Small-World Network Model of Disease Transmission

摘要

The most well-known mathematical models for the investigation of the spread of transmissible infections are compartmental models. These compartments categorize the population according to disease status, susceptibility to infection, etc. and by using coupled differential equations the models can often be solved analytically. But these models assume uniform mixing, i.e. any individual in the population has the same probability of contacting any other individual. These models require very detailed contact networks, but the large data set necessary to run the model is usually incomplete. Recently two advances have been made: one incorporates realistic assumptions about transportation and demographics as they affect person-to-person contact. The second has provided tools for describing complex networks and understanding their dynamics. Small-world networks show a small average distance between nodes (measured as the least number of connections) compared with the size of the graph. These nodes can represent either persons or locations. In this paper complicated and unrealistic modeling based on uniform mixing is replaced by a simpler, less computationally extensive, and more realistic small world network model. With this model outbreaks in various geographical locations can be rapidly characterized, analyzed, and preventive measures for outbreak control recognized and recommended.