Nonrandom Mixing Models of HIV Transmission
Kaplan, Edward H.
Paltiel, A. David
"Nonrandom Mixing Models of HIV Transmission," (with Edward Kaplan, and A. David Paltiel) in Mathematical and Statistical Approaches to AIDS Epidemiology, edited by Carlos Castillo-Chávez, Lecture Notes in Biomathematics Series, Springer-Verlag, 218–239, 1989.
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Models of HIV transmission and the AIDS epidemic generally assume random mixing among those infected with HIV and those who are not. For sexually transmitted HIV, this implies that individuals select sex partners without regard to attributes such as familiarity, attractiveness, or risk of infection. This paper formulates a model for examining the impact of nonrandom mixing on HIV transmission. We present threshold conditions that determine when HIV epidemics can occur within the framework of this model. Nonrandom mixing is introduced by assuming that sexually active individuals select sex partners to minimize the risk of infection. In addition to variability in risky sex rates, some versions of our model allow for error (or noise) in information exchanged between prospective partners. We investigate several models including random partner selection (or proportionate mixing), segregation of the population by risky sex rates, a probabilistic combination of segregation and random selection induced by imperfect information (or preferred mixing), and a model of costly search with perfect information. We develop examples which show that nonrandom mixing can lead to epidemics that are more severe or less severe than random mixing. For reasonable parameter choices describing the AIDS epidemic, however, the results suggest that random mixing models overstate the number of HIV infections that will occur.