Jan Rychtář

National Research Experience for Undergraduates Program

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

Acknowledgement

This program is an MAA activity funded by NSF (grants DMS-1156582 and DMS-1359016).

Summary

Jan Rychtar (UNCG), and Hyunju Oh (Bennett College) 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 19, 2014 to June 27, 2014, we will engage 4 African-American female undergraduate students from Bennett College, Greensboro, NC in the research projects. The students will work in groups of two under the supervision of project directors. 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 (such as Maple or a freeware program NetLogo) as well as analytical tools (optimization and linear algebra) to identify such strategies in real game theoretical models with applications in biology and medicine (such as cat vaccination to prevent Toxoplasmosis infection or bed-net use to prevent malaria).. The students will further 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 group of students will submit at least one research paper and present the finding during at least 2 conferences (held in NC during Fall 2014 or Spring 2015).

Students

  1. Aaleah Lancaster
  2. Kira Crawford
  3. Marie Laura Paulemond
  4. Chasity Dorsett

Projects

Modelling the Prevention of African Sleeping Sickness disease

African sleeping sickness is a parasitic disease transferred by tsetse flies to humans and other animals such as cows. The sickness is caused by protozoa of the species Trypanosoma brucei. We used a SIR compartment model (Damian Kajunguri, John W Hargrove, Rachid Ouifki, JYT Mugisha, Paul G Coleman, and Susan C Wel- burn. Modelling the use of insecticide-treated cattle to control tsetse and trypanosoma brucei rhodesiense in a multi-host population. Bulletin of mathematical biology, 76(3):673–696, 2014) to study the disease in the population where a proportion of cows is being treated by an insecticide to limit the tsetse transmission. The model allows us to study the basic reproduction number of the disease, as a function of the proportion of cattle being treated with insecticide per day. We used vaccination game framework (Chris T Bauch and David JD Earn. Vaccination and the theory of games. Proceedings of the National Academy of Sciences of the United States of America, 101(36):13391–13394, 2004) to get the optimal proportions of the cows to treatfor the individual farmers.

Modeling the Prevention of the Dengue Fever

Dengue Fever is one of the most important vector-borne infections that have emerged as a worldwide problem beginning in the 1950’s. This infection is transmitted by its principal vector Aedes Stegomyia aegypti. We studied and used a SIR compartment model (Marcos Amaku, Francisco Antonio Bezerra Coutinho, Silvia Martorano Raimundo, Luis Fernandez Lopez, Marcelo Nascimento Burattini, and Eduardo Massad. A comparative analysis of the relative efficacy of vector-control strategies against dengue fever. Bulletin of mathematical biology, 76(3):697–717, 2014). The model yields the basic reproduction number and the force of infection for Dengue Fever as a function of many parameters; most notably the death rate for mosquitoes, and daily rate of biting from the mosquitoes. Each of these parameters can be influenced by human behavior (for example by eliminating the standing water sites, using insecticide to kill adult mosquitos, or to limit exposure to bites). We used vaccination game framework developed in (Chris T Bauch and David JD Earn. Vaccination and the theory of games. Proceedings of the National Academy of Sciences of the United States of America, 101(36):13391–13394, 2004) to get the behavior that is optimal for the individual.

Outcomes

  • Presentations at Bennett College, June 25, 2014
  • Presentaions at NC A&T, July 18, 2014
  • Kira Crawford and Aaleah Lancaster presented the talk "Mathematical Model of African Sleeping Sickness" at 2014 Annual Biomedical Research Conference for Minority Students (ABRCMS), San Antonio, TX, November 14, 2014.
  • Marie Paulemond and Chasity Dorsett presented the talk "Dynamic Modeling for Dengue Fever" at 2014 Annual Biomedical Research Conference for Minority Students (ABRCMS), San Antonio, TX, November 14, 2014.
  • Kira Crawford and Aaleah Lancaster presented the talk "Mathematical Model of African Sleeping Sickness" at UNCG RMSC conference
  • Marie Paulemond and Chasity Dorsett presented the talk "Dynamic Modeling for Dengue Fever" at UNCG RMSC conference
  • Chasity Dorsett presented the talk "Dynamic Modeling for Dengue Fever" at the 8th Annual VA-NC Alliance Research Symposium, March 29-30, 2015
  • Aaleah Lancaster presented the talk "Mathematical Model of African Sleeping Sickness" at the 8th Annual VA-NC Alliance Research Symposium, March 29-30, 2015
  • Marie Paulemond and Chasity Dorsett presented the talk "Dynamic Modeling for Dengue Fever" at the Interdisciplinary research day at Bennett College, April 10, 2015
  • Kira Crawford and Aaleah Lancaster presented the talk "Mathematical Model of African Sleeping Sickness" at the Interdisciplinary research day at Bennett College, April 10, 2015
  • Chasity Dorsett, Hyunju Oh, Marie Laura Paulemond, Jan Rychtar: Optimal repellent usage to combat Dengue Fever, accepted in Bulletin of Mathematical Biology pdf
  • Kira Crawford, Aaleah Lancaster, Hyunju Oh, Jan Rychtar: "Optimal use of Insecticide to Combat African Sleeping Sickness, Letters of Biomathematics 2015 2:1, 91-102, DOI: 10.1080/23737867.2015.1111777