A Mathematical Model of Stochastic Phase Transitions in Breast Cancer Development

Abstract

Breast cancer, especially the estrogen receptor-positive (ER-positive) type, is one of the most common cancer among
women. Currently, tamoxifen is a common drug for treating ER-positive breast cancer. However, there is some
evidence showing that when patients have taken the tamoxifen drug for a long period of time, the breast cancer cells
become resistant. In this work,a mathematical model of the stochastic phase transition in breast cancer development,
by considering the transition between sensitive and resistant phenotypic states, including the feature of environmental
sensing of cancer cells is proposed. The results show that the model is able to find an intermittent treatment that
critically slows down cancer growth. Therefore, the model can serve as a framework for designing treatment for breast
cancer patients.