Analysis of tumor populations and immune system interaction model

Abstract

Abstract.Immune system plays a vital role in controlling the tumor growth. Therefore, this paper proposes a new mathematical model that describes tumor-immune interaction, focusing on the role of natural killer (NK) cell and CD8 + T cell. The tumor population is subdivided into two different phases, namely interphase and mitosis. This model used Ordinary Differential Equations (ODEs) and the functions involved in the model represents tumor-immune growth, responses and interaction between the cells. The stability and analysis of the model are carried out. From the analysis, the stability curve limits tumor growth region is shown. The curve from the model lie below the curve of the model with single immune response (CD8 + T cell). This result concluded that the proposed model with involvement of NK cell suppression will lower the tumor growth region.

Tumour-Natural Killer and CD8+ T Cells Interaction Model with Delay

“…Then the system (1) is said to be stable if and only if the roots of its characteristic equation have negative real parts. The characteristic equation of system (1) with τ = 0 is Equation (17). All the roots of ( 17) have negative real part if (17) satisfies conditions a, b, c and d.…”

“…The characteristic equation of system (1) with τ = 0 is Equation (17). All the roots of ( 17) have negative real part if (17) satisfies conditions a, b, c and d.…”

“…Then, it will automatically raise alarms and attack when there are new substances that are not recognised. The combination of both innate and adaptive immune strategies in immunotherapy boosts anti-tumour activities and prevents tumour re-formation [11][12][13][14][15][16][17][18][19].…”

Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

“…The tool of mathematical modeling is widely used by researchers in the field of cancer modeling too. Several significant works [ 5 – 9 ] through mathematical modeling have been done to understand the response of the immune system with tumor. In [ 5 ], the authors analyzed a cancer model by considering the interactions between cancer cells, tumor angiogenesis and endothelial cells.…”

“…Arlotti et al [ 8 ] proposed a bilinear model of integro-differential equations to describe the dynamics of cellular interaction between tumor and immune cells. By introducing two phases, namely, the Inter-phase and M-phase at which cells are generally divided, Awang et al [ 9 ] newly described the interactions between tumor cells and immune system. Zeng and Ma [ 10 ] analyzed a deterministic tumor-immune model under the Allee effect.…”