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Review of Mathematical Modelling Techniques in Breast Cancer Dynamics.

Mashasha Maxwell, Chigidi Esther

Cancer is an age related autoimmune disease initiated by genetic mutations leading to increased proliferation rate and tumor formation. Accumulation of various genetic and epigenetic changes, in normal cells gives cancer cells a selective advantage over healthy cells, and lead to cancer initiation and progression. Interactions of tumor cells with other cells within their reach, the microenvironment, is an important component in carcinogenesis. Its treatment is based on our level of understanding of its biology. Breast cancer is a collection of complex and heterogeneous diseases with distinct histopathological features. It arises due to abnormal growths of the cells lining the breast lobules hence men and women can develop it, although very rare in men (less than ). There are different types of breast cancer, and the most common are the invasive and non-invasive cancers. Usually, it is common to study breast cancer tumors as isolated entities, but its biological and molecular structure are indicative of an unstable heterogeneous disease with multiple subtypes coexisting within a tumor. Many studies with different methodologies have been carried out to understand cancer development and progression, however, another approach of mathematical oncology has emerged. This approach uses mathematical and computational techniques to unpack generation, growth and evolution of cancer cells. With this work we would like to review what has been done by others so as to improve our understanding of cancer dynamics.