A Mathematical Model of Tumor-Immune System with Fuzzy Parameters

According to cancer’s global statistics, there will be 27.5 million new cases of cancer each year by 2040, therefore, it is crucial to achieve a deeper understanding of the cancer progression mechanisems and immune system functions in response to it. Nowadays, Computational models are widely used to capture dynamics of the tumor-immune system (TIS). The proposed model on this manuscript is on the basis of the ordinary differential equations which mechanistically models the interactions of tumor cells, CTLs, NKs and MDSCs. CTLs and NK cells are the most important cells of adaptive and innate immune system, respectively that encounter with tumor cells, while MDSCs as immature immune cells suppress the immune responses in the inflammatory environments. Due to the error of the in vivo/in vitro experiments, vagueness, imprecise information, incomplete data and natural variability of the tumor-immune system emerges between different individuals, the kinetic parameters of computational models are uncertain that this uncertainty can be captured by fuzzy sets. Hence, we assign fuzzy numbers with triangular membership functions instead of crisp numbers to some kinetic parameters of the tumor–immune system model. In fact, the uncertainty in the kinetic parameters of the ordinary differential equations affects the dynamic of the system species. In this essay, for the first time, a fuzzy number has been used to model the uncertainty of the parameters of the ODE model. Our data reveals that increasing/decreasing the uncertainty region of the model's fuzzy parameters increases/decreases the uncertainty region of dynamics of species. Furtheremore, the simulations of the model in the crisp setting of parameters show that the repition of 5-FU treatment for inhibition of MDSCs dramatically inhibits tumor cells and eradicate tumor.