Learning 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 at:
http://shodor.org/tutorials/VensimIntroduction/Preliminaries.
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
http://www.shodor.org/featured/DiseaseModel
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.
Supplemental Materials:
 Agent Modeling Discussion
Spread of Disease Model
http://www.shodor.org/interactivate/activate/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.