The Study Of Some Tumor Treatment Models

The paper is mainly about the research of a mathematical model that describes the pe-riodically pulsed cycle-specific chemotherapy and drug resistance. With the use of impulsivediferential equation and optimal control therapy discussions of the dynamic behaviors of themodel, we have achieved some progress which make sense to the treatment of the cancer.Thisarticle includes three chapters.Chapter 1 is the prolegomena,which introduces the background of the research and themain works of the paper.In Chapter 2 we analyze a mathematical model of periodically pulsed cycle-specific chemother-apy and finally give the conditions of stop tumor metastasis and recurrence.In Chapter 3,we discuss the model of tumor drug resistance,in the first section ,we analyzetumor drug resistance in the process of the chemotherapy. First ,researching the drug-inducedresistance by establishing the mathematical model of homogeneous tumor. Then we get theNADIR and revise the model of general heterogeneous tumor. Considering of the transitionsbetween sensitive tumor cells and resistant tumor cells, we get the sufcient condition of tumorattenuation.Secondly,we get the best strategy of the treatment by researching non-induced re-sistance using the optimal control theory. In the second section,a mathematical model is used todiscuss the efects of multi-modality therapy .The main aspect of the model is that it takes intoaccount non-induced resistance(cell mutations) and drug-induced resistance. The mathematicalmodel is a system of impulsive diferential equations that describes tumor-normal cell interactionwith the added efects of multi-modality therapy.In this paper,we get the sufcient conditionsneeded to prevent tumor recurrence and metastasis.The mathematical results provide a reliabletheoretical strategy for the treatment of tumor.