Role of Immigration in Brexit: A Mathematical Perspective

Introduction and general view of the paper in focus
Migration, as seen over recent years has been in the center of various, the ongoing “British exit
(Brexit)”. One particular article on the role of immigration in the Brexit notes that, “...EU
opponents saw immigration as a national issue, as it affected the internal life of the country, thus
many chose the “leave” option” (Mauldin & Friedman, 2016). This might be a justification
among many on why numerous researchers have sought to examine the issue on immigration, its
causes and effects. In a paper by (Najem & Faour, 2018) which will be the focus of analysis for
this paper though in a mathematical perspective on the statistics, models and data used to achieve
the results and conclusion of the paper. The researchers, conduct a Debye–Hückel theory on
refugees’ migration, after which they realize that the radiation model inspired by the Debye–
Hückel theory better predicts refugee mobility in comparison to the performance of the gravity
model which fails.
Specifically, we examine the extent to which mathematical models are used such as the model
constructs, known strengths, and their possible influence on the results obtained, the use of visual
methods in analysis i.e. graphs which will include: the type, its relevance that might have led to
its use in the paper, shortcomings etcetera as well as determine the source of the data, its validity.
In this regard we will then examine the conclusions made with regard to the data analysis
conducted.

Article analysis
Mathematical models
Gravity Model
The paper’s mathematical models are generally derived with a basis to new econometrics’
gravity model. In practice, the gravity model has most of its use in analyses involving
international statistics whose goals are to estimate the interaction effects between, say two cities
or countries. Mathematically, the basic interaction between two regions is represented by:
1
Where G is a constant, F is the flow occurring between the two places say Syrian and Lebanese
cities as in the study’s case, D is the distance between the two cities and M is the flux i.e.
influence for moving from city A to city B. In modern times, the distance between cities can be
obtained by the help of software such as Google API. In order to maintain our flow with the
focus article mathematical modelling uses, we examine the use of an interaction analysis model
i.e. gravity and radiation model. Unlike in the paper, let’s examine a simpler form of the model
which describes the interaction between two different cities conducting trade given by:
2
3

In comparison to model 3, model 2 infers that the patterns of “...bilateral aggregated bilateral
trade flows among any two countries A and B is “proportional to the gross national products of
those countries and inversely proportional to the distance between them” (Chaney, 2011).
Therefore, we can conclude that in an econometric gravity model, the interaction between any
two cities is influenced by distance in an inverse proportion form that is the large the distance the
lower the interaction effect and where interaction might be trade, immigration, war etcetera.
Radiation model
The researchers further use a “Radiation model” sue to its lack of static compared to the gravity
model. In econometrics, a radiation model, unlike the gravity model accounts for other options
that are presented to the refugees from point A to point B, such that they might choose other
cities other than B (Simini, M, Maritan, & Baraba ́si, 2012). Basically, the radiation model
defines current average influx between two cities:
4
In equation 4, the model is parameter free and T is the total number of refugees, from city i and
ni and mi are the total number of persons in city I and j respectively. In addition, Sij is the total
population with a centered density i but touches j and excludes the origin of the refugees as well
as the destination population (Curiel, Pappalardo, Gabrielli, & Bishop, 2018). Specifically, the
radiation model is suitable in measuring human mobility, an argument that is justified from the
research results where results from the radiation model are significant while those from the
gravity model fail to estimate the mobility of the refugees.