In this paper a random discrete mathematical population model of
immigration is constructed using not only rational factors as the
gradient of economy level among the host and issuing countries, the
geography, or the regulation laws, but also hidden intentional factors
such as political interests of governments, or the business of smuggling
of migrants by mafias, which use the immigration practically as a
weapon. These non-rational factors are modeled as sudden random arrival
flow waves represented by a Poisson distribution. The period of study is
short in order to make reliable the economic forecast of the next years.
Although the study is focused in Spain, the approach is exportable to
other geographic areas by adapting the data. Results are applied to
predict the necessary national budget of the host country to afford this
social phenomenon.