Grading Guide for the

S-I-S Disease Endemic Limit Project

If you got help from someone, remember to acknowledge it in your report.  This could go right after your introduction.

General Remark on use of Help NoteBooks

The Help NoteBooks ARE intended to help you organize your project AS A MATHEMATICA NOTEBOOK, but we take offense to your leaving in the hints like:

Since a flu epidemic takes place in __ days, the number of births, deaths, and immigrations bla, bla, blah...

or

Therefore, the rate of of the fraction of the population

This sentence fragment is a HINT to help you conclude:

Therefore, the daily rate of creating new cases as a fraction of the population is  a s i,

daily rate of new cases = a s i  (in units of people per total population per day)

Please READ what you submit.  It is supposed to be clear and self-contained.  "Blah, bla, bla" is not clear and self contained.  Ask yourself, "Would my high school teacher understand this report?"
Also, the text contains clues as to how to 'solve' the probem.

Use of Mathematica as an Editor

Use text cells for text, don't type prose in input cells (adding your own returns.)

Use separate text cells for each paragraph.

Use Section, Subsection, Subsubsection cells to group appropriate portions of your project and organize your thinking.

Lab monitors can help you with these technical details.  ASK - check the sign on the door for who's on duty or go to 

http://www.math.uiowa.edu/reserv.html

Main Portions of Your Grade

This project was less technical than the others.  What I mean is that there is less Math and more Talk.  In this project clear explanation is required.

Introduction (3 pts)

This should be a very clear statement of the problem and a non-technical and inviting statement of the conclusion.  For example,

This report compares the real Hong Kong Flu epidemic of 1968-69 in New York City with the differential equation model of Chapter 2 in the main text, Calculus: The Language of Change.

We work with the best available data, the New York City coroner's estimate of "excess deaths" attributed to the strain of influenza that was first introduced in New York at that time.  These data are NOT a complete record of every person who contracted this flu. Comparison of the data and model takes this into account, as described in detail below.

"Adjusting" the data in order to make a comparison with the model, we find that there is an approximate relation between between the theoretical S-I-R influenza model and the actual data recorded.

Also include a comment on whether or not you thought that using this math model was an effective way of representing this epidemic.  Remember not to get too technical.  We'll have plenty of time for that later.

Derivation of the model  (7 pts)

Assumptions

The help notebook suggests three assumptions for the model.  These three are sufficient but if you think anything else needs to be said then do so by all means.

The descriptions of the assumptions need not be very long but they do need to be clearly and fully described.  Everything you say must make sense.  Your aim in writing this part of the project should be to write something that your room-mate could understand.

The Math bit

This is a very important section.
You need to say how you get:

daily rate of recoveries = b i  (in units of people per total population per day)

daily rate of new cases = a s i  (in units of people per total population per day)

and how these lead us to the diffential equations

\(TextForm\`\(					ds\/dt = \(-a\)\ s\ i\)\)

\(TextForm\`\(					di\/dt = a\ s\ i - b\ i\)\)

All of this is in the book.  We just want the key steps in your project.  Try to keep in clear. Make good use of spacing and don't be afraid to put the Math bits in the middle on their own.  
(We wouldn't expect your room-mate to understand this section but you must. )

Assumptions

The help notebook suggests three assumptions for the model.  These three are sufficient but if you think anything else needs to be said then do so by all means.

The descriptions of the assumptions need not be very long but they do need to be clearly and fully described.  Everything you say must make sense.  Your aim in writing this part of the project should be to write something that your room-mate could understand.

Matching the data and model predictions (4 pts)

In this section we see that the two graphs, although the same shape are on a completely different scale.
Thus we make adjustments.  State clearly how what you are changing and how you are changing it.  (Are you changing the coroner's data or the math model?)  We will have a chance to explain the why in the next section.

Justification of the time shift and scaling (5pts)

There have been suggestions in both the project book adn the help notebook as to why we can adjust the graphs. In this section you get the chance to say whether you thought these were valid reasons or whether you disagree.
This section is important.

The Wiggles at the end (2pts)

Why do we get wiggles at the end?  We can't know for sure.  We can, however, make some sort of guess.
The important thing in this section is to propose an idea and then back it up with some common sense.

Conclusion (4 pts)

We are looking for a somewhat more technical or detailed conslusion than you had in the last sentence of your introduction.

And for goodness sake...

Change that graph at the beginning of the project.  You must have a graph of your own there.