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The article discusses the use of mathematical modeling and system analysis methods to solve problems of water preparation. Models for predicting indicators of drinking water based on the quality of the source water are proposed. The technological process of deodorization of drinking water is considered. The following system analysis methods were used in the models development: correlation analysis of data, the principal component method, regression modeling, and the least squares method. Hidden relationships between indicators of drinking and source water were identified. The adequacy of the obtained results was proved by comparing them with the actual values. The obtained results approximate well the actual values. The results can be used in water supply systems to improve the quality of drinking water.

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.