Improvement of Galton–Watson Branching Process (GWBP) for Mathematical Optimization of Cancer Treatment

Biologists have uncovered some of the most basic mechanisms by which normal cells develop into cancerous tumors. These biological theories can be transformed into adequate mathematical models. For this reason, we attempt to study the evolution of cancer cells using the GWBP. The purpose of this paper is to study how the genetic algorithm (GA) can be used to follow the evolution of cancer and find optimal chemotherapeutic treatments.The development of GWBP give us the evolution of number of cancer cells for any patient if the death rate will defined experimentally, according to this value we can simulate the suitable chemotherapy treatments which cause the death of cancer, then determine the minimum dosage treatment injected using the GA optimization method. Analysis of these results gives us the objective function, who gives us a minimum in terms of number of cancer cells, with maximum in terms of cumulative treatment dosage.