Lesson Scenario - Rumor Mill (Vensim)

Basic Model:

Description

This is a system model of the spread of a rumor throughout a population. The model tracks the number of different types of people within the population: gullibles, rumor mongerers, and loyalists. Parameters in the model - including spreading probability and rationality rate - determine the number of each type of individual in the population over time. When the model is run a graph is produced depicting the change in number of people who are gullibles, rumor mongerers, and loyalists over time.

Background Information

The model of the rumor mill is a subset of an SIR or disease model. Much like with disease, a rumor is spread through infection of a population. An initial rumor starter or rumor mongerer spreads an idea throughout a population. They infect people who are susceptible to believing a rumor, called gullibles, and the rumor continues to spread. This rumor outbreak comes to an end when the population comes to their senses thus becoming loyalists. This disease type of model is helpful to try and 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 rumor outbreak.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. At the beginning of the simulation there is one rumor mongerer and the rest of the population is made up of gullibles. After each time step you have the same total population, but the make up of the total population is different. You can look at the three types of people (gullibles, rumor mongerers, and loyalists) and apply the fundamental principle to it. For example, for the loyalists, the new population of loyalists (HAVE) is equal to the old population of loyalists (HAD) plus the number of rumor mongerers and gullibles that came to their senses (CHANGE). With each time step, the following things happen:

1. Gullibles become rumor mongerers through mongerization according to the player-set variable entitled spreading probability: Mongerization = Spreading probability x (Gullibles x Rumor Mongerers)
2. Rumor Mongerers can come to their senses and become loyalists: Coming to senses = Rationality rate x Rumor Mongerers
3. The spreading probability is defaulted to set at 0.001.
4. The rationality rate is defaulted to set at 0.5.
5. Total population is determined by the summation of all sub categories of the population: Total population = Gullibles + Rumor Mongerers + Loyalists

Teaching Strategies

An effective way of introducing this model is to ask students to brainstorm how rumors get started. You can further challenge them to brainstorm other ideas that resemble this such as the spread of ideas, diseases, happiness, etc. Focusing specifically on rumors, students should be encouraged to discuss other factors that may impact the spread of a rumor such as the demographics of the population, location of the population, or facts introduced to the population. Guiding questions may include:

1. How do rumors get started?
2. How could you model new evidence or facts?
3. Where do rumors spread the fastest and why? How could you change this model to reflect that?
4. How can the spread of a rumor be prevented?

Implementation:

How to use the Model

This is a relatively simple system model with just a few parameters that can be changed. The important parameters are as follows:

1. The "Gullibles", "Rumor Mongerers", and "Loyalists" parameters determine the number of each type of person placed on the board at the start of the simulation.
2. The "Spreading probability" and "Rationality rate" parameters determine the likelihood that gullibles will turn into rumor mongerers and rumor mongerers will turn into loyalists respectively.

All of the aforementioned parameters 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 with the exception of the initial values, which take effect the next time the simulation is run. To run the simulation, click the "Run a Simulation" button. The results from the simulation are displayed immediately in graphical form. Below the model, a graph will depict the populations of gullibles, rumor mongerers, and loyalists, as well as the total population. The graph allows for visual and quantitative analysis of how the population changes with the spread of the rumor. For more information on Vensim, reference the Vensim tutorial here.

Learning Objectives:

1. Understand the relationship between the gullibles, rumor mongerers, and the loyalists
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 how the populations fluctuate or change over time. Guiding questions may include:

1. From your observations, what happens to the number of loyalists as time progresses? Gullibles? Rumor Mongerers?
2. Do you notice any patterns between the three populations? Is so, what types of patterns are they?
3. What do you think would happen if you had more Rumor Mongerers to start off the simulation? Gullibles? Loyalists?

Ask students to change the initial number of rumor mongerers, then gullibles, and then loyalists (one at a time). Do the answers to any of these questions change? Students should compare the hypotheses they made earlier to the results now and discuss any differences.

Objective 2

To accomplish this objective, have students change the parameters to see how they affect the graph. Students can do this by clicking and dragging on the parameter buttons on the model. Encourage the students to choose one parameter at a time at first. Guiding questions may include:

1. What changes do you notice in the graph if you change the initial number of gullibles and/or rumor mongerers? Are there any long-term behavior changes or does the graph look similar?
2. Which parameter causes the loyalists to develop the quickest? Is it a mixture of spreading probability and rationality rate?
3. Can you cause the entire population to become loyalists? Why or why not? If you can, how can you accomplish that?
4. Can you create a constant population, or will they continue to change? Why or why not?

Extensions:

1. Explore the use of models for predicting outcomes before they occur
2. Think about the qualities this model still lacks when compared with the real world
3. Create a more complex model based off of Extension 2 and compare both

Extension 1

Encourage the students to discuss the uses of disease models, such as the rumor mill model, in preparing for epidemics. Guiding questions can include:

1. How could you use a model similar to this to determine how to prevent the spread of a rumor, or more generally, a disease? What are some reasons why we may want to use a model for this?
2. How can this model be manipulated to represent different ideas, rumors, or diseases? For example, what changes might you make if the rumor was only slightly misconstrued as opposed to completely false?
3. What other types of situations could you use this model for? How would you change this one for those situations? How would the model be helpful for investigating those situations?

Extension 2

Have students consider the ways in which this model is accurate and then compare those to the ways it is inaccurate. Guiding questions can include:

1. What are the basic or main parts of a system where rumors are spread? Does this model accurately include those parts? Why or why not?
2. Can you think of any factors in the real world that are left out of this model? What are some examples? How would you incorporate them into the model?
3. In the real world, models such as this one do not produce perfectly smooth curves like we see in our model's graph. What are some reasons why smooth curves would not exist? Explain how they would affect the curves.

Extension 3

Have students investigate Extension 2 question 2 by reviewing the Vensim tutorial found here http://shodor.org/tutorials/VensimIntroduction/Preliminaries and adding in the new factors. Guiding questions can include:

1. How did the graphs change from when you ran the default model to your improved model?
2. Did the graphs change the way you expected? If not, how did it compare to your hypothesis?
3. What factors did you include and how did you include them?

Related Models:

Disease Epidemic Model

This is the agent model version of a Vensim disease model created in NetLogo. It follows the same idea, but models a sickness with many more variables. This model also contains a graph showing the number of people who are healthy, sick, immune, and dead. Students can compare disease in this model to the rumors in the Vensim model. Students should discuss the pros and cons of this model as a way to predict the spread of disease in comparison to the Vensim model.

Spread of Disease Model

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.