Activity
1.
Ask the students to think about how diseases like the measles,
the flu, typhoid, or SARS get spread through a population.
2.
Put up the SARS Outbreak Time Line overhead to give the students
an idea of how far SARS spread throughout the world and how
deadly it was.
Source: http://www.npr.org/news/specials/sars/timeline.html
3.
Tell the students that they are going to simulate an infection
moving through a population by “exchanging fluids.” Have
the students give examples of what this activity could represent
in real life. (Sharing IV needles, having unprotected sex,
not having washed one’s hands sufficiently well after
using the bathroom, coughing on someone, etc.)
4. Tell
the students that they must follow your instructions carefully
for the activity to work. Randomly give all of
the students a container filled with a clear liquid. At
the
same
time, make sure they all hear the following instructions: “Do
not drink it. Do not smell it. Do not touch it. And, especially,
nobody should share liquids until I give you permission
to do so.”
5. Explain
what one “fluid exchange” means.
Tell the students that, at your instruction, they are
to:
a) Find
a partner, and then wait for instructions. Nobody should
share liquids until you give permission to
do
so.
b) When you give the direction, they pour all of the
liquid from one container into the other container,
swirl the
combined liquids
gently, and then pour half of the mixture back into
the empty container.
c) Record the name of the partner they exchanged with.
They may not stay or return to this person for a later
exchange.
6. At
your directions, the students move to a new partner and “exchange
fluids” again by following the same steps as
they did with the first person. Make sure they record
the
name of their second
partner.
7. Depending
upon the size of your class and the number of people who
were infected to begin with
(which you
have determined
beforehand),
do at least one more exchange. Make sure the students
record the name of their third partner.
8. Pour
the same amount of the indicator solution into each student’s
container. If the liquid turns pink (bright or faint),
the student is infected. Ask the students how they would
begin to identify
who was (were) the primary case(s).
Teacher Cheat Sheet: One way to begin is by looking
at those students who are not infected after the
last exchange.
Let’s
label these students as “Clears.” Since
the “Clears” are
not infected, this means they did not exchange
fluids with an infected person at any time during
the activity.
Breakthroughs
in this seemingly overwhelming task
occur when a “Clear” realizes that
she/he exchanged fluids in an earlier round with
student X who tests positive at the end
of the activity. This indicates that student
X is not a primary case because student X was
not
infected at the time of the exchange
with the “Clear”. This means student
X was infected by somebody else in a later exchange
of fluids.
Eventually
it becomes clear that there are a number of students that
test positive,
and everyone
they
traded with also tests
positive. These are usually the primary cases. 9. Once
the primary cases have been identified, it is possible
to determine exactly how many people
were infected
after
each exchange and how many were still susceptible
by making lists
of who exchanged with whom. Have the students
complete a data table showing the actual total number of
infected
people,
the
number of susceptible students, and the number
of new infections at the end of each exchange.
10. Lead
the students through a discussion of how to fill in the
second data table on the page,
which
deals
with
the Least
Possible Number of Infected People and the
Greatest Possible Number of Infected People at the end
of each exchange.
The values that go in the columns will depend
upon the number
of people
who were infected at the beginning of the activity.
Teacher Cheat Sheet: Use the attached Teacher
Background Sheets to explain how these numbers
are calculated
for one, two, or
three infected people at the start of the activity.
The
students should see that the actual number of infected
people after each exchange should
be inclusively
between
the Least Possible
Number of Infected People and the Greatest
Possible Number of Infected People after
each exchange.
11. Ask
the students to calculate the theoretical probability of
becoming infected at the
first
exchange. What is
the theoretical probability of becoming infected
at the second
exchange?
Remind them that the probability of an event
occurring is the number
of favorable events over the total number
of events.
Teacher
Cheat Sheet: Let’s assume that
three people were infected at the start of the activity
and there are 30 students
in your class. Since a student cannot exchange
himself/herself, there is a total of 29 people to exchange
with. The theoretical
probability of an individual becoming infected
at the first exchange is 3/29
After exchange #1, the Least Possible Number
of Infected People is 4 and the Greatest
Possible Number of Infected
People is
6. Since a student cannot exchange himself/herself
or with the student
from exchange #1, there is a total of 28
people to exchange fluids with in exchange
#2. This
means
the
theoretical
probability of
an individual becoming infected at the
second exchange is 4/28 or 6/28. (It’s impossible to have 5 infected people.)
12. Now have the student calculate the
experimental probability of becoming infected
at the first
exchange and at the
second exchange.
Teacher
Cheat Sheet: Let’s
assume that three people were infected
at the start of the activity and there
are 30 students
in your class. Because nothing is changed,
the numbers of infected people is still
3 and the total number of possible exchanges
is still 29, the experimental probability
of an individual becoming
infected at the first exchange is the
same as the theoretical probability, which is
3/29.
Interestingly
enough, since it is impossible for there to be five people
infected
at the end of
exchange #1,
the experimental
probability of an individual becoming
infected at the second exchange is
either 4/28 or
6/28, once
again
the same as
the theoretical probability. This will
not always be the case.
13. Ask
the students if they think the theoretical probability
of an
event
will
always be the
same as the experimental
probability of the event. Have them
come up with examples where they
may be different. (Tossing a coin
10 times will not give you five
heads and five tails; rolling a single
die 12 times will not give you two
6’s;n etc.) Homework
1)
Have the students calculate
the theoretical probability
and the experimental probability
of becoming infected at the
third exchange. Are these numbers
different? Why? Does this theoretical
probability of something happening
actually tell you what is going
to happen?
2)
Look at the data table that
shows the actual total
number
of infected people, the number
of susceptible students, and
the number of new infections
at the end of each exchange.
Have the students create a
graph where the number of infected
people and the number of susceptible
students are on the dependent
variables and the number of
exchanges
is the independent variable.
(This graph should be similar
to the classic shape of a S – I
(SusceptibleInfected) relationship:
as the number of infected people
increase, the number of susceptible
people should decrease. Theoretically
the curves should be mirror
images of each other with the
line of
reflection parallel to the
horizontal axis and going through
the point
of intersection of the two
curves. See http://www.bondy.ird.fr/~bacaer/oldsars/node11.html for an example.)
3)
Using technology, have the
students find a bestfit
equation for both the number
of infected
people and the number of
susceptible people as separate
functions
of the number of exchanges.
4)
Have the students write a
paragraph describing the
relationship
between the total number
of infected people and
the number
of susceptible
students over time. What
role does the fact that
we are assuming
a 100% transmission rate,
where any contact between
a susceptible
person and an infected
person leads to a new infection,
have to do with the shape
of the two curves?
5)
Have the students write about
how
the shapes of
the two curves
would change if there
were a 1/6 chance that a contact
between
an infected person and
a susceptible person
causes
a new infection.
6)
Have the students create a
graph
with the
number
of new
infections as the dependent
variable and the number
of exchanges as
the independent variable.
Ask them to describe
what would
happen if the number
of exchanges continued
to get larger. Why
do they
think the graph would
have its shape.
(The number of new
infections would reach a peak
and
then decrease to zero
because there would
be no new susceptible people
to infect.
See http://www.biomedcentral.com/14712334/3/19 figure 1 for an example.)
Closure
By
seeing how quickly a disease can spread by doing the “fluid
exchange” simulation and by having the difficult task
of identifying the primary case, students begin to see the
difficulties of an epidemiologist in the field trying to
identify the cause of an outbreak of a disease like SARS.
Graphing the data of infected people and susceptible people
over time (number of exchanges) students can see a S – I
relationship, which is one type of model used for the spread
of diseases through a population. .
