### Mathematical Biosciences and Engineering

2021, Issue 1: 373-385. doi: 10.3934/mbe.2021020
Research article Special Issues

# A mathematical model of cell-mediated immune response to tumor

• Received: 10 September 2020 Accepted: 08 November 2020 Published: 04 December 2020
• Mathematical models of tumor-immune interactions provide an analytic framework for studying tumor-immune dynamics. In this paper, we present a mathematical model to describe tumor-immune cell interactions, focusing on the role of the natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs) in immune surveillance. According to the experimental and clinical results, we determine part of the model parameters to reduce the model parameter space. Then we analyze the local geometric properties of the equilibria of model and carry out numerical simulations to verify the conditions for the stability properties of equilibrium points. Numerical results suggest that the host immune system alone is not fully effective against progression of tumor cells, and CTLs play a crucial role in immune surveillance.

Citation: Ge Song, Tianhai Tian, Xinan Zhang. A mathematical model of cell-mediated immune response to tumor[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 373-385. doi: 10.3934/mbe.2021020

### Related Papers:

• Mathematical models of tumor-immune interactions provide an analytic framework for studying tumor-immune dynamics. In this paper, we present a mathematical model to describe tumor-immune cell interactions, focusing on the role of the natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs) in immune surveillance. According to the experimental and clinical results, we determine part of the model parameters to reduce the model parameter space. Then we analyze the local geometric properties of the equilibria of model and carry out numerical simulations to verify the conditions for the stability properties of equilibrium points. Numerical results suggest that the host immune system alone is not fully effective against progression of tumor cells, and CTLs play a crucial role in immune surveillance.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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