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The article describes the quality assessment system for infection control in penitentiary institutions that was developed using a mathematical model based on analytic hierarchy process (AHP). The following parameters were chosen as indicators of infection control quality level: HIV, tuberculosis, incidence of other infectious diseases, compliance with sanitary regulations and the water quality. The reliability and adequacy of the research has been proved. Quality assessment of infection control is an important criterion for the successful development of effective measures aimed at the improvement of the epidemiological situation in penitentiary institutions.

The study presents the stages of developing a HIV prognosis model in inmates. Correlation data analysis and regression modeling were used to develop the model. It was estimated that the developed model gives the best results for patients under the age of 40 years. On the obtained results there were developed an information system and a computer program. The study results application will help to predict correctly the HIV severity and to take timely treatment measures.

The article considers the possibility of using a point scoring system of medical parameters for HIV severity monitoring and modeling in numerical terms. There were investigated the features of the use of medical parameters in the form of a point scoring system as well as the possibility of applying a numerical model for determining the HIV severity when tuberculosis is joined. To solve the problem, it was developed a step-by-step algorithm for applying the point scoring system. Conclusions were drawn. The possibility to predict in numerical terms the outcome of the disease (in particular the AIDS progression) using the number of systematically collected medical parameters in HIV carriers is of great interest. The information system development allows to determine the most important properties of the process and to separate its non-essential characteristics. Often the information system and modeling allow us to formulate new hypotheses and gain new knowledge about the object, those which were not available during the research.

The research describes the development of the forecasting information system that can predict the outcome of a disease in inmates with HIV-associated tuberculosis. The aim of the research is to develop an additional high-precision diagnostic criterion giving the possibility of the timely correction of diagnostic, treatment and organizational measures for patients with HIV and tuberculosis co-infection that helps to improve the quality of medical care. The research material is based on the data from clinical cases of patients with HIV and tuberculosis co-infection who were hospitalized in a tuberculosis hospital providing specialized medical care to inmates from 2012 to 2018. (367 people). The study methodology was developed in several stages with the use of the methods of system analysis and mathematical modeling (logical-statistical method of optimally reliable partitions, the method of analysis of hierarchies, artificial neural network, methods of statistical grouping). The result of a complex multi-stage research makes possible the development of the prognostic index forecasting outcome of HIV-associated tuberculosis in prisoners. For the automated calculation of the developed index a software package was created. Interpretation of the received data allows timely correcting of diagnostic and treatment tactics in order to improve the quality of medical care and reduce the hospital mortality rate. The developed information system does not require complex and expensive diagnostic measures, it is easy to use and can be suggested to use as a screening method.

The article considers the possibilities of using cluster analysis and modeling of cancer monitoring in inmates. The article presents the analysis based on the hierarchical clustering, the k-means method along with F-test criterion for the main indicators monitored in the penitentiary system. The application of modeling was analyzed using the example of regression analysis of the data. The development of the model was relative to the indicator of the proportion of mortality rate to the total number of malignant neoplasms. According to the statistic data of 2018, the main statistical indicators on oncopathology in inmates reflect a similar situation in the whole country. The researchers consider the possibility to apply the results obtained not only within the penitentiary system, but also to monitor the situation with cancer in the country in general.