FUN WITH MATHEMATICS: NETWORK MODEL GAMES
How our daily life can be described as a network graph
The Model
A spread of an infectious disease critically depends on the ability of pathogen to jump from one host to another. That’s why the number of social contacts between people and the types of those contacts (whether precautionary measures were taken or not to limit the disease transmission) can impact the disease spread dramatically.
The model that can explore this problem in fine detail is a social network graph. In this form we represent individuals as points we call nodes and social contacts as lines between those points we call edges.
This modeling approach enables us to explore various aspects of disease spread that happen on individual level.
For example: some individuals meet more people than an average person meets. This makes such individuals super-spreaders.
Another example: a group of people has larger number of mutual interactions than other groups. This group characteristic helps the disease to spread faster within such closely connected cluster.
Social network graphs allow us to test how some epidemiological measure would affect infectious disease spread.
For example the impact of reducing the number of connections between people (social distancing) or exploring the ways a disease can exploit one cohort of people (e.g. young) to reach another (e.g. older people) who are much more at risk of serious outcomes.
Network models require two introductory steps:
1
setting up a network of people the game will be played on
2
selecting KN game parameters
What Are The KN Parameters?
Network games require 2 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 touch. This means that a proximity does not mean 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 disease to infect tiny droplets of saliva lingering in the air or touched surfaces.
In our game we describe this probability by throwing a dice (which has 6 numbers) and if the dice shows a number smaller or equal to K then the diseases managed to jump from one person to another.
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.
This games can be played repeatedly on the same network in two ways:
1
Keep KN parameters fixed and observe how much a chance (i.e. randomness of rolling dice) affects the game result. You can compare histograms of different game results and discuss how this randomness affects the decisions that policy makers must make to curb various epidemics.
2
Play several game sessions with fixed KN parameters. After that change the parameters and observe if and how the dynamics of game progression has changed.
Levels Of Difficulty
As with our SIR model game we designed this game in several forms each with different player skill levels in mind.
Level 1 - Indoor activity game for kids
Requires no mathematics and no computers.
It is suitable even for early elementary school kids.
All the instructions are merged into one document that can be printed and used as help sheet.
Level 2 - Introductory interactive online games
This game level can be played online on our website.
We also provide the game rules/guides.
In predetermined scenarios we use simple and small networks. These game scenarios are suitable for older children who are familiar with computer use.
Level 3 - Complex online games
After you familiarize yourself with introductory interactive games you can move to this advanced level where networks are larger and more complex.
This level is suitable for high school students, college students, and general public of similar skill level.
Level 4 - Mathematical level
This level has level 3 network complexities but with enhanced mathematics added. Suitable for college students and math enthusiasts.