Grading Guide for the

Vaccination for Herd Immunity 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 verbatim statements like:

Project Help Notebook by Keith Stroyan

or

(You will want to make additional modifications an leave the computations in your report, and then remove this remark.)

You may wish to use auxilliary variables as follows

(Hint 3.4), (Hint 3.5)

Therefore, the rate of of the fraction of the population

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?"

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

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,

In this paper we study "S-I-R diseases" that are spread by casual contact.  "S-I-R" means susceptible, infectious, removed.  Susceptible people may become infectious if they get the disease or may move directly to removed if they are effectively vaccinated.  Infectious people spread the disease and become immune and removed once they recover from the disease. ....

In the omission "..." above, you should briefly define herd immunity and how it relates to epidemics.  Describe or define the parameter  c  that is a measure of the number of potentially disease spreading contacts an infectious person makes.  Say how this parameter affects how many people need to be immunized in order to achieve herd immunity.

State what you plan to address regarding the differences between measles and polio.  If you mention the recent CDC pronouncement on measles you should either support it or argue against it in the body of your report and summarize in your conclusions.  Did you see the newspaper article last week on a hoped for world-wide eradication of polio?

Derivation of the model  (6 pts)

We are looking for a clear description leading up to:

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)

BE CAREFUL WITH UNITS

These terms are used to describe the change in susceptible, infectious and removed fractions:

the daily rate of change in s =  - new cases

(ds/dt) =   - a s i

the daily rate of change in i = ...

((d ... )/dt) =   ...

the daily rate of change in r = ...

((d ... )/dt) =   ...

Computer Experiments  (7 pts)

We are looking for ONE copy of the basic code (the later experiments can have the code in a closed cell or cut) and lots of experiments with various sizes of  c.  We are also looking for a text description of what each individual experiment means.  Compare infectious peaks and percent of initially susceptible who avoided the disease.

Use your model and experiments to make herd immunity predictions for a couple diseases, perhaps measles and the hypothetical disease.

AFTER you have determined the analytical condition of the general case (see next section), do a few computer experiments that demonstrate your analytical result. (These would naturally go after the analytical section.)

The General Case (6 pts)

Mathematically derive the condition which assures that herd immunity is attained.  Use this to determine the appropriate conditions for a few diseases.  Compare these results with your predictions in the Computer Experiments section.

Address the project issues on page 19 of the Projects book.  You may want to read the 9/13/99 issue of TIME magazine (p 64) as an example of relevant information on immunization complications.

Conclusion (3 pts)

We are looking for a somewhat more technical or detailed conclusion than you had in the last sentence of your introduction.  Be sure to cover everything mentioned in your introduction.