Mathematical model for the estrogen paradox in breast cancer treatment

Background: Breast cancer is one of the major causes of mortality in women world- wide. Estrogens are known to stimulate the growth of breast cancer but are also effective in treating the disease. This is referred to as the “estrogen paradox”. Several studies have been dedicated to describe the possible mechanisms behind this paradox. Other studies highlighted the correlations between the tumor suppressor protein p53 and the estrogen receptor alpha (ERα). Aim: We investigate possible trade-offs between the tumor suppressor protein p53 and the estrogen receptor alpha (ERα) that can lead to breast cancer elimination. Methods: We propose a novel ODE-based mathematical model describing the interac- tions between both dormant and active cancer cells, estrogen hormone, a tumor suppressor protein (p53), and a treatment combination with high-dose of estrogens (HDEs) and p53. We calculate the model’s equilibrium points and determine their global stability behavior by means of a comparison theorem. Findings: We find a range for the ratio of estrogen to p53 outside with active cancer cells can be eliminated without any treatment. Inside this range, we show that active cancer cells will grow to their maximum size, and that treatment with high-dose of estrogens can achieve cancer elimination. We carry out numerical simulation to confirm our mathemat- ical finding and investigate the scenario of low, moderate, and high ratio of estrogen to p53.