Shodor

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 days-to-recover).
  • 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 3-5
  • 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 6-8
  • 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 9-12
  • 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 6-8 and 9-12:
  The Unifying Concepts of Science consist of:
  • Systems, Order, and Organization
  • Evidence, Models, and Explanation
  • Constancy, Change, and Measurement
• Standard Course of Study Grades 6-8 and 9-12 (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 description--providing 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 predator-prey relationships
Directable Fire!! - Run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos.