Activity 1 Directions:

Using Dice to Model the Spread of a Disease You have been invited to a party with 39 other people. OH NO - it is discovered after the party one of the guest has an infectious disease. Were you infected? Procedure: We will assign each of the 39 other guest a number (1-39). You will be number 40. We first need to determine which other guest came to the party with the disease. To dothis we will use a random number generator. Use https://www.random.org/ to find a random number between 1 and 39. Record this number on your record sheet. This will be the guest with the disease. Next, we use a dice to simulate the variability of the number of infected people. The number of newly infected people caused by each infected people at each step is determined by the value of tossing a fair dice, so the infection rate is not fixed.

Number on die Number of newly infected people

• 1 0
• 2 0
• 3 1
• 4 1
• 5 2
• 6 2

Stage One

Use the random number generator, https://www.random.org/integer-sets/, to generate a list of numbers.

You should generate 40 numbers between 1 and 40 in one column. (We now use 40 numbers, since you are included in this spread of the disease.) Record these numbers on your list. On your list cross off the number of the initially infected person you found in stage one. This list is the order in which people will become newly infected.

Roll a fair die. If you do not have die you can roll a virtual die here https://www.random.org/dice/. If the die shows 1 or 2, you have no newly infected people. Leave the stage one newly infected people blank on your record sheet and move to stage two.

If the die shows 3 or 4, you have 1 newly infected person. Write down the first non-crossed off number on your list of the 40 random people under stage one newly infected people on your record sheet . Cross this number off your list and move on to stage two.

If the die shows 5 or 6, you have 2 newly infected people. Write down the first two non-crossed off numbers on your list of 40 random people under stage one newly infected people. Cross these numbers off your list and move on to stage two.

Stage Two

Roll a fair die for each infected person in the previous stages and the initially infected person. Now the disease is spreading from each infected person. Use the same procedure from stage one for each dice roll. Make sure you record the ID number for each newly infected person under the stage two on your record sheet.

Stage Three

Once you have finished crossing off the newly infected people from stage two, you now roll the die again for each of these infected people. For example if you are starting stage 3 and you had 2 newly infected people in stage 1 and 3 newly infected people in stage 2, you would need to roll the die 6 times (initial person, 2 from stage 1, and 3 from stage 3). Use the same procedure from stage one for each dice roll. Make sure you record the ID number for each newly infected person under the appropriate stage on your record sheet.

Stages Four - Six

Continue rolling the die for each infected person from the previous stage. Record the newly infected people.

Reflection

Answer the reflection questions on the record sheet and turn in your record sheet on Canvas.

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Record Sheet: Using Dice to Model the Spread of a Disease

Name _______________________________________________________________________

Initially infected person __________________________________________________________

Stage one newly infected people __________________________________________________

Stage two newly infected people___________________________________________________

Stage three newly infected people _________________________________________________

Stage four newly infected people __________________________________________________

Stage five newly infected people __________________________________________________

Stage six newly infected people___________________________________________________

Total number of people infected at the end of:

Stage One:

Stage Two:

Stage Three:

Stage Four:

Stage Five:

Stage Six:

Reflection: It's possible to doa careful mathematical analysis of the results, but for now, just use your powers of logic and critical thinking to discuss their meaning.

1.What do the results tell you about how a disease can spread through a population?

2.The transmission of many diseases can be stopped by simple steps such as hand washing, or in some cases through vaccination. How would the spread be different if many people took these steps? Could the disease be completely eradicated?

3.We didn't have to define the carrier as someone with a disease. For example, we could have defined the carrier to be someone who starts spreading a rumor, or a computer virus. What other kinds of human interactions can be modeled by this activity?

4.This is one simple example of how we can analyze data quantitatively. How does this type of analysis help improve your understanding of the situation being modeled?

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