Authors : Janar J. Yermekbayeva and Tolkynay Myrzakul
Abstract: In this study, we investigate a new mathematical models and approach of the control of tumors in organism. We consider the Immunological Model for the population dynamics of cells with control-factors representing the influence on the disease. We analysed the impact of the “D-factor” on the steady states and their stability and determine a control value. In these models, we studied the “D-factor” in “Umbilical” from catastrophe theory to impose control on tumor growth. By adjusting parameters, the models shows stationary states at which the immune system is stabilized and the number of tumor cells is either driven to zero or remains constant. Numerical simulations are carried out to confirm the theoretical findings to investigate the impact of the control parameters on the dynamic of the disease. The offered results can be used at theoretical studies for stabilization immune system at predicted level. These results are particularly relevant as new method in mathematical modeling and their applied views and for the prevention and early diagnostics of cancer and health improvement.
Janar J. Yermekbayeva and Tolkynay Myrzakul, 2015. The New Approach of Complex Control Law on Immunological System. The Social Sciences, 10: 1177-1182.