The basic structure of the population model is very simple, even if the implementation becomes more complex. The core of the model is fundamentally an accounting system around the age-sex distribution (AGEDST) with 5-year age categories—and an elaboration of that into single year categories (FAGDST)—in which people age over time, with births added into the bottom age category each year and deaths subtracted from the appropriate age and sex category.  The key to long-term dynamics lies primarily within change in the fertility and mortality distributions, with migration playing a secondary role for most countries.

A 5-year cohort fertility distribution (FERDST) multiplies the age distribution (AGEDST) to produce births (BIRTHS). The total fertility rate (TFR), or total number of births expected to a woman during her lifetime, modifies the fertility distribution over time. The fertility distribution itself moves from the initial empirical, country-specific pattern to an ultimate fertility distribution (ULTIMATEFERTILITY) as GDP per capita (PPP) moves towards a specified level (currently $45,000). The ultimate fertility distribution is exogenous to the model in a file and not available for the user to change via the model's interface. We will see the computation of TFR in our discussion of fertility.

where

In the above equation and other documentation of the population model: 

r=region/country

c=age category

p=sex (because s is used elsewhere in the model for economic sector)

d=cause of death

Deaths (DEATHS) are computed in the health model of IFs, see the documentation of that model.  They are the sum of age, sex, and cause-of-death specific mortality forecasts. Life expectancy (LIFEXP) is also computed in the health model.

There is, however, a legacy model of mortality and deaths that now is very rarely used but can be activated by changing the hlmodelsw parameter from 1 to 0.  The legacy calculation of deaths parallels that of births in that it relies on a product of the age distribution with a mortality distribution (MORDST). As with fertility, the mortality distribution itself moves from the initial empirical, country-specific pattern to an ultimate mortality distribution as life expectancy moves towards a specified level (currently 85 years).  In the legacy model, life expectancy is computed from the mortality distribution.

Most of the model uses the 5-year age categories of the age distribution (AGEDST).  But 5-year categories can introduce a significant problem when we advance the model over time.  Specifically, it can lead to diffusion of births or deaths too quickly up the distribution (for instance, if a surge of births entered the bottom 5-year category one year, 1/5 of those could potentially move up to the next category the following year already, because a model that only used 5-year categories would not recognize their recent arrival in the category). 

Hence in the first year of the model we spread the 5-year categories that come to us from UN data into a 1-year or annual age distribution (FAGEDST) using a spline function and use that annual distribution for our accounting dynamics across time. One-fifth of deaths in each 5-year category reduce the appropriate annual age category and those in each age category advance to the next year (all surviving infants advance to age 1). We also add one-fifth of net migration by 5-year category into each underlying single-year category. Births enter the infant category of the age distribution.

Once the full age distribution has been advanced for the next year, it can also be collapsed back into into the 5-year cohorts of the age distribution (AGEDST), which is used for the calculations of births and deaths in the next year and for display in the model. The population (POP) is a sum across this distribution.