The size of urban population (POPURBAN) in the very near future is probably best forecast by using a growth rate (POPURBGR) computed initially from historic data, but gradually coming to represent the dynamic growth rate of urbanization calculated by the model. The growth rate applied to past urban population provides an initial estimate of urban population each year PopUrbanGro).

In the long-term future, urbanization must saturate as the portion of the population urbanized approaches 100%.   Moreover there is a relationship between income levels of countries and urbanization level that should affect the growth of urban population.  Thus  a function estimated cross-sectionally against GDP/capita at PPP was used to provide a target (PopUrbanTar) for urbanization that could gradually replace the value of growing urban population (PopUrbanGro) calculated by use of the growth rate –countries with very high levels of GDP/capita have already begun to approach saturation; algorithmic modifications help assure that the target is reasonable and also that it approaches saturation smoothly. 

where

and

with algorithmic modifications for smooth behavior over time and as saturation is approached.

Once the urban population has been updated in each time cycle, it is possible to compute the actual growth rate (POPURBGR), which will then be the starting point for growing urban population (PopUrbanGro) in the next time cycle.