What Newton Can Teach Us About Migration?
Sir Isaac Newton’s law of universal gravitation teaches us more than just how two masses attract each other from a distance. His famous equation relates the gravitational force between two objects to their respective masses and the distance separating the objects:
F = G m1m2
r2
Interestingly, an essentially identical equation may be constructed that is capable of approximating migration flows between two locations, but this time as a function of population sizes (or even other measures) and distance separating the two locations. Generally, the equation below is referred to as a gravity model:
Mij = G PiαPjβ
rijγ
where Mij represents the migrant population, Piα represents the population of the origin location (i), Pjβ represents the population of the destination location (j), and rijγ represents the distance between the two locations. G is just a proportionality constant for scaling purposes. α,β and γ are parameters usually estimated from data.
My work this semester focused on estimating vaccine stockpile quantities for Nipah virus, a zoonotic virus (often transmitted by bats to humans) prevalent in India and Bangladesh. Estimating migration flow is of particular importance in modeling Nipah virus as it dictates how a disease may spread from location to location, via human travel. In turn, this will determine how and where vaccine stockpiles should be allotted.
Often, data availability can be a barrier to research, since what data are available play a crucial role in what questions can be posed and answered. Thus, it is often necessary to create models that can closely approximate the unavailable data, based on a series of reasonable assumptions. In my case, because data on migration in India and Bangladesh are extremely scarce, a gravity model proved to be useful in providing estimates of population migration at the district level. I had data on district population and distances between districts, but needed to find values for the exponents in the model: α,β,γ. Briefly, the modeling process proceeded with reviewing travel and migration literature to understand how to properly parameterize the gravity model. After coding the model in Python, I tested various reported exponent values and plotted the results. I also attempted to validate my migration population data with summary-level data on migration in India. This served as a reality check to make sure the results were reasonable compared to what was expected. After some adjustments and scaling, the model output yielded promising results.
In the larger scheme of the project, these migration estimates would feed into a larger model of Nipah virus transmission dynamics that would inform vaccine stockpile distribution. Vaccine stockpiling is an extremely important topic because it is one of our first lines of defense against the rampant spread of an epidemic or pandemic. It essentially puts the concept of prevention as the best form of a cure into practice. Additionally, estimates like these give policy-makers and vaccine manufacturers concrete, quantitative information on how to prepare for and prevent the spread of disease.
Andrew Tiu (NHS `21) is an undergraduate studying human science and statistics. He is a student fellow with the Global Health Initiative.