Developing and studying the dynamical behavior of a nonlinear mathematical model for cancers with tumor by considering immune system role

Abstract

We are constrained by widespread cancerous diseases to improve treatment methods which save patients and provide better living conditions during and after the treatment period. Because of the complexity of the treatment process, mathematical models need to be used in order to have a better understanding of the process. However, deriving an adequate complex model that can capture the disease pattern which could be confirmed by simulations and experiments has its own barriers. In this paper, a new mathematical model is developed concerning immune system effect on cancer. The model is introduced using nonlinear ordinary differential equations. Also, the qualitative behavior of the proposed system is studied in order to examine the extent of the model with respect to the nature of tumor evolution. Thus, number and status of equilibria points in line with the existence of limit cycles are obtained for sub-systems and the whole system. Meanwhile, possible bifurcations are mentioned, and the consequent evolutions are described. It is shown that the model conforms well to natural possibilities, cancer growth or remission. Thus, the model would be fit for further studies for prediction and contemplating treatment method, especially for immune stimulating drugs and immunotherapy.