Dynamical Analysis of Tumor Growth Model with Immunotherapy

Abstract

In this paper, the analysis of tumor growth model with immunotherapy involving dendritic cells is discussed. The model consists of four compartments namely the tumor cells, the active CTLs, the T-helper cells, and the dendritic cells. The growth rate of the tumor cells in this model follows the logistic model. The dendritic cell therapy functions as an inhibitor of tumor growth without causing side effects on the other cells so that the spread of tumor cells can be minimized. Next, dynamical analysis is performed by determining the stability analysis of the equilibrium point. It shows that the model has six equilibria consisting of three tumor-free equilibria namely $E_0, E_1, E_2$ and three tumor equilibria namely $E_3,E_4,E_5$. The equilibria points $E_0$ and $E_3$ are not stable since there are positive eigenvalues while other equilibria will be stable if those meet certain conditions. Furthermore, the simulation results support the analysis result.