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The Effects of Estrogen and Chemotherapy on the Dynamics of Invasive Carcinoma of Breast Cancer Patients

In this paper two mathematical models are used to examine two different drug treatment regiments on estrogen receptor-positive breast cancer in women. The first regiment is a combination therapy of estrogen stimulation followed by chemotherapy and the second regiment is a single treatment of chemotherapy alone. The method under consideration is to first use estrogen therapy on a diagnosed advance staged breast cancer patient to move the tumor cells into the proliferating stage, at which time chemotherapy can be applied to kill the proliferating cancer cells. Utilizing both analytical and numerical approaches, a study of the efficacy of combination treatment and the single treatment is completed. Two partially decoupled models are created to study both a healthy cell population and a cancerous cell population in the breast. At first the cancerous cell population (tumor growth) is analyzed separately from the healthy cell population, and then later composed with the healthy cell model to examine the dynamics of cancer and treatment on the body. Both of the populations are divided into quiescent and proliferating stages in order to account for the cell cycle specific treatment that are later applied. The resulting models are given by four dimensional nonlinear systems.

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Cindy Coralie Jackson, California State Polytechnic University-Pomona
Lindsey K. Lauderdale, University of Illinois at Urbana-Champaign
Nicholas Earl Millett, The University of Maine
Samantha Anne Smee, Oregon State University
Adrian Smith, University of Washington
Graduate Mentors:
Kevin Flores, Arizona State University
Faculty Advisors:
Faina Berezovskaya, Howard University
Stephen Wirkus, Arizona State University-West