Optimal Study For Some Disease Models

In this paper two mathematical models are researched.(1) The optimal controls of tumoranti-angiogenesis;(2)the optimal controls of tuberculosis with cellular immunology. We discussthe dynamic behaviours of the models and have achieved some progress which make sense tothe treatment of the cancer and tuberculosis in real world. Concretely, the article include threechapters.In chapter1, the preface is presented, which includes the background of the research,summary of our main works and several important lemmas.In chapter2, we analyze a mathematical model of tumor anti-angiogenesis. By use ofthe Pontryagins Maximum Principle, we obtain the optimal value, along which the tumor willshrink.In chapter3, we discuss a tuberculosis mathematical model with cellular immunology. Inthe first section, we consider the efect of a constant input of drug on the model. By constructingLyapunov Function, we get the condition for the global stability of disease-free equilibrium andendemic disease equilibrium. In the second section, we consider the efect of nonconstant inputof drug on the model. We consider both quadratic and linear control cases, separately. Thereby,we provid a theoretical strategy for the treatment of tuberculosis.