A mathematical model of tumor-immune interactions incorporated with danger model

This paper presents a new mathematical model of the interactions between a tumor and a immune system by incorporating the danger model. A key feature of the mathematical model is the introducing of the danger signal into the dynamics of immune system, which is rarely considered by previous works. The populations involved are tumor cells, CD8⁺-cells, natural killer-cells (NK-cells), dendritic cells (DCs) and cytokine interleukin-12 (IL-12). Based on the constructed mathematical model, we discuss the location and stability properties of equilibria, which will be helpful to get a broad understanding of the specific system dynamics and guide the development of therapies. In the end, numerical simulations of the system with chemotherapy by using specific parameters are presented to illustrate that proper therapy is able to eliminate the entire tumor.