Non-stationary mathematical model of world human growth

The mathematical model of human population growth is suggested. World population is seen as united system consisting of some groups of different ages. Averaged coefficients of birth-rate and death-rate for wide range of time are defined as a result of reverse problem using the population dynamics statistics solving. World population growth during period of time from the beginning of our era (0 year) to 2100 year is described adequately by the model. The stability of model is analysed. It is shown, that the critical time-dependent value of birth-rate coefficient $k_{cr}$ exists, so that $k<k_{cr}$ results in fast decrease of population number which does not to be recompensed by the death-rate coefficient decrease.