Cancerous Tumour Model Analysis and Constructing schemes of Anti-angiogenesis Therapy at an Early Stage

Anti-angiogenesis therapy is an alternative and successfully employed method for treatment of cancerous tumour. However, this therapy isn't widely used in medicine because of expensive drugs. It leads naturally to elaboration of such treatment regimens which use minimum amount of drugs.The aim of the paper is to investigate the model of development of illness and elaborate appropriate treatment regimens in the case of early diagnosis of the disease. The given model reflects the therapy at an intermediate stage of the disease treatment. Further treatment is aimed to destroy cancer cells and may be continued by other means, which are not reflected in the model.Analysis of the main properties of the model was carried out with consideration of two types of auxiliary systems. In the first case, the system is considered without control, as a model of tumour development in the absence of medical treatment. The study of the equilibrium point and determination of its type allowed us to describe disease dynamics and to determine tumour size resulting in death. In the second case a model with a constant control was investigated. The study of its equilibrium point showed that continuous control is not sufficient to support satisfactory patient's condition, and it is necessary to elaborate more complex treatment regimens. For this purpose, we used the method of terminal problems consisting in the search for such program control which forces system to a given final state. Selecting the initial and final states is due to medical grounds.As a result, we found two treatment regimens | one-stage treatment regimen and multi-stage one. The properties of each treatment regimen are analyzed and compared. The total amount of used drugs was a criterion for comparing these two treatment regimens. The theoretical conclusions obtained in this work are supported by computer modeling in MATLAB environment.DOI: 10.7463/mathm.0315.079087