

4. Explain briefly how to access and use the simulation, then direct students to use it to test their assigned characteristic. Explain that teams should test four different levels of their assigned characteristic and that they have 15 minutes to complete this work before reporting their findings to the class.
You may wish to explain the following features of the simulation:
You may want to suggest that teams that are assigned the virulence characteristic select four levels from the low end of the available range (less than 0.1 or 0.2) to test. Because of the levels students will be using for duration of infection and rate of transmission, any disease that has moderate to high virulence rapidly dies out in a population. Students will have more interesting results if they use the lower levels for virulence.
A range from 0.001 to 0.1 encompasses estimated rates of transmission for many infectious diseases. The algorithm for this simulation assumes that each infected person makes 100 contacts per day. Thus, the range of settings available to students is 0.1 (0.001 . 100) to 10 (0.1 . 100). The simulation would have to be adjusted for populations that are more or less dense than the one assumed by the simulation.
Note to teachers: The simulation will allow students to enter values for the disease characteristics that are outside the indicated range. However, the results of those simulations may not be reasonable.
5. Reconvene the class and ask questions such as, "Did your predictions match what you discovered using the simulation?" or "Were you surprised by the results of the simulation?" Ask one of the teams that investigated the effect of varying virulence level to read its summary statement to the class. Invite other teams that investigated that characteristic to add more information to the statement or to disagree with it. Repeat this process for the other three characteristics the teams investigated.
Students should have discovered the following, according to the computer simulation:
Virulence: A disease that is not very virulent remains at a low level in the population, whereas those that are quite virulent rapidly die out. Real disease examples that show this are colds and Ebola hemorrhagic fever. Colds are not very virulent, and infected individuals remain contagious for several days. Thus, colds tend to remain at a fairly constant low level in the population. Ebola fever is very virulent (5090 percent mortality) and death occurs shortly after infection, lessening the opportunities for an infected individual to spread the virus beyond his or her immediate surroundings. Therefore, at least until recent improvements in travel in areas where Ebola has occurred, it tended to occur in isolated outbreaks that died out fairly quickly.
Duration of infection: As the duration of infection increases, infected individuals have more opportunities to transmit the infection to others. In turn, each secondarily infected individual has more opportunity to infect still others. Therefore, because larger numbers of people become infected within a short period of time, epidemics become apparent sooner after introduction of infected individuals into the population, reach a higher peak incidence, and last longer. Real disease examples showing this are influenza and chicken pox.
Rate of transmission: According to the computer simulation, a disease dies out at low levels of transmission, whereas it stabilizes and becomes endemic at high levels. Real disease examples of this include malaria and many diarrheal diseases. Public health measures and access to medical care result in dramatically decreased transmission of these diseases in the United States, but they remain endemic in developing countries where such public health measures and medical care are not readily available.
Level of immunity: With virulence, duration of infection, and rate of transmission set at the values for twoday disease, the computer simulation predicts that an epidemic will not occur when the proportion of immune people in the population is greater than 15 percent.
6. Explain to students that computer simulations such as the one they have explored are useful tools for epidemiologists, who use them to make predictions about the likelihood of an epidemic occurring in a particular population or to estimate the level of vaccination coverage they must achieve to prevent epidemics in the population.
7. Challenge students to work in their teams to use the simulation to estimate the level of immunization required to prevent epidemics of three real diseases: smallpox, polio, and measles. Assign each team one of the diseases and display Master 4.5, Characteristics of Smallpox, Polio, and Measles, which provides the settings they need for the simulation. Tell teams they have 10 minutes to complete their work.
Smallpox was declared eradicated from the world in 1980. Because epidemiologists knew it would not be possible to vaccinate everyone in the world, they used mathematical models of the spread of disease to estimate the level of vaccination coverage they needed to achieve and maintain to establish herd immunity in a population. (The computer simulation in this activity is based on a similar mathematical model.) Epidemiologists knew smallpox would eventually be eliminated because there would not be enough susceptible people to transmit the smallpox virus. Polio and measles are among the next targets for global eradication.
8. Poll teams for their results and add them to the appropriate column of Characteristics of Smallpox, Polio, and Measles. Explain that epidemiologists using more sophisticated simulations make similar predictions: 70 to 80 percent for smallpox; 82 to 87 percent for polio; and 90 to 95 percent for measles.
Based on the computer simulation, students should suggest the following percentages be vaccinated to avoid an epidemic: smallpox—no epidemic if 78 percent or more of the population is immune; polio—no epidemic if 86 percent or more of the population is immune; measles—no epidemic if 90 percent or more of the population is immune. The critical proportions of the population to be immunized for eradication, above, are reported by Anderson and May (1992). You may want to write those percentages beside the students' findings.
9. Explain to students that the predictions made by models are sometimes inaccurate: A predicted epidemic may or may not occur in a real population. These comparisons between actual disease epidemics and epidemics predicted by models reveal the limitations of a model. For example, additional factors, not accounted for by a model, may have an impact on the spread of a disease.
10. As an example of the limitations of their model of the spread of a disease, display Master 4.6, Cases of Smallpox in Niger and Bangladesh. Tell students to make an observation about how accurate their prediction for smallpox was for each of the two countries.
Students should observe that, even though both countries had about the same level of vaccination coverage (79 percent for Niger and 80 percent for Bangladesh), outbreaks of smallpox apparently occurred in Bangladesh (0.23 cases per square kilometer) but not in Niger (0.00002 cases per square kilometer). The students' model predicted that if 76 percent of the population is immune, such outbreaks would not occur.
11. Ask students to suggest factors their model did not take into account that may explain discrepancies between their prediction and the actual result in Bangladesh. Then, add the following information to the transparency: In 1969, Niger had 310 people per square kilometer, while in 1973, Bangladesh had 50,000 people per square kilometer.
Students may note that crowded conditions will affect the spread of a disease because a sick person would be able to contact and transmit the disease to more people. This "population density" factor appears to be the explanation for the occurrence of outbreaks of smallpox in Bangladesh even though recommended levels of vaccination had been achieved. (The impacts of different population densities are not accounted for in the computer simulation in this activity, which assumes the same population density for all populations.)
This step gives students an opportunity to revisit the idea of herd immunity and to reflect on their expanded understanding of the concept. 
Other factors not accounted for in the simulation that also may affect the likelihood of epidemics include the general health of the population, the nutritional status of the population, and the level of sanitation in the population. Point out that the immune system is stressed when it is combating a disease, so people who are already sick are more susceptible to additional diseases. Similarly, good nutrition is essential for a healthy immune system, so people who are malnourished are likely targets for pathogens. Unsanitary conditions provide greater opportunities for transmission of infectious agents. All of these factors will increase the proportion of the population that must be immune to achieve herd immunity.
12. Ask students to think about the ways they used the computer simulation in this activity and what the results of their simulations revealed about the spread of diseases. Then, ask them to write down one thing they learned from the activity. Ask several students to share what they learned and clarify anything that students have misunderstood.
The major point of this activity is that the characteristics of diseases vary and these characteristics have an impact on the likelihood of epidemics. Similarly, these characteristics have an impact on the percentage of people in a population who must be vaccinated to achieve herd immunity.
The World Health Organization maintains a Web site that includes information on infectious diseases that are targeted for eradication. Ask students to review the site and report (1) the vaccination coverage goal for a particular disease, (2) the challenges that face health care workers for meeting that goal, and (3) the strategies epidemiologists are using to meet their goals.
The address for the site is http://www.who.int/dracunculiasis/eradication/en/.
The disease transmission simulation simulates the spread of twoday disease in a population. Explain to students that during the first simulation, all the students will be susceptible to twoday disease. When 25 percent or more of the class is sick, they are experiencing an epidemic.
Give each student one red card, one pink card, and one black card. Explain that on the first day they become sick, they will hold up a red card. On the second day of their illness, they will hold up a pink card, which signifies that they are recovering but still infectious. On the third day, they will hold up a black card to show that they have recovered and are immune. They will hold the black cards and remain immune until the simulation ends.
Tip from the field test. Have the students stack the cards with black on the bottom, pink in the middle, and red on top.
Simulation 1
0% immune, 100% susceptible
1. Write "Simulation 1—0% immune, 100% susceptible" at the top of one of the transparencies of Master 4.3, Following an Epidemic. Tell students to do the same on one of their copies of Following an Epidemic.
2. Identify one student sitting in the center of the class to be the individual who introduces the disease to the population. Tell that student to pick up his or her red card. This is Day 1. On the transparency, tally the number of currently sick people and the number currently immune. Tell students to record those results on their copies as well.
3. Tell the sick student to tap one person he or she can reach from a seated position, then announce the end of Day 1.
4. Announce the beginning of Day 2 and remind the original sick student that he or she is still sick, but recovering and should be holding the pink card. Remind the tagged student that he or she is now sick and should be holding the red card. Complete the Day 2 row of the table, asking students to do the same.
5. Tell the sick students to tag other students they can reach from their seated position. Announce the end of Day 2.
6. Announce the beginning of Day 3. The original sick student should now put down the pink card and pick up the black card to indicate that he or she is immune. The student tagged first should put down the red card and pick up the pink card. The two newly tagged students should pick up their red cards. Complete the Day 3 row of the table.
7. Tell the sick students to tag other students they can reach from a seated position. Announce the end of Day 3.
8. Repeat Steps 6 and 7 until all students have had the illness or until transmission of the disease stops because there are no susceptible students near sick students.
9. Ask students to raise their hands if they were sick at some point during the simulation. Count the number of hands and record this number at the bottom of the transparency.
10. Plot the data from the table onto the graph and draw the curve on the graph. Tell students to do the same and then ask them to make three or four observations about the table and graph the class has created.
Simulation 2
50% immune, 50% susceptible
1. Write "Simulation 2—50% immune, 50% susceptible" at the top of the other transparency of Following an Epidemic. Tell students to do the same on their other copy.
2. Tell students to restack their cards, with black on the bottom, pink in the middle, and red on top.
3. Explain that they will complete the simulation again, but this time half of the students in the class will be immune to the disease. Note that, as is often the case in real life, students will not know who is immune and who is susceptible. Give half the students a folded card that says "immune" and half a folded card that says "susceptible." They should read their card, but they should not share this information with anyone.
4. Explain that if they received a card that says "immune," they are not to pick up their black cards until they are tapped by a sick student. Write the number of immune cards you distributed in the "Day 1/Number of People Immune" cell on the transparency and tell students to do the same on their copy of the table. This is the initial number of immune people.
5. Identify one student sitting in the center of the class to be the individual who introduces the disease to the population. Tell that student to pick up his or her red card. This is Day 1. On the transparency, tally the number of currently sick people and the number currently immune. (For the latter, add the number of people who are newly immune to the number who were already immune.) Do not ask students to indicate by a show of hands how many people are immune, because this will reveal who is immune and who is susceptible and may influence the choices students make as they transmit the disease. Tell students to record the number sick and the number immune on their copies as well.
6. Continue the simulation as before, but this time, when an immune student is tapped, he or she should immediately hold up the card that says immune. He or she is not infectious and so will not tap another student. (Do not add this person to the number who are currently immune, because he or she was already included in the initial count of immune individuals.)
7. Continue until either all students are immune or have had the illness, or until transmission of the disease stops because there are no susceptible students near sick students.
8. Ask students to raise their hands if they were sick at some point during the simulation. Count the number of hands and record this number at the bottom of the transparency.
9. Plot the data from the table onto the graph and draw the curve on the graph. Tell students to do the same and then ask them to make three or four observations about the table and graph the class has created.
