Final answer:
Geographic Information Systems (GIS) is the tool that would best help the graduate student to visualize and analyze the spread of dengue fever and mosquito vectors in the Southern United States.
Step-by-step explanation:
The application that would enable the graduate student to effectively illustrate patterns of vector and disease spread is Geographic Information Systems (GIS). GIS allows the visualization, analysis, and interpretation of data related to positions on Earth's surface. This can help reveal patterns, trends, and relationships in the form of maps, globes, reports, and charts.
Given that the student has data on locations where the vector has been detected and incidences of dengue fever in both vectors and humans, GIS can critically assist in understanding and communicating how the disease is spreading geographically.