Analysis of tumor populations and immune system interaction model

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.