Contagion and the Spread of HIV through Opiate Abuse
The Center for Disease Control and Prevention has identified opiate abuse as a major factor in the spread of HIV. Addicts tend to share and reuse needles when injecting drugs such as heroin into their blood stream. This is a practice that is particularly widespread among white addicts, as 45 percent of which reported sharing needles in a recent study. In order to combat the spread of this disease, the CDC has spearheaded the development of syringe services programs. These services enable drug users to exchange used needles for sterile ones.
The branching process model can depict the epidemic of HIV. K is the amount of neighbors each node has, which is the number of opiate users with which a user shares his needle. P is the probability at which an opiate user with HIV passes the contagion to another user. In this scenario, decreasing the value of K is a more difficult goal to obtain, as the CDC cannot isolate users from other users. In promoting syringe exchange programs, the CDC is attempting to decrease the value of P, as the probability that the disease will be spread by an individual with the virus is lower if that user does not share infected needles with others. In decreasing the value of P, the basic reproductive number decreases as well, indicating that the expected number of new cases is lowered.
http://www.unionleader.com/article/20161204/NEWS12/161209766