Analysis of Mathematical Model on the Development of Tumor Cells after Drug Therapy

Mathematical modeling way to explain the reality to the mathematic equations. One of the phenomena that can be modeling is the development of tumor cells after drug therapy. Tumor cells defend mutations with a process of cell reproduction and cells will be a move to all of the body. Cells occupy one of the other organs. Splitting about this case used drug therapy or chemotherapy. This research has the purpose of identifying and analysis mathematical models on the development of tumor cells after drug therapy. Identification of mathematical modeling includes the fixed point, the stability around the fixed point, and computer simulations. System of equations in this research using system differential equations non-linear of the first order and it is using four variables. They are immune cells I(t), tumor cells T(t), normal cells N(t), and drug therapy u(t). This system of equations obtained two fixed points is a fixed point of disease-free tumor and influence tumor. Stability around the fixed point will be stable when the fixed points of tumor cells T(t) = 0 and T(t) not equal to 0, with the fixed point tumor cells T(t) = 0,6900203854 cells/㎣, immune cells I(t) = 0,3671110057 cells/㎣, normal cells N(t) = 0,1835555029 cells/㎣, and drug therapy u(t) = 1 pg/ml. From the numerical simulation results can be the comparison between the graph model populations of tumor cells before and after administration drug therapy. Before the population of tumor cell given drug therapy will be increased and decline after being given drug therapy, whereas immune cells and a normal cell is increasing. This suggests drug therapy can impede the growth of tumor cells and increase the population of immune cells and normal cells.