摘要
In this paper,a mathematical ordinary differential tumor-immune model is proposed based on an immune checkpoint inhibitor,which is an innovative method for tumor immunotherapies.Two important factors in tumor-immune response are the programmed cell death protein 1(PD-1)and its ligand PD-L1.The model consists of three populations:tumor cells,activated T cells and anti-PD-1.By analyzing the dynamics of the model,it is found that there is always a unique tumor-free equilibrium and at most two tumor interior equilibria.The nonexistence of nontrivial positive periodic orbits is established by using the new Dulac function,and then a global dynamics of the model is obtained.The conclusions of our analysis show that increasing the possibility of T cells killing tumor cells(p),early detection of tumor cells,or the use of PD-1 inhibitors to activate T cells are effective in eliminating tumor cells.
