The Power Law in Sexual Networks
https://journals.plos.org/ploscompbiol/article/fileid=10.1371/journal.pcbi.1006748&type=printable
Gonorrhea is a serious illness with a reported rate of almost one million cases a year in the United States and some cases in that number have reported resistance to antibiotics. Can the rate of gonorrhea be presented as a power law distribution over a given period of time? Well, sexual networks can because sexual behaviors are still mostly heterogeneous so there isn’t a big problem including both groups. Sexual networks are found to obey the power law where the probability of have k partners is proportional to kcover a given period of time, especially in today’s generation where people are very opened. The value of c is found to be 1 to 4 in both heterosexual and homosexual models. The power-law distribution shows that heterosexual individuals have a relatively small network, while a few have a large network. Therefore, the relationship of partners reported to have gonorrhea over a given period of time can be represented like a power law to some extent. The risk of passing on gonorrhea not only depend on the individual’s sexuality and behavior, but it also depends on their position in the sexual network. In this particular power-law, gonorrhea rate depends on whether their partner has the disease and how many partners they have over a given period of time rather than its presence in a group of potential partners. This paper further analyzes how to calculate the power law for the rate of gonorrhea and the number of partnerships over a given period of time.
To further analyze whether the rate of gonorrhea could be represented as a power law, researchers from PLOS Journal first analyzed the number of partners reported in the National Survey of Sexual Attitudes and Lifestyle that was conducted in 2010-2012 in the UK. The number of partners over a given period of time followed a power law distribution. The exact c value was estimated to be about 2 for the power law, b/kc. Collecting and incorporating data on reported gonorrhea cases, three network structures were created: fully-connected, static, and dynamic. There was a similar relationship between the expected number of transmissions and the number of partners over the year, but it showed a weak power-law presentation in the static structure. Specifically, the correlation is weaker for individuals who have more than 5 partners. This makes sense because the number of parenthood clinic visits was decreasing with increased condom demand. This explains how there was a strong power-law distribution between gonorrhea transmissions and rate of interventions used to prevent it in the dynamic structure.
I don’t think that was a strong power-law distribution between gonorrhea rate and the number of partnerships within a given time period because it is very unpredictable in this case. Particularly, we shouldn’t depend on measuring those two variables to test the power law because the number of partnerships depend on many factors. Romance relationship depends on your cultural, personal, and religious norms. For example, some people prefer serious relationship while others are opened to exploring new experiences. Therefore, those two factors are not directly correlated to an extent. In the other case, it’s better to report gonorrhea transmission rates with one’s sexual practices because the sexual behavior clearly impacts the transmission and it used real data from clinics and such. Indeed, this model shows a strong representation of the power law between the rate of gonorrhea transmission and the rate of interventions used over a given period of time. Although sexual networks are a power law, it can’t be used to relate or predict many factors in a relationship because it is too complicated and unpredictable in certain terms such as the number of partnerships which is relatively biased and inaccurate.