  Breast Cancer is a major public health problem and the most common diagnosed
malignancy in woman. There have been significant developments in clinical
approaches and theoretical experimental to understand the interactions of
cancer cells dynamics with the immune system, also developments on analytical
and computational models to help provide insights into clinical observations
for a better understanding of cancer cells, but more are needed, especially at
the genetic and molecular levels mathematically. Treatments such as
immunotherapy, chemotherapy, hormone therapy, radiotherapy, and gene therapy
are the main strategies in the fight against breast cancer. The present study
aims at investigating the effects of estrogen derived from recent models, but
this time combined with immunotherapy as a way to treat or inhibit the cancer
growth by a mathematical model of breast cancer in situ, governed by a
simplified model of nonlinear-coupled ordinary differential equations, that
combines important interactions between natural cells, tumor cells, immune
cells, ketogenic diet in the presence of an anticancer drug. Another
contribution was to introduce the inhibition effect epsilon for new results and
conclusions, A qualitative study was performed and biological interpretations
were included to understand the conditions of stability in a realistic way.
