Dynamic analysis and numerical simulation in a cancer model in dealing with finite duration inputs

Dynamic analysis and numerical simulation in a cancer model in dealing with finite duration inputs

Permanent change in the dynamic characteristics of a system, by exerting an input in a finite duration, is a very interesting and challenging topic in control engineering. We show that if an input affect on the parameters of the system instead of its states and change them, it can alter the dynamics of the system even after its elimination. Then, the application of this subject is used in cancer modeling and dynamic analysis. In this paper, a novel mathematical model is developed for tumor–immune system with positive immune response, focusing on the role of external inputs in the progression of cancer which is not considered yet. We also conducted an investigation in to the effects of input on a dynamic system, and provide a comprehensive discussion of how cancer has variable behavior patterns throughout the lives of patients. The behavior of the cancer (with inputs) is studied using the trajectory patterns and stability analysis. We show that Hopf bifurcation may occur due to change in the normal rate of changing of ECs into the tumor site caused by external inputs. Therefore, the present analysis suggests that a proper treatment method should change the dynamics of the c