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A MATHEMATICAL MODEL OF IMMUNE RESPONSE TO TUMOR INVASION INCORPORATED WITH DANGER MODEL

XUEFANG LI

Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore

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and

JIAN-XIN XU

Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore

Corresponding author.

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https://doi.org/10.1142/S0218339015500266Cited by:8 (Source: Crossref)

Abstract

In this paper, a new mathematical model of the interactions between a growing tumor and an immune system is presented by incorporating the danger model. The populations involved are tumor cells, CD8⁺ T-cells, natural killer cells (NK-cells), dendritic cells (DCs) and cytokine interleukin-12 (IL-12). A key feature of this work is the inclusion of the danger model into the dynamics of the immune system, which is rarely considered by previous works. Regarding the constructed mathematical model, both the location of equilibria and their stability properties are discussed, which are useful not only to gain a broad understanding of the specific system dynamics, but also to help guide the development of therapies. Moreover, numerical simulations of the system with chemotherapy and immunotherapy by using specific parameters are presented to illustrate that proper therapy is able to eliminate the entire tumor. In addition, we illustrate cases for which neither chemotherapy nor immunotherapy alone are able to control tumor growth, but a combination treatment is sufficient to eliminate the tumor cells.

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