Mathematical models of dynamics of population of earth for long-term forecasting of world needs for energy resources and strategic planning of development of an oil and gas complex

Samarin I., Fomin A.

The known mathematical models of dynamics of total number of the population on Earth are considered and critically analysed. For accounting of the new significant factors shown in the last decades on the basis of several consecutive stages of generalization the new mathematical model is offered. It is based on the differential equation of dynamics of population. Parameters of this model are determined from the solution of a problem of mathematical programming on minimization of a mean square relative mismatch between model and real values by the number of the people living on Earth. High precision of modeling at the level of 0,33% is as a result provided. Use of mathematical model for forecasting shows that there is a limit of growth of population approximately in 12 billion people. His existence is caused by application of the effective state measures for restriction of growth rate of the population operating within several decades in many countries. In the offered mathematical model global demographic transition contacts concrete measures for restriction of birth rate, allowed to reduce average growth rate more, than by 3 times.

Keywords:hyperbolic law, demographic transition, dynamic, differential equation, life-saving technologies, mathematical model, method, minimization, parameter, growth limit, statistical series, rate, formalization, population, numerical methods, objective function.