Disease Model: For Instructors
This is an agent model representing the spread of a disease in a population. The "agents" in this
model have been given behaviors that affect how they react to different conditions or encounters
with other agents (see the
Learner page for more details on agent behaviors). The resulting model illustrates the various factors
that can affect how quickly and how far a disease can spread.
Essential Questions to Explore with your Students:

How does population density affect the spread of a disease?

Set the initial population to 2000 people. Run the model a few times. Record the number of
people who are recovered and the number of people who died when the infection stops
spreading.

Why is an epidemic especially dangerous in a crowded city like New York?

Try again with about 1500, 1000, and 500 people. Record the number of people who are
recovered and the number of people who died when the infection stops spreading.

Density as a factor. A disease can spread more quickly the denser a population is.

How does a quarantine help to stop the spread of an infection?

When is it appropriate to enforce a quarantine?

What can be some of the ethical problems with quarantining individuals?

Run the model a few times with no limitations on travel. Next, try different numbers of
openings. Observe the results when different regions close themselves off. In particular,
you may see a second peak in the number of infected people on the graph if the infection
breaks out into one of the adjacent regions.
You can use this model to teach various subjects. Here are some objectives you could address:
In the Science Curriculum (Biology and Health Sciences):

Systems, Order, and Organization

Demonstrate how group behavior emerges from individual behavior. With an agent model you
can't predict an individual's outcome, but you can say what will likely happen to the group.
(ie: about 20% of the population will become infected)

The individuals have random behaviors, but "random" doesn't mean "unpredictable."

Evidence, Models, and Explanation

A model should demonstrate both internal and extrernal consistency. Do the elements of the
model fit together, and are the results in line with what you observe?

Explanatory power — Does the model help you see cause and effect?

Predictive power — Does the model help you to predict what will happen in
different conditions?

Inquiry — Check between what you observed versus your explanation of the
phenomena.

Constancy, Change, and Measurement

What causes an individual to change in the model? How can we use what we know about that
change to predict the behavior of the system?

If we measure more outcomes, the average approaches the expected outcome. How can you
measure outcome? What do you need to measure to understand what is happening? Look for
patterns in the results.

Biotic Factors
(Ecology, Environment, & Interaction of species)

Talk about the biological phenomenon of infectiousness. What factors contribute to the
spread of a disease?
In the Mathematics Curriculum:

Demonstrate randomness

Run the model several times without changing any settings. Ask the students to observe the
outcome. Point out that this model has random outcomes because the agents move randomly.

Motivate the ideas of chaos

Show how there is an overall pattern that results from seemingly random events (such as the
spread of infection from the original infected person).

Demonstrate how the final outcome of the model becomes unpredictable because of a small
change in the parameters (try changing infectiousness or daystorecover).

Point out that with chaotic systems like disease spread, we have to be careful about how far
into the future we can predict.
Standards Addressed:
National Council of Teachers of Mathematics:

Grades 35

Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data

Formulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them

Understand and apply basic concepts of probability

Grades 68

Algebra

Use mathematical models to represent and understand quantitative relationships

Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data

Formulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them

Numbers and Operations

Understand meanings of operations and how they relate to one another

Grades 912

Algebra

Use mathematical models to represent and understand quantitative relationships

Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data
North Carolina Standards:

Standard Course of Study Grades 68 and 912:
The Unifying Concepts of Science consist of:

Systems, Order, and Organization

Evidence, Models, and Explanation

Constancy, Change, and Measurement

Standard Course of Study Grades 68 and 912 (Biology):
COMPETENCY GOAL 5: The learner will develop an understanding of the ecological relationships
among organisms.
Objectives
5.01 Investigate and analyze the interrelationships among organisms, populations, communities,
and ecosystems.

Abiotic and biotic factors
National Science Education Standards:

Content Standard A Science as Inquiry
Abilities necessary to do scientific inquiry

Develop descriptions, explanations, predictions, and models using evidence. Students should
base their explanation on what they observed, and as they develop cognitive skills, they
should be able to differentiate explanation from descriptionproviding causes for effects
and establishing relationships based on evidence and logical argument. This standard
requires a subject matter knowledge base so the students can effectively conduct
investigations, because developing explanations establishes connections between the content
of science and the contexts within which students develop new knowledge.
Related Activities from Shodor
Rabbits and Wolves  An agent model simulating predatorprey relationships
Directable Fire!!  Run a simulation of how a fire will spread through a stand of trees, learning about probability
and chaos.