**SYSTEMS ANALYSIS** — set of the methods and means used in the analysis, development and designing of any complex systems (technical, ecological, organizational, etc.). At the heart of S.a. systems approach as the all-methodological principle to studying of complex systems which is at the same time further development of the theory of operational research and the theory of management lies.

Especially intensively S. and. develops in relation to studying of large-scale problems of technology, economy, ecology (see), health care (see), etc. In the USSR these works are coordinated by committee on systems analysis at Presidium of Academy of Sciences of the USSR, councils for systems analysis for the separate directions, in particular council for systems analysis in biology and medicine are a part to-rogo.

In the field of S.'s health care and. is a basis for comparative study of development of health systems of large regions, for the forecast of the main indicators of public health (see. State of health of the population ), for comparison and the choice of alternative programs of development of a health system on long time slices.

From positions C. and. the functional block diagram of a health system is developed, edges reflects its main internal interrelations, and also bonds with external systems. This scheme forms base for development of the mathematical description of system of the Soviet health care in general and its separate subsystems. In relation to health care within S. and. methods of aggregation of large volumes of statistical information on indicators of health of the population and about development of a health system, methods of imitating modeling in health care, model and algorithms of distribution of limited resources taking into account specific features of health care are considered (see. Modelling , Planning of health care ).

Practical application of S. and. in the field of health care it is complicated by difficulty of obtaining rather complete information about indicators of health of the population, high complexity of the health system as object of management, difficulties of determination of criteria of quality of functioning of this system, etc. Therefore the formalized description of large-scale health systems is developed to a lesser extent, than, e.g., the formalized description of economy.

At S.'s use and. in the field of health care the great value is gained by the so-called dialogue procedures including the decision-maker (i.e. the person making the decision) and the simulation model of a health system realized on the COMPUTER.

The simulation model functionally corresponds to the block diagram of a health system and contains its mathematical description sufficient for problem solving, facing the decision-maker. Participation of the decision-maker in dialogue with model allows to bypass, to a certain extent, difficulties of formalization of criteria, and sometimes and the difficulties connected with a lack of basic statistical data.

The mathematical description put in model shall provide use of all information in the maximum degree, the cut has the decision-maker, and decision-making formally comes down to search of the program (or programs) managements, at a cut a set of quantitative indices interesting the decision-maker φ_{ i } (where i = 1..., N) on the set interval (or in the set timepoint) it is belonging a nek-swarm of area (Φ) of values, acceptable for the decision-maker.

This result shall be achieved within the located decision-makers of resources *And* and taking into account influence of development of external systems V, and also taking into account action of possible unexpected factors.

During the work of the decision-maker with a simulation model as a preliminary stage verification of model, i.e. development of trust of the decision-maker to the results received during work with model is. During practical work with model the following types of results are possible. 1. Do not exist And, at to-rykh a desirable set of results is achieved. In this case decision-makers are provided the next ways of the further solution of the standing task: change of borders of area F, change of set of indicators f/, justification of the new request for resources, development to external systems of special requirements, performance to-rykh will entail such change of V, at Krom the task will be solved. 2. There is several various And, at to-rykh desirable values are reached for all g. In this case the decision-maker receives nek-ry freedom of choice And yes the final choice is caused by additional reasons, napr, stability of the decision in relation to possible unaccounted indignations, a possibility of expansion of set f *, changes of borders F, etc. 3. There is an only thing And, at Krom the desirable result is achieved at all g. In this case the freedom of choice is Also absent and the decision-maker can test a certain uncertainty in implementation of the planned program because of influence of unaccounted factors. With such uncertainty the procedure of development should be carried out according to the first scheme.

Final result of work with a simulation model is development of the program of distribution of material and human resources for subsystems of health care for the set time (the horizon of forecasting), requirements of information and algorithmic support of control of implementation of programs, the recommendation to external systems.

One of options of a simulation model of a health system is the so-called kompartmentalny model, according to a cut the population of the region breaks on a nek-swarm number of the subgroups reflecting ideas of the decision-maker of quantitative and qualitative distinctions between separate categories of the population. «Entrances» to model are data on flows of newborns and migrants; the dead for one reason or another (including on age) form the relevant absorbing subgroups. The main variables in such model are the number of individuals in subgroups (lump-partmentakh) and intensity of intergroup transitions.

During the work with model set borders of subgroups, initial densities of population and initial intensity of transitions. Due to the incompleteness of initial information there is an important problem of assessment of the specified numerical characteristics on nepolnsh to data (e.g., assessment of intensity of incidence on observed dynamics of mortality and data of selective inspections). The main managed variables in model are intensity of inter-group transitions, i.e. rates of change of density of population of subgroups. Intensity of such intergroup transitions may contain both the continuous, and spasmodic components (reflecting * e.g. implementation in medical practice new to lay down. means).

Imitating modeling of activity of a health system demands use of the corresponding mathematical apparatus, in particular probability theory (see. Probabilities theory ), allowing in the principle to solve the listed above problems.

The main difficulty of practical implementation of this method consists in shortage of initial information. When this shortage is «moderate», by means of kompartmentalny models of subsystems of health care this difficulty manages to be bypassed. So, in the USSR simulation models of nek-ry epidemic diseases are almost realized, in the USA similar models are constructed for the nek-ry types diseases characteristic of the senior age groups of the population.

See also Mathematical methods , System , Control system .

**Bibliography:** Afanasyev V. G. Scientific management of society, M., 1973; Venediktov D. D. International problems of health care, M., 1977; Moiseyev H. H. Mathematical problems of systems analysis, M., 1981, bibliogr.

*A. M. Petrovsky*