General Information
| Student: | Kaitlin Pollet |
|---|---|
| School: | Muhlenberg College |
| Major: | Mathematics |
| Minor: | Economics | E-mail: | kpollet@muhlenberg.edu |
| Project: | Social Distancing Mechanism |
Project Description
This summer, I worked with Dr. David Pennock and Dr. Amelie Marian to understand how we can relate game theory to coronavirus and strategies based on this theory that we can use to limit the spread of coronavirus. Everyone in the country is strategizing in the game to limit the spread of the coronavirus and a strategy that we can use to limit the spread of the virus is partitioning people into groups to limit the spread.
Weekly Log
- Week 1:
- Week 2:
- Week 3:
- Week 4:
- Week 5:
- Week 6:
- Week 7:
- Week 8:
- Week 9:
05/26/20 - 05/29/20: This week started out with orientation and an introduction to the DIMACS REU program. I met with my mentor a few times this week to start brainstorming some ideas about the project. Also, I attended a workshop to learn about setting up a webpage and going over simple HTML code. We would like to use graph theory to simulate social interactions to see how different strategies work in preventing the spread of coronavirus while being able to return to some degree of normalcy. I am going to be reading some more about graph theory, modeling disease spread, and game theory this week to familiarize myself more with some of these relevant concepts.
06/01/20 - 06/05/20: This week started out with presenting introductions to our research projects. I enjoyed watching my fellow REU participants present and was interested that some of the other students are also doing research involving coronavirus. Also, I began to read about percolation theory and decision theory this week and thought about different connections to how it can relate to my project on coronavirus. Furthermore, I began to think and look into ways to simulate a social networking graph and different programs on how to program this. Overall, this week, I did a lot of reading of various theories that may relate to my research and built many connections across different theories. At the end of the week, we had our first seminar talk by Dr. Lydia Chilton and I found some interesting ways that her AI thoughts can relate to my project.
06/08/20 - 06/12/20: I attended a data science workshop this week where I learned more about different visualization tools and statistical methods available in Python. Also, I began to use Python in my own research project where I have started to develop social networking graphs. Some of my readings for this week included more information about prisoner's dilemma, the Watt's-Strogatz Model, and small-world networks. I spent a lot of the week learning more about how to program in Python and developed some of my own code. I began to look more into optimization with constraints to think about how we can minimize problems and maximize normal life when returning to normal in a coronavirus world.
06/15/20 - 06/19/20: Throughout this week, I have been developing my Python code more and began to think about more complex situations and how to model those situations in a graph. I have read about graphical congestion games this week as well as a quantal response equilibrium. Furthermore, I have started to focus on how we can implement social distancing strategies on colleges and I have been reading numerous colleges plans on returning to campus in the fall. I have started to develop some of my own strategies based on what I have read and thinking about all of the different elements that need to be thought about when it comes to social distancing such as classes, dining, dorm-living, social life, campus activities, etc. Also, I attended a talk this week by Mykhalo Tyomkyn that related to graph theory and I found some interesting connections to my project.
06/22/20 - 06/26/20: This past week started out with an interesting talk by Lenka Zdeborova and this week was a bit of a turning point in my research experience. The past few weeks, I have been researching my topic involving many different theories and concepts, but this week I really began to narrow down my topic and develop a strong focus. Furthermore, I have devleoped my Python code some more this week by modeling and thinking about how connections amongst people have different weights and how to account for this in a model. Also, I have began to look into different types of graphs such as the connected caveman graph. I am beginning to think of the coronavirus as a graphical congestion game and have been modelling different graphs as well as looking into model some strategies of social distancing mathematically.
06/29/20 - 07/03/20: Overall, this week was spent mostly focusing on further developing my code in Python with a connected caveman graph in order to start being able to run my simulations which I will hopefully do next week. By the end of the week, I developed the code for my connected caveman graph as well as developing my color mapping and simulating of the virus spread. Next week, I hope to test out different size cliques in my caveman graph and different numbers of cliques as well as simulating if all nodes have an equal chance of getting it (varying probabilities) as well as if some nodes have a less or greater chance of getting it due to possible precautions taken by people such as wearing a mask or washing their hands.
07/06/20 - 07/10/20: This past week was mostly spent finishing developing my code and I collected a lot of my data through my python simulation. I began to simulate the spread of the virus over my caveman graph by looking at different sized cliques as well as a different number of cliques along with different probabilities of each node infecting the next node. I began to analyze some patterns of the data and looking into different ways to display my data graphically. Next week, I will continue to analyze my data and figure out how to display it in the best way as well as work on my final presentation and final paper.
07/13/20 - 07/17/20: This week, I figured out how to display my data in the best way to show my results and I drafted out most of my final scientific paper as well as creating my final presentation. Next week, I will continue to edit and finish my scientific paper and practice for my final presentation on Wednesday.
Presentations
Additional Information
-
My Mentors
- Mathematical Modeling of Disease Outbreak
- Game Theory
- Percolation Theory
- Decision Theory
- Small World Networks
- Graph Theory
- Prisoner's Dilemma
- Watts-Strogatz Model
- Graphical Congestion Games
- Quantal Response Equilibrium
- Colleges Fall 2020 Planning with Social Distancing
- Vaccination & Game Theory
References
Acknowledgements
I completed this research program through the DIMACS REU program of 2020 and I would like to thank the NSF for funding this project through the NSF Grant CCF-1852215. I would also like to thank Dr. David Pennock, Dr. Amelie Marian, and Dr. Lazaros Gallos for running this program despite the virtual challenges.