Analysis of Tumor-Immune Response Model by Differential Transformation Method

Abstract

In this research work, a four-dimensional tumor-immune response model is considered. The considered tumor model is a system of four differential equations consisting of four different cell populations (variables): the tumor cells (TCs), effector cells (ECs), helper tumor cells (HTCs), and Tregs. The interaction among these cell populations is represented by the system of ordinary differential equations (ODEs). The solution of the system is obtained by using the differential transformation method (DTM). DTM is a straightforward method and gives the series solution of the system. Numerical simulation and graphical analysis are also done by choosing four different initial conditions of the system. The solution series of a system for four different cases are obtained and finally compared with each other. The analysis shows that the model behavior is Chaotically dependent on initial conditions.