Influenza Outbreak

							Project AMP                        Dr. Antonio Quesada – Director, Project AMP


Influenza Outbreak Abstract
Subject: Advanced Algebra, Precaclulus, Calculus, Statistics

Strand: Data Analysis

Topic: Regression

Grade: 11-12

Objectives:
       1. Use a graphing calculator to calculate and graph a suitable regression for a given
           problem situation.

       2. Determine the reasonableness of a mathematical model by relating it to the problem
          situation.

       3. Synthesize findings in a written report and/or electronic presentation including charts
           and graphs
Materials:    TI-83, Worksheet

Expected Time: 2-3 days
Project AMP                        Dr. Antonio Quesada – Director, Project AMP


Influenza Outbreak
Overview
      Authors: Dave Erb & Donna Duve

      Description: Graph, explore, interpret, and calculate data pertaining to a logistic equation.

      Keywords: Regression, logistic, calculus, precalculus, disease control, statistics

      Prerequisites: Some knowledge of how to calculate a regression equation on a TI-83

      Grades: 11-12

      Subjects
             Economics
             Social Sciences
             Life Science
             Mathematics
             Speech
             Writing

Concept
      1.Estimation and prediction by use of mathematical models is an essential skill in a
      competitive market place.

      2. Available technologies have a large impact on society.

      3. Effectively communication of ideas is a necessary life skill.

      4. Working cooperatively with peers is essential to the success of individuals and
      companies.

Assessment
      Rubrics
      Student presentation
      Written explanation

Sharing
      Electronic presentation software or overhead projector can be used for students to present
      their regression models and analysis of the model of best fit. Presentations will be made
      to other teachers and classes as well as in class.
Project AMP                        Dr. Antonio Quesada – Director, Project AMP


Results

      Students will have explored the effects of the introduction of a disease to a fixed
      population. They will have a better understanding of how the Centers for Disease Control
      and Prevention (CDC) are able to predict outcomes and epidemics. Students will also
      have a better understanding of regression models and the logistic function in particular.

Learning Objectives

      4. Use a graphing calculator to calculate and graph a suitable regression for a given
         problem situation.

      5. Determine the reasonableness of a mathematical model by relating it to the problem
         situation.

      6. Synthesize findings in a written report and/or electronic presentation including charts
         and graphs

      The following is a list of the Learning Outcomes associated with this lesson lab
             OPO              Ninth-Grade                 Math 12
             OPO              Twelfth-Grade               Math 5
             OPO              Twelfth-Grade               Math 6
             OCBM             Grade Eleven – Integrated Strand One – 3
             OCBM             Grade Eleven – Integrated Strand Five – 8
             OCBM             Grade Eleven – Integrated Strand Five – 10
             OCBM             Grade Eleven – Integrated Strand Eight – 2

Project/Task

      Graph, interpret, and calculate a regression model related to the spread of disease in a
      fixed population

Learning Strategies

      1. Begin by having students explore the CDC website (http://www.cdc.gov)
      2. Present project through worksheet
      3. Group students to analyze data and prepare presentations
      4. Have students prepare presentations for CDC “experts”
      5. Conduct presentations.

Tools/Resources

      TI-83 or TI-83+ Calculator
      TI-Graph Link
Project AMP                      Dr. Antonio Quesada – Director, Project AMP


      Teacher prepared data and problem statement
      Computer programs for web browsing and electronic presentation

Do and How
      1. Access CDC website for information on disease spread prediction
      2. TI-graph link is a cable and software package from Texas Instruments, which allows
      the user to place calculator screens into word processing documents and presentation
      software.

Classroom Management
      Assign small groups of three students. Discuss teamwork and cooperation by helping
      students set up team structure and accountability processes.

      Teacher should introduce problem and emphasize what is to be accomplished. Teacher
      will oversee completion of analysis and development of presentation materials.
Project AMP                         Dr. Antonio Quesada – Director, Project AMP


                                           Addendum
                                      The Spread of Disease

        Epidemics are a major threat to human, animal and plant population. The worst epidemic
in recent times was the global influenza epidemic of 1918 and 1919. About 2o million people
died worldwide, including about 500,000 in the U.S.
        The Center for Disease Control (CDC) was established to promote health and quality of
life by preventing and controlling disease, injury, and disability. As a result, they are very
interested in studying diseases and how they spread.
        Recently, on a local college campus of 5000 students, one student returned from vacation
with a rare strain of a very contagious 3-day flu virus. The virus was so easily transmitted that
any contact with an infected person resulted in the virus being passed. The situation became even
more complex when it was discovered that the virus carries a twenty-four hour incubation
period, during which the infected person is contagious but often shows no symptoms. Thus,
many people did not even know they had come into contact with the virus. The only good thing
about this virus is that once you had contracted it and been ill, your body’s immune system was
able to build antibodies that would prevent you from getting the virus again.
        The records of the number of people infected were just recently found, but they were
incomplete. It appears the Campus Medical Center was so over run with infected patients and
staff members, that accurate records were not recorded. The only data that could be found was
the following table written by the Doctor at the Campus Medical Center.
                         Day                   # of people infected
                          1                             2
                          2                             5
                          3                            11
                          5                            54
                          10                          1868
                          15                          4851

        The CDC would like to know more about this virus and how it spread through this
population so they can possibly prevent it from happening again. As your math teacher, I gladly
volunteered your services to them in order to create a mathematical model that reasonably fits
this data. My friend Dat, who is a data analyst for a major corporation, suggests that you examine
the quartic, exponential, and logistic regression models to determine which one best fits the data
and the circumstances.
        Since these results must be presented to the CDC, you will need to compile your
information into a report to be presented to them. They’ve informed me that they will be in our
area within the next three days and that they will need to review your models at that time. Your
presentation can be done using a computer presentation system or by creating your own visual
aids. Be sure to include some screen shots from your TI-83, the CDC really likes to see proof of
what lead you to your conclusion of the model of best fit.
        Since this is such a large and important project, I think I will put you into groups of three
to prepare your presentations. The groupings will be posted soon, so prepare to get busy on this
project.