Title here
Summary here
flusim
Github Link Report Document Python package on TestPyPI
2023/09-2023/12 Python Simulation Markov Processes LaTeX
Basic Info
This was a project that I worked on in the class Simulation (ISYE-6644) at Georgia Tech’s OMSA program.
The Idea
The project idea was one of those given in a proposed project topics in this course. Roughly speaking, the original topic has the following settings and the corresponding questions posed:
Settings
Consider a population of size 31, and a flu going on in this population. The flu has some properties:
- Day 0, the number of sick students if 1
- An infected person has a probability p=0.02 infecting any healthy person
- An infected person will remain infected for precisely 3 days
- This flu doesn’t kill people
Problem
- Calculate the distribution and expected number of number of people infected at day 1, 2
- Simulate and find an approximation of the distribution of end-date of flu
My idea was then to write a Python class (and eventually it became a Python package, though no people use it) that has the following functions:
- Supports calculations of exact statistics
- Supports simulations for approximation of statistics
- Supports basic visualizations of the fluspread process
My Works
I first formulated a more general version of this problem (where population size, infecting probabilities can be tweaked) mathematically, and designed pseudocodes for exact solvers, simulations for statistics (such as {distributions / expectations / variance} of {number of infected people / end dates}).
The related theory I used for designing the exact solver was that of Markov chain1, where some of the statistics can be done via such general methods - for example, expectations, variance of end dates are analyzed via first step analysis techniques.
Some Screenshots
Fragments of final report (page 1, 5, 8, 11)
Final Thoughts
It was pretty cool seeing the things I derived with the theory of Markov chains matching the simulation results, a type of “mathematical joy” I would say.