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Who Gave It to You?

By: Brink Harrison


Time: 1 days
Preparation Time: 10-20 minutes to prepare containers
Materials: Plastic cups (1 per student)
Phenolphthaleine solution (see chemistry teacher)
Distilled water

Abstract
Students will model the spread of a disease through a population by doing a “fluid exchange” simulation. (Other options will be discussed below if you are hesitant to use liquids) All of the students will have containers with a clear liquid in them, but a teacher-determined number of unknown “infected students” will have a clear phenolphthaleine solution instead of distilled water. At the teacher’s direction, pairs of students will exchange “fluids”. Each student will then, at the teacher’s direction, move on to a new partner and repeat the procedure. After a given number of exchanges have occurred, an indicator solution is used to determine which students have become infected. Doing an epidemiological study, students locate the primary cases. Once having identified the primary cases, from the data of who exchanged fluids with whom, students will also construct a graph showing the number of people infected and the number of susceptible students versus the number of exchanges.
Knowing the number of infectious people there were at the start of the activity, students will calculate the theoretical probability of their becoming infected at each exchange. By knowing the actual number of students infected after each exchange, the students can calculate the experimental probability of their becoming infected at each exchange.

Objectives

Students will be able to:-

  • Use logic to locate the primary cases, the people who started the spread of the disease through the population.
  • Graph the data of the number of people infected over time (exchanges) and determine an equation that best fits the data
  • Understand a S-I (susceptible-infected) model of a disease moving through a population over time (number of exchanges) by constructing a graph showing the number of people infected and the number of susceptible students versus the number of exchanges
  • Calculate the theoretical probability of their being infected after each exchange of fluids by knowing the original number of infectious people in the population.
  • Calculate the experimental probability of their being infected after each exchange by knowing the actual number of people infected after each exchange

Math Standards
Probability
- Understand and apply basic concepts of probability
Problem Solving
- Apply and adapt a variety of appropriate strategies to solve problems
Reasoning and Proof
- Select and use various types of reasoning and methods of proof
Connections
- Recognize and apply mathematics in contexts outside of mathematics


Teacher Background
Infectious diseases continue to be a major cause of human suffering and death, both in the United States and around the world. In developing countries where much of the population lives in conditions of extreme poverty, infectious diseases remain the leading cause of death. In the United States, prevention and control of infectious diseases have been so successful in the past half century that many people view infectious diseases as either a thing of the past or minor illnesses easily treated and cured, except among the very young, very old, or seriously ill.

In recent years, however, Americans have been shocked by the emergence of a variety of “new” infectious diseases. For example, Escherichia coli strain 0157:H7 caused severe vomiting and diarrhea among patrons of Jack in the Box restaurants in Washington State in 1993 and among children swimming in public pools in Atlanta, Georgia, in 1998. And a previously unrecognized virus (a hantavirus) caused a frequently fatal respiratory illness among apparently healthy young people in the Southwest.

Likewise, many diseases, once were thought to be adequately controlled, appear to be making a “comeback.” In developed countries, public health measures such as sanitation, sewage treatment, vaccination programs, and access to good medical care including a wide range of antibiotics have virtually eliminated “traditional” diseases such as diphtheria, whooping cough, and tuberculosis. However, many of these diseases are becoming a public health problem once again, as immunization programs and other public health standards are enforced less vigorously and, especially, as antibiotic-resistant pathogens evolve.
Source: http://www.science.education.nih.gov/supplements/nih1/diseases/guide/activity1-1.htm

There are many compartmental models for the spread of diseases. These models are called compartmental because the population is separated into discrete groups of individuals depending upon which category fits the condition of the individual. The most commonly used categories are:

a) susceptible (S),
b) exposed (E),
c) infected (I)
d) recovered or removed from population (R)

The model used here is S-I (susceptible-infected) because the individual is either susceptible to the disease or infected with the disease. Accordingly, there are several assumptions in this activity:

  • All of the members of the population, other than those infected, are susceptible to contracting the disease. There are no immune people in the population.
  • Nobody recovers, thereby gaining immunity, during the activity.
  • The probability of transmission of the disease occurring when an infected person contacts a susceptible person is 100%. In other words, any exchange with an infected person transmits the infection.
  • The students are immediately infectious once they contract the disease through exchange. There is no “exposed” portion of the population where individuals have the disease, but are not yet infectious for a period of time.
  • There is homogeneous mixing of the population. This means that individuals make contact at random and do not mix mostly in a smaller sub-group. The students must exchange with anyone who asks them to exchange.

The “fluid exchange” activity itself has been described many places on the Internet. Most teachers recommend using distilled water as the “normal liquid”, a dilute base solution (0.1 M) of sodium hydroxide (NaOH) as the “infectious agent”, and phenolphthaleine as the indicator,as phenolphthaleine turns pink in the presence of a base. However, care must be taken to insure that no liquid is spilled because NaOH is caustic, and can irritate skin and eyes. Aprons and goggles should be used if available.
(Source: http://www.accessexcellence.org/AE/AEC/AEF/1996/good_virus.html)

I would recommend doing the activity the other way around. Use distilled water as the “normal liquid”, use phenolphthaleine as the “infectious agent”, and dilute base solution (0.1 M) of sodium hydroxide (NaOH) as the indicator. This way the teacher is the only person handling the sodium hydroxide. In any case, you should check with a chemistry teacher first to make sure this will work and to get help making the solutions.

If you are uncomfortable using chemicals or liquids in the classroom, there are other options you can use. One option is to use flour as the “normal liquid”, baking soda as the “infectious agent”, and vinegar as the indicator. In this case, if baking soda is present in the mixture after the exchanges, the vinegar will make the mixture foam. If there is no baking soda in the mixture, the vinegar will sit on top of the flour and not foam.
(Source: http://www.lessonplanspage.com/ScienceHowVirusesTravel58.htm )

Another option is to use Glogerm powder.(Source: http://www.glogerm.com ) as the “infectious agent” and have students shake hands as the “fluid exchange.” Using a black light as the indicator, the students’ hands will turn blue depending upon how much powder is present. The one problem is that the infected students will know that they are infected since they had to put on the powder initially. Perhaps one way to avoid this is to have other students put baby powder on their hands. This way there are two white powders, one “normal” and one “infected”, and the students will not know which they have used.

Depending upon the size of your class, you need to decide before doing the activity how many people are going to be infected at the beginning of the activity and how many “fluid exchanges” should occur. See attached sheets showing the number of people infected after four exchanges if one, two, or three people are infected at the beginning of the activity. You want to make sure that after the last exchange there are still some people who are not infected. If everybody is infected, the students will not be able to track backwards to find the primary case(s).

Related and Resource Websites
http://www.accessexcellence.org/AE/AEC/AEF/1996/good_virus.html
http://www.lessonplanspage.com/ScienceHowVirusesTravel58.htm
http://www.glogerm.com
http://www.npr.org/news/specials/sars/timeline.html
http://www.bondy.ird.fr/~bacaer/oldsars/node11.html
http://www.biomedcentral.com/1471-2334/3/19

 

 

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 (Susceptible-Infected) 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 best-fit 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/1471-2334/3/19 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. .

Embedded Assessment
Students should be assessed informally on their ability to use logic to track the way back to the primary source of the infection. Students should also be informally assessed on their ability, when knowing the original number of people infected, to determine the Least Possible Number of People Infected and the Greatest Possible Number of People Infected after each exchange. Having to find the theoretical and experimental probability also provides an idea of how well the students have a grasp of simple probabilities.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


PULSE is a project of the Community Outreach and Education Program of the Southwest Environmental Health Sciences Center and is funded by:


an
NIH/NCRR award #16260-01A1
The Community Outreach and Education Program is part of the Southwest Environmental Health Sciences Center: an NIEHS Award

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Supported by NIEHS grant # ES06694


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Last update: March 7, 2007
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