Discipline: Science and Mathematics Education
Subcategory: Mathematics and Statistics
Session: 1
Room: Park Tower 8212
DaLisa Denham - Virginia State University
Co-Author(s): Mikaili Abdula, Morehouse College, Atlanta, Georgia; Andrew Tran, Virginia State University, Petersburg, VA;
Chemovirotherapy, is a combination of chemotherapy, the use of anti-cancer
drugs, and virotherapy, the exploitation of modified anti-cancer lytic viruses. Chemotherapy is currently widely used and effective at cancer treatment, but virotherapy is a novel treatment method, and hasn’t been observed to be effective alone. We believe the use of a hybrid chemo-viro treatment method will lead to a more successful treatment program than a single component treatment. In this paper, we study a mathematical model of tumor cell interactions. The proposed model illustrates the interaction of the chemotherapeutic drug, the viral agent, at the tumor microenvironment using a coupled system of four nonlinear ordinary differential equations. Analysis is supplied for a controlled introduction of chemotherapeutic drug and virus. The control function is the chemotherapeutic drug intervention. We aim to minimize both the drug dosage and the number of untreated tumor cells. We provide first-order necessary conditions for the optimal control and solve the optimal control problem numerically. Through our research, we discover that by optimizing the drug intervention and using a combination of the virotherapy and chemotherapy treatments, the tumor cells could be eliminated faster compared to stand-alone treatments and non-optimized drug intervention.
Funder Acknowledgement(s): National Science Foundation
Faculty Advisor: Younjin Lu, ylu@vsu.edu
Role: I assisted with applying Pontyragin's Optimal Control Theory to our research. I ran programmed simulations that resulted in graphs that gave a visual representation of our results.