Mathematical Model Of Immune Escape Of Cancer Cells Based On Two Phenotypes

Cancer cells that differentiate into two different phenotypes:"cooperative"phenotype cancer cells and "selfish" phenotype cancer cells through different defense mechanisms against the immune system in this thesis."Cooperative" phenotypic cancer cells deploy countermeasures that increase the chance of survival of every cancer cell,while "selfish" phenotypic cancer cells develop defense mechanisms that benefit the individual cell.The main characteristic of the "cooperative" phenotype of cancer cells to avoid immune damage is immunosuppression,whereas "selfish"phenotype of cancer cells to avoid immune destruction is their concealment against immune cells.We mainly consider two phenotypic cancer cell models under immune evasion in this thesis.In Chapter 1,we introduce the biological background of two phenotypic cancer cells' immune evasion briefly,the model of interaction between tumor and system without immune editing mechanism and the model of interaction between tumor and system with immune editing mechanism,as well as the basic concepts and theories of ordinary differential equations.In Chapter 2,a mathematical model of immune escape based on two phenotypes of cancer cells is presented and studied.The cells in the tumor immune system were divided into three types:"cooperative" phenotypic cancer cells(xc),"selfish"phenotypic cancer cells(xs)and lethal T cells(y),and three dimensional dynamic ordinary differential equations were constructed.According to the experimental and clinical results,some parameters of the model were determined,the parameter space of the model was reduced,the dynamic analysis of the model was analyzed.Finally,the stability condition of the non-negative equilibria of the model were verified by numerical simulation.In Chapter 3,we study the changes of more parameters in the model,by chang-ing the size of the parameter values ?c,?c,a,rs,it is found that there is a certain effect on the tumor growth trajectory and tumor steady-state size.It has been concluded that improving the efficiency of the immune system,reducing immuno-suppression,increasing the strength of immune function,and resisting tumor con-cealment have a good effect on the treatment of cancer.In the last chapter,the principal research results of this thesis are summarized,and we also introduce the deficiencies discussed in this thesis and future research directions.