Dynamical analysis of a tumor growth model involving interferon gamma

I.J.T.R. Tamsih; Trisilowati; U. Habibah

doi:10.1063/1.5094274

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Dynamical analysis of a tumor growth model involving interferon gamma

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I.J.T.R. Tamsih, Trisilowati, U. Habibah

2019 AIP Conference Proceedings Vol. 2084 Conference paper Cited by 0 SDG 3

Abstract

Tumor is a group of cells that grow uncontrollably and possibly become malignant, meanwhile our immune system turns out to have inhibitory factors in preventing the tumor development. This paper aims to construct and analyze a mathematical model of tumor and its interaction with some important immune cells namely macrophages, activated CD8+T, and the immuno- stimulatory cytokine interferon gamma (IFN-γ) by using a system of four coupled ordinary differential equations. It describes the effect of IFN-γ which activates macrophages in tumor decay process. Furthermore, dynamical analysis is conducted to investigate the existence and the stability of equilibrium points. Regarding to the result, the tumor-free equilibrium point always exists and the endemic equilibrium point exists if it satisfies cardans condition. The equilibrium points are stable under some circumstances. By using some estimated parameters from the literature, it is shown that tumor cells will decrease as the activation of macrophages get higher. It also takes longer time for tumor to reach the equlibrium point. © 2019 Author(s).

Affiliations

Mathematics Department, Faculty of Natural Science, University of Brawijaya, Indonesia

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