N. I. Ivanasheva, G. S. Lebedev

In present days conditions of increasing health programs funding, the development of methodological approaches to health programs management, monitoring and evaluation (M&E), development of program management, information system with M&E function (PMIS) using constructed mathematical models are of actual values. The introduction of PMIS using formal mathematical models and methodical approaches can help program managers to determine, which areas of the program require more efforts and quickly and timely adjustments to the program for more successful implementation. The construction of a formal semantic ER-model of the application domain related with programs indicators and measures is described. The basic attributes of indicator description are shown, the relations of indicators with other entities (categories, periods, activities and territories) are considered. The detail description of each indicator in accordance with generally accepted international standards, together with methods of data collection promote a common approach to working with indicators for all program participants. Methodological approaches include formal definitions and descriptions of the calculation of main type of indicators (absolute/relative/logical). The calculation of different types of indicators for a given period and cumulatively at various levels in the hierarchy of territories is formalized. To describe the structure of data needed to develop the PMIS and the relational database, the domains and relations were identified, in accordance with described entities and relationships of the application domain. Examples of PMIS database typical queries using Codd's relational algebra are also presented. Also identified were the formal mathematical criteria and methods of their calculation of program evaluation in terms of achieving indicators target values: standard deviation and percentage deviation of the indicator fact value from its planned value, average deviation of the fact values of the indicator for the assessment period, the indicator of reaching the planned value of the indicator. An approach to assessing the achievement of the target values of the indicator by calculating the Euclidean distance, Manhattan distance and Chebyshev distance is presented. The evaluation criteria of advance planning the programs events and timely reporting on the program's activities in the PMIS are shown. Constructed semantic and relational models and described methodological approaches were used as the basis of PMIS, which was introduced to the number of health Russian projects and programs. The developed mathematical models, methodological approaches and PMIS can be implemented in various application domain and fields of activity.