Pyramid Population Prediction using Age Structure Model

Heni Widayani, Nuning Nuraini, Anita Triska


Population composition in a country by sex and age-structure often illustrated through the Population Pyramid. In this study, an age-structure model will be constructed to predict the population pyramid shape in the coming year. It is assumed that changes in population are affected by natality and mortality number in each age group, ignoring migration rates. The proposed age structure model formulated as a first-order partial differential equation with the non-negative initial condition. The boundary condition is given by the number of births which is proportional to the number of women at childbearing age. Then, this age structure model implemented utilizing United Nations Data to predict population pyramids of Indonesia, Brazil, Japan, the USA, and Russia. The population pyramid prediction of the five countries shows different characteristics, according to whether it is a developing or developed country. The results of this study indicate that the age structure model can be used to predict the composition of the population in a country in the next few years. Indonesia is predicted to be the highest populated country in 2066, compared to the other four countries. This result can be used as a reference for the government to plan policies and strategies according to age groups to control population explosion in the future.


Population Pyramid, Prediction, Age-Structure Model

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Cecilia, L. R., Oscar, C., Patricia, M., & Antonio, R. D. (2011). Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure. Information Sciences, 181(3), 519-535.

Christina, K. (2011). Lecture Notes: Reaction-Diffusion equations with applications. Munich: TU Munich.

Euler, L. (1923). Recherches Generales sur la Mortalite et al Multiplication Du Genre Humain. Teubner: Operia Omnia.

Hayes, A., & Setyonaluri, D. (2015). Taking Advantage of The Demographic Dividend in Indonesia: A Brief Introduction to Theory and Practice. UNFPA.

Jia, L., & Brauer, F. (2008). Continuous-time age-structured models in population dynamics and Epidemiology. In Mathematical Epidemiology (pp. 205-227). Berlin: Springer.

Lotka, A. J. (1931). The structure of a growing population. Human Biol, 3, 459-493.

Luiss, M. A., Oscar, A., & Juan, C.-M. (2005). Age-structured population models and their numerical solution. Ecological Modelling, 188(1), 112-136.

Magal, P., & Ruan, S. (2008). Structured population models in biology and epidemiology. Lecture Notes in Mathematics Mathematical Biosciences Subseries, 1936.

Malthus, T. (1992). An Essay on the Principle of Population. Cambridge: Cambridge University Press.

Pitoyo, A. J., Ulhaq, M. D., Wahid, A., & Taqiyyah, S. (2018).

System Dynamics Modeling of Indonesia Population Projection Model. IOP Conf. Series: Earth and Environmental Science 145, 012117.

Richmond, M. (2020, February 21). Retrieved February 21, 2020, from http://www/

Thomas, G. (2018). Compact Course: Numerics for Reaction-Diffusion Equations. Depok: University of Indonesia.

United Nation. (2020, February 22). Demographic Yearbook – 2016. Retrieved from

Verhulst, P. (1847). Deuxieme memoire sur la loi d'accroissement de la population. Mem. Acad. R. Brux, 20.



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