The doctoral thesis consists of Introduction, 4 sections and Conclusion. In the Introduction of the thesis the problem sphere and actuality of the topic is introduced. Based on this actuality a main goal and tasks of the thesis are defined. Also in the introduction research objects, methods and the achieved novelty of science is described. 1. Section is devoted for the development of a mathematical model for functioning systems. At the beginning of the section a survey and formal aspects of topological modelling are described. Then a topological model for multiple diseases has been created; 2. Section is based on the analysis and processing of the developed topological model. At first decomposition is performed to provide detailed views of the model. After the decomposition a cycle detection procedure is performed. Within the section three parameters of topological models’ elements are introduced. For the evaluation of an external influence (in diseases case: a therapy) five performance criteria are used. Further these criteria are used as an input information in decision making process; 3. Section is devoted to the method of an optimal solution’s selection. Within the section two subtasks are solved. In the first one a full search multi-objective optimization methods are used and in the second case multi-objective genetic algorithms are applied; 4. Section covers a description of a medical computer system which is created as an implementation of the proposed method. A literature review of available medicine systems for similar tasks is carried out. The structure of the system is based on the typical structure of an expert system. The performance and precision of the system is evaluated by several tests. Tests also include the analysis and comparison of the results provided by the system, a doctor and by the overall treatment guidelines. In the Conclusion a summary, results and the goals of the further research are provided. The outline of the thesis: 157 pages, 66 figures, 26 tables. Bibliography consists of 211 records and thesis has 9 appendices: 1. Functions of organism subsystems, 2. Side effects of therapies, 3. Topological model in Powersim software, 4. Tables of initial values of nodes; 5. Parameters of organism subsystem’s nodes; 6. Parameters of side effect nodes, 7. Link parameters, 8. Therapy cost comparison, 9. Test example of the computer system.