# Notes on Lab #6

IMPORTANT: Discussing ideas with each other is fine, but
you need to be able to do the actual work on these labs on your own, or
ask for help from me.
If I see you simply copying from someone else's screen, I will ask you to
leave the lab, and you will get a zero on it.
## Part 1: Spread of Disease

Remember the
H1N1 (Swine Flu) outbreak of 2009
and the
SARS outbreak of 2003? These viruses have received some recent
media attention, and now would be an appropriate time
to experiment with a model of the spread
of disease. Read the beginning of the Spread of SARS material, stopping at the
SARS model itself (pp. 131-136). Because the full SARS model is so complicated
(see p. 139), we'll stick with the simpler SIR model.

When you're done reading, copy the **SIR.mdl** model from the Vensim models
folder to wherever you prefer to work. Then skip ahead to p. 143 and do **Projects 1
and 2** on modeling the effect of vaccinations. The idea is that vaccination
represents another outflow from susceptibility – if you're vaccinated or
already infected, you're no longer susceptible. If you start with a vaccination
rate of zero, you have the orginal model, which is a nice way of doing the
comparison specified in the projects. As usual, there is something slightly
different between the downloaded model and the specifications in the book;
in this case, you have to change the time units from months (the default)
to days, to make the plots sensible. Also, according to
this
reference, *vaccination* and *immunization* are the same thing,
which simplifies the task for Project 2. Don't fret over the
obi-wan error
on the interpretation of "after three days"; just make sure that there are two or
three initial days during which the vaccination rate is 0, after which it is
0.15. I'll leave it to you on how to implement this. A good model should make the parameters
(start time, vaccination rate) visible, and not hide them in the formula for the variable
that they affect.

Submit the final model (for Project 2). Your writeup should have five labeled
plots (no immunization, 15% per day starting immediately, 15% starting after three days,
25% starting immediately, 25% starting after three days),
along with a brief qualitiative description of the effects of the various
immunization schedules.
## Part 2: Predator/Prey

The
Lotka-Voltera model
of predator/prey dynamics is a classic that would be a
shame to skip. So along with the spread-of-disease model, I've picked it out of the
systems dynamics models from the textbook as something for us to work on.

Read pp. 118 - 124. The four constants have somehwat confusing abbreviations, but
there's a nice summary of them at the top
of p. 122, which you might use to annotate the figure at the top of the page.
Then make a copy of the **Predator-Prey.mdl** file from the Vensim
downloads. Again, the model won't really work "out of the box"; you'll
have to change something to get it to run without errors or warnings.
(*Hint*: this is what we studied in Lab #5.)
Then do **Project 3bc** on p. 126. (The author's description suggests simplifying the
fishing component by using a single fishing rate for both predators and prey.) For extra credit, do parts a and/or d.
You can solve for the equlibrium values by setting *ds/dt* and *dh/dt* to zero and using algebra,
or you can just look at the equilbrium formula on
the Wikipedia page.
Submit the model and the writeup. Your writeup should include figures like
Figure 4.2.4 (p. 124) for various values of the fishing rate, as well as a
separate plots for predator (sharks) and prey (tuna) at the equilibrium value
for for the fishing rate. Finally, briefly describe the key similarity between this
predator-prey model and the SIR model from the first part of the lab (*Hint*: bottom
of page 119).