Learning Scenario - SIR with Scroll Bars (Excel)

Basic Model:

Description

This is a system model of the spread of disease in a population, which classifies people into three categories: susceptible (S), infected (I), and resistant (R). It tracks the proportion of the population that is infected by the disease on any given day. The infection rate, recovery rate, and time step are user-controlled parameters. By the end of the model, the disease has stopped spreading because there are no longer any infected people. A graph depicts the change in the number of people who are healthy (S), sick (I) and recovered (R) over the progression of the epidemic.

Background Information

Health organizations around the world are always working to gather and share information about potential epidemics, and to try to understand how diseases spread and how they could play out in individual communities, states, and countries across the globe. A vital part of these efforts involve the use of computational models that make quantitative predictions about how the disease will spread, based on measured data and scientific understanding of the biological and systematic processes involved. This model can be used to learn about these processes and how they interact to determine the severity of the disease outbreak.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. The overall shift in the number of people in the different populations each time step depends on the number of healthy people who are susceptible to disease, as well as the number of sick people who can infect them and/or recover.

Each time step, the following things happen:
1) Healthy people become infected according to the player-set variable infection rate, recovery rate and the number of healthy and sick people:
Current Infected = last Susceptible - (Infection Rate * last Susceptible * last Infected* Time Step(DT)) - (Cure Rate * last Infected * Time Step(DT))
2) Sick people recover according to the player-set recovery rate:
Current Recovered = last Recovered + (last Infected * Cure Rate * Time Step(DT))

Teaching Strategies

An effective way of introducing this model is to ask students to brainstorm how sicknesses such as the common cold spread, for example through physical touch or bacteria put in the air by coughing and sneezing. Then start focusing on more dangerous diseases such as the swine flu. Ask the following questions:

1) What do people do to avoid catching colds?
2) Where are you more likely to catch a cold? In a school or at home? Why?
3) Considering that, why is an epidemic especially dangerous in a crowded area such as New York City?
4) How does population density affect the spread of disease?
5) What diseases would be most dangerous in a high population area? How can the spread of disease in these areas be prevented?

Implementation:

How to use the Model

This relatively in-depth model has a number of parameters that can be manipulated to produce different results:

1) The "Susceptible", "Infected", and "Recovered" variables in "Initial Values" determine the number of susceptible, infected, and recovered people in the population at the start of the simulation.
2) The "infection rate" parameter determines the likelihood that an infected person will infect a susceptible person.
3) The "cure rate" parameter determines the likelihood that an infected person will recover every time step.
4) The "DT" parameter refers to the Delta Time, or Time Step. It determines the how often the chart and graph collect new data on the populations.

The "Susceptible", "Infected", and "Recovered" parameters are adjusted by replacing the number to the right of the parameter with the number you want and pressing enter. The "Infection Rate", "Cure Rate", and "DT" are manipulated by clicking and dragging their respective sliders. The maximum, minimum, and step values for each parameter are pre-set. Any changes made to the sliders take effect immediately. The results from the simulation are displayed in graphical form. The graph depicts the populations of susceptible, infected, and recovered people from the model. For a complete tutorial on how to use Excel, please go to the following link: http://shodor.org/tutorials/excel/IntroToExcel.

Learning Objectives:

1) Understand the relationship between the proportion of the population that is healthy and the spread of the disease
2) Understand the effect of each parameter on the populations over time

Objective 1

To accomplish this objective, have students run the simulation with the default parameters, and observe the graph. They should specifically pay attention to the rate at which the populations of susceptible and infected people increase and decrease. Ask the following questions:

1) From your observations, what happens to the rate at which people are infected when the number of susceptible people is high? What about when the number of susceptible people is low? Why do you think this happens?
2) Do you notice any patterns in the relative numbers of infected and susceptible people? If so, what types of patterns are they?
3) What would happen if there were more infected people at the beginning of the model? What if there were more susceptible people and fewer infected people? Why?

Ask students to change the initial number of susceptible people. Do the answers to any of these questions change? Students should compare the hypotheses they made earlier to the results now, and discuss any discrepancies.

Objective 2

Have students play around with each of the parameters to see the effect on the graph. Ask the following questions to guide their exploration:

1) What changes do you notice in the graph if you change the initial number of infected people and/or susceptible people? Are there any changes to the long-term behavior of the graph?
2) What changes when the infection rate increases or decreases? Why do you think these changes occur?
3) How does the cure rate affect the total number of people who are infected by the disease? Why does it have this affect?
4) Which sets of parameters cause the disease to spread the least? Which cause the disease to spread the most? Why? Don't forget to change the initial population as well as the infection rate and cure rate.
5) How does changing the DT (time step) affect the way the graph looks? Why? What are the pros and cons for higher and lower DT values?

Extensions:

1) Explore the use of models for predicting outcomes before they happen
2) Think about the qualities this model still lacks when compared with the real world
3) Determine the rate of change equations for the SIR model. This serves as an introduction to differential equations.

Extension 1

Encourage the students to discuss the uses of disease models in preparing for epidemics. Ask the following questions:

1) How could New York City use a model similar to this to decide the best way to prevent the spread of an infectious disease? What parameters could be added to make the model more realistic? Why?
2) How can this model be manipulated to represent different diseases? For example, what changes would you make to the model to effectively simulate AIDS in comparison to the flu?
3) Why would we want to use a model to prepare for an epidemic? Explain.
4) What other phenomenon could you model on a computer? Consider natural disasters as well as man-made situations. How would computer models be helpful in preparing for these disasters?

Extension 2

Have students consider the ways in which this model is not an accurate representation of the real world. Ask the following questions:

1) What factors can you think of in the real world that this model leaves out?
2) In the real world, disease models are not perfectly smooth curves like we see here. What are some reasons that disease might not spread exactly the way this model predicts? Can you think of any ways to take these factors into account in this model?
3) Look at the numbers in the chart to the left of the graph. Are these numbers accurate counts of populations? Why or why not? Hint: Do you ever count humans using decimals other than .0?

Extension 3

This model can be used as an introduction to differential equations. Have students write rate of change equations to show the movement of people between the susceptible, infected, and recovered populations over time.

1) In this model when a person recovers from the disease, he/she gains permanent immunity to the disease. Considering that, will the number of susceptible people ever increase? Explain.
2) What factors cause someone to stop being susceptible? How would you write that in equation form? Explain. How would you add this to the "rate of change" equation for the susceptible population over time? Why?
3) When people stop being susceptible, what population do they go to? Do any of them go straight to the recovered population? Why or why not? How would you show this movement of susceptible people in the infected population rate of change equation?
4) Are there any negative factors in the rate of change equation for the infected population? Why or why not?

Related Models

Disease Epidemic Model

http://www.shodor.org/featured/DiseaseModel/

This is a more thorough epidemic model created using AgentSheets. Students should discuss the additional variables and how they assist in predicting the spread of disease. This can also be used to discuss the differences between agent and systems models.

Spread of Disease Mode

http://www.shodor.org/interactivate/activities/SpreadofDisease

This is a simpler agent model of disease spread that focuses on the longevity of the disease. This model is unique because the agents do not gain permanent immunity to the disease after they recover. Students should discuss the affect this has on the spread of disease and how this changes the methods used to prevent the disease.

http://www.shodor.org/refdesk/BioPortal/model/ASdiffusionSquare

NCSI Talks

SIR with Scrolls Bars Learning Scenario (Web)