The radiation law is way of modeling human mobility (geographic mobility, human migration) and it gives better empirical predictions than the gravity model of migration which is widely used in this subject.
[1] Waves of migration due to displacement by war, or exploitation in the hope of geographical discoveries could be observed in the past, however with new technological advancements in transportation keep making it easier and cheaper to get to one place from another.
With intercontinental flights we even can travel to another continent, on a business trip for instance, and come back within a few hours.
Radiation models appeared first in physics to study the process of energetic particles or waves travel through vacuum.
The model in the social science describes the flows of people between different locations.
The potential employment opportunity (e.g. conditions, income, working hour, etc.)
Individuals then chooses the job which is closest to their home county and provides the highest
This optimization gives the migration flows (called commuting fluxes) between counties across the country.
An important feature of the model is that the average flux between two counties does not depend on the benefit distribution, the number of job opportunities and the total number of commuters.
The fundamental equation of the radiation model gives the average flux between two counties, where
The Gravity model gives bad predictions both on short and long distance commuting, while the prediction of the Radiation model is close to the census data.
In 1971 famed economist William Alonso produced a working paper that describes a mathematical model of human mobility.
[3] In that manuscript Alonso remarks: "It is almost as if an urban area were a radioactive body, emitting particles at a steady rate[.]"
In addition to many of the same mathematical terms used by Simini et al., Alonso's radiation model includes measures of climate (degree days) and wealth (per capita income) for both the emitting and receiving locales, but only includes the distance between these urban areas as opposed to a radial measure of intervening population density.
The model predicts, that the migration flow is proportional to the population of the cities/countries, and it is reciprocal in a quadratic order in the distance between them.
Although, it is an intuitive description of the flows, and it is used to describe gravitational forces in physics, in terms of migration it does not perform well empirically.
Moreover, the model just simply assumes the given functional form without any theoretical background.