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Complex Networks

4. Networks and epidemics

To understand the way that an epidemic spreads, one needs to be very sensitive to issues of culture and social networks. When the SARS epidemic started in November, 2002, the problem of trying to contain the epidemic was complicated by the very complex fabric of travel that exists in early 21st century society. Someone in a rural area of China one day can become contagious and get on an airplane a few days later. This individual can spread a highly infectious disease to people who are primarily going to one destination but may also rapidly go on to many other locales. By contrast, AIDS is a relatively non-contagious disease, and its spread is restricted by social networks of a particular kind. In the very earliest days of the AIDS epidemic the disease was largely confined to a network of homosexual males and tracking the cases of the disease could benefit from an understanding of the the network of sexually active individuals. At the current stage of the AIDS epidemic, local information about social networks might be of some use in some specific countries but in a country like the United States it would perhaps be of more limited value. Similarly, charting the pattern of infection for diseases such as syphilis, polio, tuberculosis, and gonorrhea requires special assumptions about the interplay between the nature of the disease and the networks in which the disease might spread.

In terms of the mathematical models that are made of individual diseases, it is clear that knowledge of the network that affects the individuals who currently have the disease is an important factor in getting insight into how and how rapidly the disease will spread. Insights into the nature and structure of networks can have many rewards for society.

  1. Introduction
  2. Some history and a network primer
  3. Random networks
  4. Networks and epidemics
  5. Insights from probability and statistics
  6. The Erdős graph
  7. References

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American Mathematical Society