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.