Numerical Solution of Tumor-Immune Model with Targeted Chemotherapy by Multi Step Differential Transformation Method

Abstract

In this paper, a tumor-immune model having four compartments; population of tumor cells, CD8 T killer cells, CD4 T-helper cells and amount of targeted chemotherapeutic drug are considered. We have depicted a qualitative analysis for the proposed model, which includes the existence and the boundedness. The dynamics of the proposed model is presented by examining the stability and admissibility of the model at tumor-free and co-existing equilibrium points. The situation for local stability of all equilibrium points are derived by using Jacobian matrix and Routh-Hurwitz criterion. Numerical calculations are presented to verify the theoretical results so obtained for tumor free equilibrium points. The calculations are carried out with a new method known as multi step differential transformation method (MsDTM). We have expressed that the model is fit for removing large initial population or size of tumor, with passage of time.