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Disease and Epidemics - Math Lessons
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Diseases & Epidemics Icon In the mathematics lessons of the "Diseases and Epidemics" unit, students will explore how the study of diseases and epidemics can be understood from a mathematical perspective. Issues addressed are finite geometric series, calculating threshold values, and statistical models of the spread of disease.

  1. Students learn about the spread of disease and two models of susceptibility
  2. Students will be able to calculate the threshold value for the number of susceptible people needed for the epidemic to occur
  3. Students will use the closed form for the sum of a finite geometric series to calculate how much of a specific antibiotic remains in the body over time.
  4. Students learn to change from the expanded form of a finite geometric series to the closed form of a finite geometric series and calculate the sum of the series.

Each big idea is addressed by a learning cycle. At the completion of each big idea’s learning cycle students should be able to answer the corresponding question. At the end of the unit, the students will be able to apply their new scientific understanding to the Major Project where they provide a public service message that is checked in advance by local public health officials for accuracy.
Lesson Title & Description
Objective
Students will:
Class period & week
Who Gave it to You?
Students will be able to model the spread of disease through a population.

1. Use logic to locate the primary cases, the people who started the spread of the disease through the population.

2. Graph the data of the number of people infected over time (exchanges) and determine an equation that best fits the data.

3. 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

4. Calculate the theoretical probability of their being infected after each exchange of fluids by knowing the original number of infectious people in the population.

5. Calculate the experimental probability of their being infected after each exchange by knowing the actual number of people infected after each exchange

Week 2
1-2 days
What does Math have to do with Getting Sick?
Students will be able to use the Susceptible-Infected-Recovered Model for Epidemics.

1. Explain the meanings of all of the terms and variables used to develop the rate of transmission of a disease

2. Explain how the rate of transmission of a disease is used in determining the rate of change in the number of susceptible people in the population.

3. Explain how the rate of recovery is calculated

4. Explain how the rate of transmission of a disease and the rate of recovery tare used to determine the rate of change in the number of infected people in the population.

5. Calculate the number of susceptible people, infected people, and recovered people are in a population at a given day of an epidemic
Week 3
1-2 days
Who makes an Epidemic?
Students will be able to calculate the threshold value for the number of susceptible people needed for the epidemic to occur 

Calculate the threshold number of people needed in the susceptible group for the epidemic to occur.
Week 4
1-2 days
Take Your Medicine 1
Students learn to change from the expanded form of a finite geometric series to the closed form of a finite geometric series and calculate the sum of the series.

Change from the expanded form of a finite geometric series to the closed form to facilitate calculating the sum of the series.

Week 7
1-2 days
Take Your Medicine 2
Students will use the closed form for the sum of a finite geometric series to calculate how much of a specific antibiotic remains in the body over time.

1. Use the sum of a finite geometric series to calculate the amount of antibiotic in the body just after the nth dose is taken, given the percentage of the original given amount of the antibiotic is present at the end of a given time period.

2. Use the sum of a finite geometric series to calculate the amount of antibiotic in the body just before the nth dose is taken, given the percentage of the original given amount of the antibiotic is present at the end of a given time

3. Draw a graph that shows the quantity of the antibiotic in the body between doses as a function of time.

4. Draw a graph that shows the cumulative amount of the antibiotic in the body over time.

5. Explain why the graph approaches a constant amount of antibiotic in the body.
Week 8
1-2 days

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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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Last update: November 10, 2009 		  Page Content: Rachel Hughes
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