The Same Difference: the spread of rumors, catching the flu, and more math
A research rotation for Southwestern's Science Training and Education Program or
STEPS

Description that the students saw to decide between session offerings:
What do gossip and disease have in common? Come and learn the mathematics that describes them both. We will use the computer to virtually spread disease or rumors, perform computations, and create graphs. No previous computer skills are needed. Students will present our simulations and their meaning.

I had two great groups of students, and we met in the small computer lab MBH 118.
One group of 4 students met Jun 11-15; the other group of 3 students met Jun 18-22. As we went, we wrote a description of our procedures and results in Microsoft Word. Our breaks included fun calculator tricks.
In general, this is what each group did:

Session 1

• Students set up rules and expectations.
• File hierarchy; set up the USB drives and on the PC that the student used with a folder called STEPS. Worked on the PC and copied files to the USB. Safely removed USB drive.
• Notes in a Word document.
• Coded a multiplication table in Microsoft Excel with an appropriately addressed formula.
• Simulation of disease spread within a small group by drawing papers with names.
  Entered data into Excel.
• Intro to Excel: save a file; copy, paste; relative addressing; entering a formula; dragging to create an arithmetic sequence.
• Wrote up our procedure.

Session 2

• From our paper-drawing simulation, made a graph in Excel of the total number of infected.
• Discussed random and pseudo-random number generation, including with dice, a spinner, differently shaped objects, and with software. Discussed some things that would keep our process from being truly random.
• Simulation of disease spread within a small group by using software to generate random values.
  Excel: generate a table of 20X20 random values, copy and paste values so they do not keep changing, highlighted the same number of random values that we had people who were infected at the last step.
  We made a table of 0s; typed 1 for a particular person when that person catches the infection.
• for each row (trial, week), we summed up the 0s and 1s to get the total number of infected people.
• Wrote up discussion in Microsoft Word, including our graphs. (Covered handy tips for pasting into Word.)
• File naming conventions.

Session 3 (a shorter session)

• Discussed indicator functions, which is the collection of our 0s and 1s for each person to say that a person does not have the disease yet (0) or has caught it (1).
• We noticed two properties of our graphs that made them sigmidal.
• Viewed this website and discussed careers in math, study skills, developing a relationship with the high school counselor, etc.

Session 4

• In Excel, "move and copy sheet" with "create a copy" selected. Performed a 3rd simulation.
• Found influenza data from the CDC site, copied and pasted the data into Excel, made a table and a scatterplot.
• Discussed the difference between what the CDC counted and what we counted.
• Performed calculations so that we had both types of "# infected" for our simulation from random numbers and for the CDC data.

Sessions 5 and 6

• Discussed the REASON for the shape of the graphs
• "S-I" model, for "susceptible" and "infected." Mentioned other models that include "recovered" and "immune."
  Discussed assumptions for our model -- fixed population; no one leaves the group and no new people enter.
  If a person was sick in the last run and we chose that person again, s/he remained in contact with only him/herself or with other sick people.
• In my 1st rotation of students, the discussion led us to code the sum of two dice and their probabilities in Excel to talk about which results were equally likely. In my 2nd rotation of students, the discussion led us to code the running sums two different ways in Excel and discuss recursive and non-recursive methods.
• Went through the "fish simulation" in each rotation. In the 2nd rotation, we also went through the "market simulation."
• Wrote up discussion in Word. (In the 2nd rotation, we used EasyBib.com to build a bibliography from our resources.)

- - - - - - - C E L E B R A T I O N ! ! ! - - - - - - -

Fri, Jun 29

• Banquet and Presentations

- - - - - - - R E S O U R C E S - - - - - - -

Career Info

US Bureau of Labor and Statistics

We Use Math

American Mathematical Society

Society of Industrial and Applied Mathematics

Duane Kouba

References

"CDC - Seasonal Influenza (Flu) - Flu Activity & Surveillance." Centers for Disease Control and Prevention. Web. 11 June 2012. http://www.cdc.gov/flu/weekly/fluactivitysurv.htm. Also http://www.cdc.gov/flu/weekly/weeklyarchives2009-2010/data/AHDRA20.htm for earlier data and http://www.cdc.gov/flu/weekly/weeklyarchives2011-2012/data/senAllregt22.htm for current data.

Freiberger, Marianne. "Pan(dem)ic?" Plus.maths.org. Web. 11 June 2012. http://plus.maths.org/content/pandemic.
The home site is edited by Freiberger and Thomas.

Matthew, Keeling. "The Mathematics of Diseases." Plus.maths.org. Web. 11 June 2012. http://plus.maths.org/issue14/features/diseases/.

"Logistic Growth." Connecting Concepts: Interactive Lessons in Biology. Web. 26 15 June 2012. (produced collaboratively at the University of Wisconsin-Madison) http://ats.doit.wisc.edu/biology/ec/pd/t2.htm

Schreiber, Michael. "Logistic Sigmoid Market Model." Wolfram Demonstrations Project. Web. 25 July 2010. http://demonstrations.wolfram.com/LogisticSigmoidMarketModel/.