Jan Rychtář

National Research Experience for Undergraduates Program

[2013] [2014] [2015] [2016]

Acknowledgement

This program is an MAA activity funded by NSF NSF (grant DMS-1359016).

Summary

Hyunju Oh (Bennett College) and Jan Rychtar (UNCG)received funding from the Mathematical Association of America (MAA) for the for the “Game Theory and Applications” project. The award is part of the National Research Experience for Undergraduates Program funded through MAA by the National Science Foundation's Division of Mathematical Sciences. During the 6 weeks, from May 15, 2016 to June 25, 2016, we will engage 4 African-American female undergraduate students from Bennett College, Greensboro, NC in research projects. The students will work under the supervision of project director Hyunju Oh (Bennett College).Jan Rychtar (University of North Carolina at Greensboro) will assist Dr. Oh with leading the students. We will introduce the students to the fundamental game-theoretical concepts such as Nash equilibria and evolutionarily stable strategy and teach them how to use computational tools, as well as analytical tools (optimization and linear algebra) to identify such strategies in real game theoretical models with applications in medicine - “vaccination games” where individuals have to make decisions whether to protect themselves from infectious diseases by taking costly actions such as taking a vaccine. The students will be trained in all aspects of research, starting with the ethics code, going through the workshops on using library and online resources and ending with training in delivering oral presentations as well as in using LaTeX to write mathematical papers. We expect that each student will submit at least one research paper and present her findings at at least 2 conferences (held in NC during Fall 2016). This project is part of the growing collaboration between UNCG and Bennett College (HBCU).

Students

  1. Dana West
  2. Chasity Dorsett
  3. Sydney Meeks
  4. Hakimah Smith

Projects

Toxoplasmosis vaccination.

Over 60 million people in the United States carry the parasite Toxoplasma Gondii, and the Center for Disease Control (CDC) has classified Toxoplasmosis among the Neglected Parasitic Infections disease group targeted for control by the CDC. In recent years, there has been significant progress towards the development of a practical vaccine, so vaccination programs may soon be a viable approach to controlling the disease. Anticipating the availability of a toxoplasmosis vaccine, we are interested in determining when cat owners should vaccinate their own pets. To investigate this, we will create a mathematical model describing the conditions under which vaccination is advantageous for a person living with cats. The core of the conflict in this (and similar games) is that if all cat owners decide to vaccinate their cats, there will be only a very small chance of an unvaccinated cat to contract the parasite and the disease. Consequently (especially if the vaccine is expensive, either in a form of a dolar cost or in a form of bad side effects), it may become beneficial for a cat owners to leave their cats unvaccinated. On the other hand, if almost nobody vaccinates their cats, the risk of getting the disease is large and thus the cat owners should vaccinate their pets. The important question thus is, given the cost of the vaccine, what is the appropriate level of pets vaccination. The project will built on a recent results by Rychtar and his students published in Theoretical Population Biology.

Ruminant Vaccination to Control Rift Valley Fever (RVF) virus.

RVF virus is transferred among animals and humans by mosquitoes. It has first been isolated in Kenya in 1930, but there is a growing concern it can spread to US. Currently, there are two types of vaccines (for animals) available. One is relatively expensive but safe; the other is relatively cheap but with many dangerous side effects such as abortion and fetal abnormalities. In this project, we propose to build on results from 2014 NREUP where we developed models for the control of African sleeping sickness by spraying cows by insecticide (manuscript appeared in Letters in Biomathematics 2015 2:1, 91-102) and controlling dengue fever by using insect repellent (currently under minor revisions in Bulletin of Mathematical Biology). We will adopt the techniques used in those two papers for the RFV virus.

Outcomes

  • Chasity Dorsee was accepted in NCA&T Applie Mathematics Graduate Program
  • Dana West was accepted into UCLA's MII RISE summer internship program for summer 2017
  • Sydney Meeks had a poster presentation "Using a Game Theoretic Approach to Analyze the Rift Valley Fever Virus " at MAA Student Poster Session, 2017 Joint Mathematics Meetings, Atlanta, GA, January 6, 2017
  • Chasity Dorsett had a poster presentation " Dynamic Modeling for Yellow Fever" at MAA Student Poster Session, 2017 Joint Mathematics Meetings, Atlanta, GA, January 6, 2017
  • Chasity Dorsett and Hakimah Smith: Yellow Fever Vaccination and The Theory of Games, UNCG RMSC, November 12, 2016
  • Sydney Meeks and Dana West: Using A Game Theoretic Approach to Analyze the Rift Valley Fever Virus Vaccine, UNCG RMSC, November 12, 2016
  • Chasity Dorsett and Hakimah Smith: Yellow Fever Vaccination and The Theory of Games, International Conference of Undergraduate Research, UNCG location, September 2016
  • Sydney Meeks and Dana West: Using A Game Theoretic Approach to Analyze the Rift Valley Fever Virus Vaccine, International Conference of Undergraduate Research, UNCG location, September 2016
  • Chasity Dorsett and Hakimah Smith: Yellow Fever Vaccination and The Theory of Games, UNCG RMSC Conference, November 2016
  • Sydney Meeks and Dana West: Using A Game Theoretic Approach to Analyze the Rift Valley Fever Virus Vaccine, UNCG RMSC Conference, November 2016
  • Chasity Dorsett and Hakimah Smith: Yellow Fever Vaccination and The Theory of Games, Joint REUs minisymposium, NC State University, June 17, 2016.
  • Sydney Meeks and Dana West: Using A Game Theoretic Approach to Analyze the Rift Valley Fever Virus Vaccine, Joint REUs minisymposium, NC State University, June 17, 2016.