Mathematical Model of Development Level for Social Security System

Abstract

Social security system which is a necessary means to retain social stability and economic development is an important sign of modern nations and society with civilization. Firstly, this paper analyses the relations among the sub indexes of development level for social security systems. Secondly, it sets up differential equations model to quantitatively analyze the relations among the sub indexes based on the hypotheses. Finally, it studies the solutions by the entropy method and estimates the parameters by the nonlinear least square method. Through the development of more than several hundreds years, since the adoption of the poor law by industrialized nations, the contemporary social security system has formed a relatively complete system and a major component of the socio-economic system of all countries.(1) But the premature social security system coverage and imbalance development levels are differential between different provinces. Establishing and strengthening the social security system that matches the economic development is a guarantee to the stability of a nation. There are two main methods to measure the development level: one is the absolute quantity method, the other is the relative level method.(2) The micro level absolute quantity method is the ratio of expenditure for social security to social wage, while the middle level absolute quantity method is the ratio of expenditure for social security to public finance expenditure; the macro level absolute quantity method is the ratio of expenditure for social security to GDP.(3-4) The vertical design procedure which based on time series analysis compares the evaluation indicator in only one region at different time. The horizontal design procedure which based on factorial analysis compares the evaluation indicator in different regions at the same time.(5) This paper which based on the modern theory of social security systems combined with related mathematical methods and control theory, set up a differential equations model to quantitatively analyze the relations among the evaluation indexes of development level for social security systems. This research is theoretical important for studying the sustainable development for social security systems.