Page 53 - IJPS-9-3

International Journal of
Population Studies Intentional random mathematical model of immigration

flow driven by economic reasons. However, new strategies large areas, leading to the risk of famine, along with rising
are emerging from non-democratic countries, which energy prices and overall inflation. These exceptional
use immigration as a political tool to exert pressure on factors, characterized by their random nature, result in
boundary countries with the aim of gaining political or sudden waves of immigration that should be taken into
economic advantages (Greenhill, 2010; Greenhill, 2021). account in the model. Each population category or entry of

Well-known cases related to the European context the vector () as given in Equation I depends on the factors
include examples from Turkey and the Republic of in a different way, but they always follow a similar pattern:

Belarus. In the case of Spain, the main countries involved Zn 1 Zn [ Zn Zn 1, ] (II)
are Morocco and Algeria. This coercive political factor can where Δ[(), ( + 1)] denotes the population
be somewhat unpredictable, as it depends on the timely transition from () to ( + 1).
decisions made by governments seeking advantages,
often arising from diplomatic tensions between countries. 2.2. Deterministic historical trends
Regular immigration is closely related to the economic
behavior of the host country and is measured using the Table 1 compiles yearly historical data on irregular
unemployment rate as an economic indicator. In this immigration during the period 2013–2021 (Ministerio del
paper, we categorize the immigration population into four Interior, 2023). Our model’s hypothesis assumes certain
groups: unaccompanied minors under the age of fourteen characteristics that match this historical data. The arrival
(), unaccompanied minors aged between 14 and 18 (), of irregular immigration is influenced by two main factors.
adult irregular immigrants (), and regular immigrants (). One factor is predictable and deterministic, depending on
the political orientation of the Spanish Government, which
We intentionally chose a short study period to better is influenced by the differences between the main parties:
assess hypotheses regarding future economic indicator the Spanish Socialist Workers’ Party (PSOE) and the
estimations and potential relevant changes in conflicts or conservative People’s Party (PP) in their approach to the
tensions among boundary countries. The study period immigration phenomenon. These differences are evident
spans from 2019 to 2027 and is discretely divided into early in Table 1, as immigration tends to increase more during
time steps, starting with = 0 corresponding to 2019 and PSOE governments compared to PP governments, with the
ending at the final time step, = 8. The relevant population data from 2013 – 2017 in Table 1 corresponding to socialist
vector () takes the following form: governments, while 2018 – 2021 is linked to conservative
T governments. The non-predictable irregular immigration
,
,
Zn CH nM nI nL n (I) has two different sources, both of a political nature, but they
,
depend on the host countries and the issuing countries. In
where () represents the number of unaccompanied fact, the so-called “call effect” corresponds to a relaxation
minors under the age of 14 (9 – 14 years) at the end of year in the irregular immigration controls. This effect induces
; while () indicates the number of unaccompanied a stable trend of irregular immigration. Once the “call
minors aged between 14 and 18 years old; () denotes effect” occurs, the irregular business of transporting and
the number of irregular adults at the end of year , and facilitating the entry of irregular immigrants follows
() signifies the number of regular immigrants at the end market rules: when there is an expectation of benefit, the
of year . The population’s transition from year to the offer grows. For instance, with the arrival of the PSOE
(+1)-th depends on various relevant factors, with the host party to government, following a censure motion in May
country’s economy, in this case, Spain, being measured by 2018, a “call effect” was produced, leading to a significant
the unemployment rate. increase in the number of irregular immigrants in Spain,
jumping from 21,971 in 2017 to 57,498 in 2018. This
Another important factor is of a political nature, and explains the outlier data in Table 1 corresponding to 2018.
it is heavily dependent on the issuing countries, mainly The second non-predictable or random source arises from
Morocco and Algeria in our case. This political factor the political interests of issuing countries seeking political
exhibits a deterministic historical trend, but it also possesses or economic advantages using the immigration process
a random component stemming from the coercive use of as a political weapon (Greenhill, 2010; Greenhill, 2021).
immigration as a strategic weapon to gain advantages in Consequently, our model assumes a random component
the political relationships among the boundary countries. in the incoming immigration process due to random
From the perspective of the host country, regulatory laws events, such as sudden changes in political relationships
depend on political agreements with the issuing countries. between Spain and Morocco or Algeria, unexpected
However, random events, such as neighboring war conflicts inflation spikes, and political upheavals in neighboring
like the one in Ukraine, can worsen living conditions in countries. This was particularly evident in 2020 and 2021,

Volume 9 Issue 3 (2023) 47 https://doi.org/10.36922/ijps.478