FUN WITH MATHEMATICS: SIR MODEL GAMES
A simple game with important messages about pandemics
The Model
SIR Model is one of the simplest mathematical models of infectious diseases. This model breaks down the whole problem into three compartments – or groups of people who:
...are susceptible
to the infection
(S)
...contracted the infection
and are now infectious to others
(I)
...recovered
and are now immune
(R)
How This Model Works
People from the compartment S are moved to compartment I based on a probability of social contact between those two compartments (i.e. how often susceptible people come close to infectious people) and a probability of a transmission of a virus between those in social contact (i.e. how easily a susceptible person can catch some specific virus during a close contact with an infected person).
Once a person is infected it takes some time to recover form the disease and to get healthy again.
After that the recovered become immune to the virus, lowering the chance of re-infection.
We developed a game that demonstrates the SIR model approach.
Depending on a level of difficulty, the game can be played by a group of children or by a group of students.
Depending on a level of difficulty, the game can be played by a group of children or by a group of students.
Age Suitable For This Game
The game is suitable for players aged five or older.
The precise age is related to different versions of the game that require either none, some or more advanced mathematical skills.
And What About Mathematics In The Game?
This game can be played in several forms. We designed each form based on mathematical skill of players.
BASIC level
no explicit mathematics
The key insight gained from this game is how the number of healthy, infected and immune people change over time based on predetermined parameters. Public policies are based on such modeling results. For instance health measures (like mask wearing) are passed to change the trends in those numbers.
This game level is ideal as an extension to school topics on personal hygiene and disease spread prevention. It can also help children to understand why the adults require them to accept certain daily routines and behaviors.
No mathematical skills are required at this game level. This game is designed so that epidemiological outcomes are visible and easily understandable by grouping the players in the playing space so that players can see how the quantities of healthy, infected and immune players change.
MEDIUM level
whole numbers and summation
On this level we introduce some basic arithmetic. Players play through various scenarios form the basic level but monitor the quantities of healthy, infected and immune players using visualization tools like histogram or graph.
EXPERT level
basic mathematical operations
This game is currently in preparation.
MASTER level
introductory programming skills
This game is currently in preparation.
How Many Players Can Participate in a Game Session?
We suggest at least 5 players in SIR games.
There is no upper limit on the number of players, hence it is set by the ability of the game moderator to keep a large group of children to stay focused on the game.
What Are The Game Parameters?
SIR games require three numbers to be set before the start of a game:
K
probability of disease transmission
When two people come close to each other, a virus or a microbe cannot simply jump from one person to another. It must be transferred via infected droplets or by physical touch. This means that proximity of an infected person does not result in 100% chance of disease transmission. The actual probability of disease transmission between two people depends on the context of their interaction and the ability of the virus particles to be contained in a tiny droplets that float in the air or rest on surfaces.
In our game we model this probability by rolling a dice (which has 6 sides). If the rolled number is smaller or equal to the parameter K then the disease was able to jump from one person to another.
P
number of potentially infected people
Tracing of individual interactions between people is messy and complicated endeavor. Throughout our day we meet various people and under different conditions.
That’s why in SIR models we look at the average interaction. This means that we work with an average person meeting an average number of other people every day. If such an average person is infected, then the average number P of other people are exposed to the disease and potentially can become infected, too.
N
duration of illness
Once we get ill, we stay at home or go to hospital, we take medications, etc. It takes some time to recover and get back to normal life. In SIR model games we define the number of game steps (think of it like days) that an infected player needs to wait before it gets back into the group of healthy players.
In our game instructions we provide two tables from which KPN parameters can be selected:
- • one for games that will result in a fast growth of infected players (game A)
- • one for games where the spread of disease is slowed down (game B)
Play The Games - Download The Instructions
BASIC LEVEL
- For older kindergartners and early elementary school kids.
- Requires at least one moderator/game host (e.g. educator).
- At least five players suggested, while the upper limit is set by the ability of the moderator(s) to handle and engage a larger group of players.
- No mathematical skills required. Epidemiological outcomes are visible and easily understandable by grouping the players in the playing space.
MEDIUM LEVEL
- Same as the basic level except that the game progression is monitored with visualization tools like histogram and graph.
- This level of the game can be used as a great extension to basic arithmetic courses.
EXPERT LEVEL
This game level is currently in preparation.
MASTER LEVEL
This game level is currently in preparation.