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:

Gullibles become rumor mongerers through mongerization according to the player-set variable
entitled spreading probability: Mongerization = Spreading probability x (Gullibles x Rumor
Mongerers)

Rumor Mongerers can come to their senses and become loyalists: Coming to senses = Rationality
rate x Rumor Mongerers

The spreading probability is defaulted to set at 0.001.

The rationality rate is defaulted to set at 0.5.

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:

How do rumors get started?

How could you model new evidence or facts?

Where do rumors spread the fastest and why? How could you change this model to reflect that?

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:

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.

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:

Understand the relationship between the gullibles, rumor mongerers, and the loyalists

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:

From your observations, what happens to the number of loyalists as time progresses? Gullibles?
Rumor Mongerers?

Do you notice any patterns between the three populations? Is so, what types of patterns are
they?

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:

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?

Which parameter causes the loyalists to develop the quickest? Is it a mixture of spreading
probability and rationality rate?

Can you cause the entire population to become loyalists? Why or why not? If you can, how can you
accomplish that?

Can you create a constant population, or will they continue to change? Why or why not?

Extensions:

Explore the use of models for predicting outcomes before they occur

Think about the qualities this model still lacks when compared with the real world

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:

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?

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?

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:

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?

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?

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.

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.

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.