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).