Analysis And Simulation Of Bistable Problems In Two Types Of Tumor Models

The long-term existence of dormant tumor cells are malignant tumors difficult to completely cure and the reasons for tumor recurrence and distant metastasis.The immune escape phenomenon of tumors is the reason why tumors are difficult to treat.Dormant tumor cells and immune escape of tumors are two major problems in tumor treatment.Therefore,elucidating the relevant mechanism of tumors can help effectively treat tumors.The main contents of this paper are divided into two parts: The first part studied the dynamic system of tumor dormancy with Logistic increase,and the second part studies the dynamic system of tumor immune escape with immunotherapy.In the first part,the stability of the model was studied and the tumor rebound threshold and elite control threshold were obtained.Using the immune strength as the research parameter,it was found that the tumor would rebound when the immune strength was lower than tumor rebound threshold,happens when the immune strength within the scope of the two control threshold,system occur bistable,when the immune intensity is higher than the elite control threshold,the tumor is controlled and the body is relatively healthy.And proves that the saddle node bifurcation and the Hopf bifurcation.In the second part,Logistic growth was used to describe the proliferation of tumor cells and immune escape tumor cells,and join the treatment of immune.The equilibrium,threshold and stability of the model are also studied.The results show that the model had two control threshold,respectively tumor rebound threshold and early warning threshold.When the immune intensity is within the range of two control thresholds,the system shows bistable behavior,and tumor rebound occurs when the tumor is lower than the rebound threshold,the tumor is controlled and the body is relatively healthy when the tumor is larger than the early warning threshold.This part also proves the existence of saddle node bifurcation.