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Braess’s Paradox and Diseases

In class, we discussed Braess’s Paradox, the phenomenon that adding an edge in a network, such as building an extra road, can actually decrease the efficiency of a system due to Nash Equilibrium. Four scientists, Hai-Feng Zheng, Zimo Yang, Zhi-Xi Wu, Bing-Hong Wang, and Tao Zhou have observed a similar phenomenon in epidemiology, the branch of medicine relating to the spread of diseases. The paper focuses on a few issues, but I will only discuss the issue relating to Braess’s Paradox. In their paper, they observe 3 responses that people can take to prevent the contraction of disease: “laissez-faire” (doing nothing), self-protection techniques (such as washing hands or limiting time spent outdoors), and vaccinations.

They observed how much a disease could spread given how much self-protection people used effectively. They did not notice anything strange when there were no effective self-protection techniques or when the self-protection techniques were very effective (0% effective and 100% effective, respectively). However, in the middle of this spectrum, they noticed a phenomenon similar to Braess’s Paradox. Around the middle of this spectrum, when people tend to use more self-protection techniques that work, the spread of the disease actually increases. This is because other people realize that the technique might work, and so they don’t get vaccinated. As this happens, it is much easier for a larger percentage of the population to contract the disease. And as the self-protection techniques used are less effective, the spread of disease decreases due to more vaccinations. So while slightly different, “This is very similar to the so-called Braess’s Paradox, which states that adding extra capacity to a network when the moving entities selfishly choose their route, can in some cases reduce overall performance.”

http://www.nature.com/srep/2013/131121/srep03292/full/srep03292.html

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