Enhancing the SIR model

Invent a clever name for an infectious disease. It can be light-hearted and whimsical, or grisly and macabre. Come up with some symptoms for it, and a method by which it will be passed from human to human.

Then, build upon the SIR model we did in class in the following ways:

This disease is often fatal. You'll thus have a Dead stock with a morbid flow into it.
This disease (as is fairly common among diseases) has an incubation period during which an individual who has caught the disease is not yet infectious him/herself. We'll use standard epidemiological terminology here, even though I find it confusing: such individuals are called "Exposed." The "Infected" population, on the other hand, are those who are actually infectious. (So to be clear: both Exposed and Infected individuals are sick. The difference is that the former are in the early stages of the disease, and cannot yet pass it on to others; the latter are at the point where they're communicable.) So the lifecycle for an individual who recovers is S→E→I→R, and for those who die, S→E→I→D. (This is assuming that the individual is not quarantined, as explained in the next bullet.)
The panicked society reacts to this epidemic by implementing a Quarantine procedure. When individuals become Exposed (and show symptoms indicating this) some fraction of them are immediately moved to an isolated location (with other exposed individuals) for some period of time, until they are deemed recovered (or dead). Thus during their infectious period, they are unable to contaminate others. After they are no longer infectious, they are returned to the general population to resume their lives. So the lifecycle for an individual who gets quarantined is S→E→QE→QI→R (and for those who die, S→E→QE→QI→D).

To do

On paper, or using some kind of electronic drawing tool, create a stock-and-flow diagram that enhances the original SIR diagram by including the following additional four stocks:
1. E -- exposed individuals who are mingling in the general earth population. (As described above, these individuals do exhibit symptoms of the disease, but they are not yet contagious.
2. QE -- exposed individuals who are isolated from the rest of humanity and are bored.
3. QI -- infected individuals who are isolated from the rest of humanity and are bored. They are contagious, but s'aight, they're locked in a cell and can't infect anybody else.
4. D -- dead. :(
Obviously, your stock-and-flow diagram will also have additional flows. Consider carefully what those should be. It will also contain additional parameters (little circles). Consider carefully what those should be, and what units they should be in.
For the code, begin with the SIR model we wrote in class. Do a git pull or just copy the file to your system from github.
Modify your Python code to incorporate your changes to the stock-and-flow diagram.
Carefully experiment with different values of your parameters to ensure that the simulation's behavior makes sense. (Take your time here. Don't rush.) Investigate anomalies and curiosities, debugging if necessary.
When you're confident it passes sanity check, produce two plots:
- A representative plot using a single set of reasonable parameter choices. This plot should have time on the x-axis, and should show a line for the populations of each of the seven stocks. It should be well-labeled and neat. It should have a legend and a title. It should either be in color (if you have access to a color printer) or use different line widths/styles to distinguish between the different stocks (if you don't).
- Two plots representing the results of a parameter sweep on some independent variable (your choice). One plot should show the total percentage of the population that gets the disease on the y-axis, and your independent variable on the x-axis. The other should show the total percentage of the population that dies on the y-axis, and your independent variable on the x-axis. Ditto the previous comments about neatness, labels, and colors.
Using a word processing program, write a three-paragraph blurb of text that (1) describes your fictitious disease and its humorous and/or grisly symptoms and transmission method, and (2) summarizes in words what you learned about the model's behavior through running the simulation in the previous step. These paragraphs should be grammatically correct, with no spelling errors; they should be compelling, intriguing, inspiring, and contain writing worthy of a college student, not a high school student.
Print out (on a printer) your code, your write-up, and your two plots. Staple them (with a stapler) together with your legible and beautiful stock-and-flow diagram from step 2, above.
Stick your finished packet of paper in the "420" manilla envelope hanging outside my office door in James Farmer 044.

Warnings and notes

DO NOT wait anywhere remotely close to the deadline before completing your stock-and-flow diagram. You cannot do that successfully at the last minute. It will require unrushed, uncluttered, unpanicked thought to get right.

I am more than happy — nay, overjoyed — to discuss the stock-and-flow diagram with you in office hours or to answer questions about it over email. Ditto the Python implementation.

Getting help

Come to office hours, or send me email with subject line "DATA 420 Homework #3 help!!"