Term of Award

Spring 2017

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Hua Wang

Committee Member 1

Yan Wu

Committee Member 2

Guang Peng

Abstract

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on it. Observing the effects of the changes we see the interactions each gene has with other genes within the network. Using the observed interactions we construct a set of differential equations that represent the network dynamics. Using numerical methods and the rough system of equations, we find an approximated system of equations that accurately predicts the dynamics of the normal gene network.

Research Data and Supplementary Material

Yes