Simulation of Tumor Growth Model and Its Interaction with Natural-Killer Cells and T Cells

Cholifatul Maulidiah, Trisilowati Trisilowati, Ummu Habibah


This research studies about tumor growth model by involving immune system. Cells in the immune system, for instance natural killer (NK) cells and T cells, have prominent role in recognizing and eliminating tumor cells. In this paper, we construct the tumor growth model consisting of four populations namely tumor cells, NK cells, CD8+T cells, and CD4+T cells which is in the form of a non-linear differential equation. The analysis result shows that there are three tumor free equilibrium points and one coexisting equilibrium point. Some tumor free equilibrium and tumor equilibrium point exist and it is stable under certain conditions. Finally, numerical simulation is carried out to illustrate analysis result. From sensitivity analysis, it is found that the most  sensitive parameter that influence the growth rate of tumor cells are the reciprocal carrying capacity of tumor cells and the killing rate of CD8+T cells by tumor cells.


immune system;tumor cells;simulation

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