The world population growth is considered. Based on the concept of life-saving technologies we explain the squared relationship of the growth rate on the population. We derive a master equation of the theoretical demography determining the balance between the level of life-saving technologies and the number of people. Mechanisms of this equation stabilization in fast time, especially a crisis emerging under demographic overheating, are considered. The demographic transition results from life-saving technologies verging towards their natural limit. In this connection the intensive technological development come in the stead to the extensive one. Such approach allows constructing a phenomenological model of the demographic transition being in a good agreement with the demographic data.

Mathematical modelling in actual problems of science and technics