On the Numerical Solution of Mathematical Models of Cancer Growth and Optimal Cancer Therapy

In the recent years, much mathematical research has been observed in the description of tumors' growth, in the early detection of cancer and in the optimization of cancer treatment planning. In this paper, the Crank-Nicolson method is proposed for the solution of different mathematical models of carcinogenesis and cancer therapy and a Genetic-Algorithms-based method for the optimal cancer therapy is also presented. First we intend to provide the Crank-Nicolson for a tumor-immune system interaction, which describes the early dynamics of cancerous cells, competing with the immune system, potentially leading to either the elimination of tumoral cells or to the viability of a solid tumor. Secondly we provide the Crank-Nicolson method for the brain tumors and a Genetic-Algorithms-based method for the optimal cancer therapy for the brain tumors is also presented.