Mathematically modelling proportions of Japanese populations by industry

•The logistic equation extended to describe temporal changes of industrial structure.•The extended model keeps variables non-negative whose sum equals to 100%.•The extended model fits the Japanese historical data very well.•The future prediction for industrial structural change is also provided.

I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.