A Population Pyramid Dynamics Model and Its Analytical Solution. Application Case for Spain

This paper presents the population pyramid dynamics model (PPDM) to study evolution of a determined country or society, deducing as crucial objective its exact analytical solution. The PPDM is first-order linear partial differential equation whose unknown variable density (population per age unit) depending on time and age, jointly an initial condition in boundary given by births zero age. In addition, dynamical patterns crude birth, death, immigration emigration rates time, with mathematical pattern ages, take part PPDM. These can be obtained from historical data. An application case solution presented: Spain, 2007–2021 period for validation, 2021–2026 future forecasting. also permits obtain forecasting limits comparing data those provided Other variables that pyramids data, such dependency ratio life expectancy at are considered.