The United States is currently facing an
overwhelming influx of illegal immigrants, mainly from Central America, through
the border between Mexico and the United States. This controversial issue interested me, after
realizing that it could be applied to a mathematical social dynamics model, and
help project future undocumented immigration population numbers. Weidlich and Haag’s previously derived social
dynamics model that is used for this research, accounts for the movement of two
populations between two regions. After
analyzing this particular social scenario, my mentors and I soon noticed that
the model would have to be expanded in order to properly represent this
situation. Much of my research has consisted
of expanding this model so that it can account for the movement of two populations
between three regions. Our expanded
model better describes the current immigration situation as the two populations
represent children and adults, while the three regions include the United
States, Mexico, and a third region created by the grouping Guatemala, Honduras
and El Salvador into its own region. Legislation
is represented by regulatory parameters that are added to the end of the model.
In the long run, I hope to be able to create dynamic functions that properly
represent legislative proposals concerning undocumented immigration, and use
them as the regulatory parameters. My long-term
goal is to introduce this research to legislators so that it can be used as a
tool to help accurately predict the outcomes of proposed legislations.
My weekly schedule involves analyzing the
expanded model to see how it fits into the changing undocumented immigration
situation. As new laws are implemented
and migration incentives change, it is important to understand how the model
can represent these changes. Since I
have been regularly presenting this information, it is crucial to study the
expanded model on a regular basis. I
have found that I learn more about the math behind this model every time I
prepare to present it. The deeper
understanding I have of the mathematics behind this model helps me provide a
stronger explanation when presenting this research.
