienced in Lombardy. The next question is:

• does the number of people starting an epidemic affect the speed of spreading?

Try different combinations of population and initially infected people to see what happens.

### Modelling Exercise 3: Vaccination

The SIR model gives a very good way of understanding the impact of vaccination. Vaccination reduces the number of people in the population who are susceptible, making the blue curve start lower down. This can have a big impact on the spread of epidemics.

• approximately what percentage of the population has to be vaccinated to create herd immunity?

Experiment with different population sizes and vaccination rates.

## Discussion of the first modelling exercises

If you were able to run the program you will have seen

• as the population size increases it takes longer for an epidemic to peak.

• as the number of people initiating an epidemic increases, the peak is reached sooner.

• in my experiments it required about 65% of the population to be vaccinated to prevent an epidemic - but lower rates of vaccination had a significant effect.

Close the simulation window when you have finished. Any changes you have made will not be saved.

If you were not able to run the program on a laptop or PC, or had any other problems, let us know saying which browser, version, operating system etc. you used and any other information that might help us understand why.

In the next step we’ll dig a bit deeper into the computer model and find out what those mysterious beta and gamma boxes are used for and their relationship with the infection rate R.

## What do you think

Was this the first time you have used a computer model like this? Or are you an old hand? Do you think the results are valid - at least qualitatively? Did you spend longer on this than you expected? Let us know what you think so we make such exercises as engaging and interesting as possible for future members of the course.