DATA 420 - Modeling and Simulation - Spring 2024
Systems Dynamics Models I
Possible experience: +40XP (or even +50XP)
Due: Friday, Feb. 16 Sunday,
Feb. 18, midnight
1. Temperature
Modify the
furnace simulation we developed in class to model Air Conditioning
(A/C) instead (5XP). Then, answer the following
questions, and include plots illustrating your answer to each:
Suppose we set our thermostat at 72°F, and it's a whopping 95°
Virginia day outside. Suppose further that our insulation is fairly crappy, and
leaks heat at a rate of .2 (degrees/hr)/degree. Then:
- About how strong an A/C unit would I need (in degrees/hour) for the
house to be able to maintain my desired temperature at all? (5XP)
- About how strong a unit would I need in order for it to maintain my
desired temperature and only be running half the day on average? (5XP)
- Suppose we fast-forward 100 years, to the point where global warming
has made much of the planet (including Fredericksburg) intolerable. It is now
125°F outside in the summer. If your A/C had the power you computed in the
previous item, what percentage of the day would it be running now? (5XP)
2. Drugs
Use the drug
simulation we developed in class to complete one of the
following items (choose wisely):
- A new medication has been developed to treat patients with a particular
kind of liver deficiency. The MEC for this medication is 250 μg/ml and the
MTC is 500 μg/ml. Its half-life is estimated to be about 15.5 hours. Develop
a dosage schedule for adults (assumed to have between 2.7 and 3.3 liters of
plasma each) and another one for children (assumed to have between 1.25 and
1.75 liters). Each dosage schedule should be in the form of "take X milligrams
every Y hours," and should be accompanied by plot(s) demonstrating that such a
schedule, when followed properly, will maintain proper levels of the drug in
the patient's blood 24/7, for any patient within the above plasma assumptions.
(+20XP)
- Up to now, we've modeled only the elimination of the drug from the
patient's system as a time-varying quantity: the metabolism into the
bloodstream has been instantaneous. Remedy this inaccuracy by extending the
model to a two-compartment model. This somewhat amusing term means that
you'll represent the human body as having two "compartments" into which the
drug travels: first, the digestive tract (which in reality has many component
parts, but which in your model will be just one big box), and then, the
bloodstream (plasma). It takes time for the drug to metabolize from the first
box to the second, but only the concentration of the second box has any
therapeutic effect. (+30XP)
Your revised simulation should correspond to the model below:
After writing and debugging your simulation, analyze its behavior with respect
to how the metabolism constant and the elimination constant interact.
Experiment with values where the metabolism is higher, and where the
elimination constant is higher, and where they are roughly equal. Produce plots
demonstrating this behavior, and a brief analysis describing it.
Turning it in
For this assignment, send an email to data420submissions@gmail.com
with subject line DATA 420 System Dynamics I turnin and with a zip file called
"yourumwuserid_SD_I.zip" as an attachment. In it, should be all
of the relevant files for parts 1 and 2 of this homework.
These relevant files are:
- A single PDF file (in PDF format) with all of your analysis and plots from
the various problems you chose. Be very explicit and specific about which
item of which part you are answering with a given narrative/plot. Do not
make me guess.
- The .py files demonstrating the code (for each simulation) with
your changes made to it. Each Python program, if I run it, should produce one
or some of the plots you included in your PDF file. (I understand that for some
items, you will be running the simulation several times with different
parameter choices. You do not need to include an entire separate
.py file for each such version. Just one representative version is
okay. Please name these .py files sensibly; for instance,
part1.py and drugs.py are both good names.)
Getting help
Come to office hours, or send me email with subject line "DATA 420
System Dynamics I help!!"