Dynamic Analysis On Differential Equation Models Of A Tumor Growth With Immune Therapy

Immune therapy is the fourth category of tumor chemotherapy treatment. Anumber of experiments suggest that immunotherapy with the interleukin-2mayimprove the immune system to eliminate tumors. In order to compare the differencebetween constant infusion immune cells and pulse shots, so two types of tumorgrowth differential equation models with immune therapy are established.This paper is composed of four chapters.In the first chapter, the background of dynamics model on tumor growth isbriefly reviewed. Furthermore, we simply introduced the main work in this paper.In the second chapter, we illustrate the role of IL-2and ACI immune therapythrough mathematical modeling the dynamics between tumor cells, immune effectcells and IL-2. The sufficient condition of local stability of the equilibrium under theno treatment case is obtained, and the local stability of the tumor-free equilibrium isanalyzed. Finally, the numerical simulation verified the theoretical results.In the third chapter, a periodic pulse differential equation model of tumor growthis established by considering the periodic and transient behavior of injection immunecells. Using the comparison theorem and Floquet multiplier theory of the impulsivedifferential equation, we proved the boundedness of the model solution, the existenceof the free-tumor periodic solution and the condition of extinction and persistent ofthe free-tumor periodic solutions are given. Computer simulations are carried toconfirm the main theorems.