نيما حاضري

Cancer is a dangerous disease that causes human deaths every year. Scientists are just looking for new ways to diagnose, treat and deal with this disease, which can be of great help to the research beyond the dynamics of cancerous tumors in the body. Given the priority of preserving life, studying the characteristics of tumor growth in the body is very difficult and sometimes impossible, in such cases the mathematical model and in silico studies can be very helpful. Investigating the role of growth speed profile on controlling self-remission cancer and analysing stability of equilibrium points is the main purpose of this study. Concerning this research, the Richards growth function is used to adjust the speed profile. To reduce the parameters numbers of the model, the system’s equations are expressed non-dimensionally. The physiological equilibrium points of the system have been studied regarding different values of the system parameters. Furthermore, the stability of equilibrium points is eva‎luated locally via linearization of the system around its equilibrium points. Permanently having a stable equilibrium point is indicated by previous researches. To stabilize other unstable equilibrium points a nonlinear optimal controller is utilized which results in asymptotical stability. Moreover, the proposed controller is robust against disturbances comprised of sudden changes of density. Eventually, the outcomes of this research prove this claim. Delay in activating hunter predator cells by resting predator cells is an inherent characteristic of the tumor; hence the stability of the system is assessed anew according to this issue. The maximum allowable activating time of hunter predator cells to avoid instability is calculated by using analyzing the stability of the delayed system. If the amount of delay is slightly more than the obtained critical time, the system will tackle the limit-cycle and even if the amount is more severe than the mentioned delay, the system will be conducted to chaotic behavior.

سرطان , مدلسازي سرطان , تابع ريچاردز , بهبود خود به خودي

Cancer , Cancer Modelling , Richards Function , Self-remission

Nima Hazeri

Dr S.Hojat. Sabzposahan