Marital Shopping and Epidemic AIDS

Elements of these models may still have severe epidemiological consequences because variations in the behavior of a small fraction of individuals may cause huge swings in prevalence. I return to this point in the conclusion.

This trend is not unique to South Africa, nor is it a recent observation. Although good mortality records do not exist for other countries in sub-Saharan Africa, individual medical studies have revealed similar age-death profiles from HIV in Uganda (Sewankambo et al. 2000) and the Democratic Republic of Congo (Pictet et al. 1998). Anderson et al. (1991) provided an early documentation of this age pattern in an influential review. Despite the long-standing awareness of this trend, to my knowledge, previous work has not used it to assess the plausibility of behavioral models.

Templeton et al. (1996) considered all in vitro fertilizations in Britain from 1991 to 1994, whereas van Noord-Zaadstra et al. (1991) considered all artificial inseminations in two fertility clinics in the Netherlands during the clinic-specific period when fresh (rather than frozen) semen was used (1973–1980 for one clinic, and 1973–1986 for the other), and restricted analysis to married women whose husbands were azoospermic and who had never previously given birth or received an artificial insemination. Sample sizes are tiny in both studies for women older than 40, so the adjustment may be unreliable for these groups.

This analysis cannot rule out age-changing preferences regarding sexual variety, a possibility discussed at greater length later in this article.

One may imagine many ways by which network formation may covary with age. However, the assumptions needed for networks to create age-decreasing risks are strong. All members of a network are at similar levels of risk, so if network members are both young and old, then we have age-independence. If networks of partners are stratified by age, one could imagine a situation wherein uninfected older individuals match separately from more infected younger people. However, the dynamics of these networks are very difficult to justify. For example, if everyone in one network matches only with people born before January 1, 1970, then such a network could exist, but not if everyone matches with people who are within one or two years of his or her age.

Results are not sensitive to making this piece-wise linear specification more flexible.

The African studies cited here are from Nigeria, Uganda, Kenya, and Malawi. I am not aware of a similar documentation in South Africa. However, given that researchers frequently hypothesize that it is exposure to Western culture and the development process that leads to this shift, we may expect the courtship and marriage paradigm to be at least as important in South Africa as in other parts of Africa.

Individuals in this model draw only one partner at a time. Although age-independent concurrencies perform poorly against the age-risk profile, search with multiple concurrent draws would have similar predictions to this model, with even more severe implications for epidemic prevalence.

In a more sophisticated model, individuals may consider the state and future path of the HIV epidemic in making their spousal choices. However, if individuals have rational beliefs about HIV, the distortion in behavior is minimal. Because early in a relationship, the risk from drawing a new partner is extremely close to the risk from staying with the current partner, individuals are only very marginally willing to lower their reservation in response. Given that the rational difference is extremely small and that I have no way to assess what South Africans actually believe about the transmission rate or the future path of the epidemic, I abstract from this analysis.

Koopman et al.’s (1997) model is a more traditional epidemiological model than the one described here and as such differs strongly in focus. There, transitions between phases of high and low sexual activity are not brought about by any behavioral process but rather by outcomes of exogenous (and calibrated) chance. Similarly, systematic matching between individuals in different phases is specified rather than the outcome of a behavioral process like spousal search. This makes it more difficult to derive policy predictions like those employed in this article because the motivations for risky behavior are not identified. Koopman et al. also assumed a higher transmission rate and an order of magnitude more partners than those employed here, with individuals in their model accumulating a staggering two new partners per month.

I chose 1/6 because in simulations, about one-sixth of single, HIV-positive individual-months are spent in acute infection for those who don’t enter already infected. Varying this fraction has only a small impact on results.

It is natural to suspect that coital frequencies decline as people become increasingly sick in mature infection. Wawer et al. (2005) followed transmission rates and coital frequencies approaching death and found that coital frequencies decline gradually over 6–30 months before death, from a rate of 10.0 coital acts per month earlier in infection to a rate of 8.7 coital acts per month in months 16–25 before death and 6.2 acts per month 6 months before death. However, transmission rates increase faster than coital frequencies decline, and Wawer et al. documented that transmission occurs about 3.65 times as frequently over months 6–30 prior to death. I use that frequency in my calibration.

Because cohorts of simulated partners must build up over time, HIV entry is delayed to minimize the effects of time dynamics in homophily in age. (Simulations suggest that this time delay has a slight and conservative effect on HIV prevalence.) In fact, the role of age-specific homophily in the spread of HIV is somewhat unclear. If people match nonrandomly with others in a similar age category, this may lead to more explosiveness in the HIV epidemic as people in high turnover phases with greater likelihood of acute infection match systematically with others in the same phase. This observation makes the role of homophily in the spread of HIV an important avenue for future research, particularly as it interacts with messages about relative risks (Dupas 2011), which persuade girls that older men have higher prevalence and, hence, that younger boyfriends are safer. Fortunately, the lower pregnancy rates found by Dupas for girlfriends of young and presumably high-turnover boys suggest that lower fertility demand may overwhelm this concern.

This is true to a gross approximation. With most specifications, the declining reservation quality with age is relatively slight until very near mortality; this has consequences for marginal relationships only (although the odds of marriage can be boosted by not terminating during a few stochastically marginal periods). As I show later, when I turn transmission off at the beginnings of relationships, much of the risk that singles are exposed to enters through “bad” relationships that are easily rejected; this behavior is hardly affected by declining reservation quality with age. For example, in the preferred specification, about 71% of relationships last only one month in years 1–18 of a 20-year lifespan (SD = 0.015), based on 2,500 observations of simulated life spans, and there is no statistical age trend across these years.

These assumptions create an integer problem because the individual is then sexually active for only some fraction of the year in which she or he first has sex. Because the age at which one first has sex is the absolute earliest she or he could start risky search, I assume that young adults begin searching (and hence reach the full single risk level) in their first full year of sexual activity. However, the potential for heightened pre- and post-nuptial coital frequencies suggest that married individuals may start on the married risk rates in the year in which they get married; the figures presented reflect this assumption. Resolving the integer problem in different ways results in very similar fits.

In fact, the fit outperforms that of the current state-of-the art epidemiological model for South Africa, the ASSA (2005) AIDS model, with sum of squared deviations of about one-half the magnitude.

Except concerning the eventual marital behavior, such a model is very similar to that described in Koopman et al. (1997).

The Cape Area Panel Study Waves 1, 2, and 3 were collected between 2002 and 2005 by the University of Cape Town and the University of Michigan, with funding provided by the U.S. National Institute for Child Health and Human Development and the Andrew W. Mellon Foundation. The data set is described in further detail in Online Resource 1.

An external additional test of the model would be to input transmission dynamics of a different sexually transmitted disease in a different context and evaluate the age profile. Unfortunately, transmission probabilities of most sexually transmitted diseases are little understood, and cases of them are often undocumented. Gonorrhea in the United States, however, provides a good case study (although extremely low prevalences may cause some concern over selectivity). I complete this analysis in Online Resource 1; once again, male and female patterns are differentiable from each other and do resemble infection rates, although the fit is less close than in the HIV case, possibly because of low and nonrandom prevalence.

Other values of δ have their multiplier reduced similarly under this policy.

African PPY transmission rates are 8%–12%, which contrasts with U.S. and European rates of 5%–10%. This similarity in the face of lower condom use, more circumcision, and higher STI prevalences led Gray et al. (2001) to reject the hypothesis that HIV-1 subtypes in Africa are more infectious. Still, these similar PPY transmission rates contrast sharply with the large differences in Oster (2005), who uses a per-partnership transmission rate (Downs and De Vincenzi (1996) advocate the per-partnership measure because HIV infections do not appear to be binomial in contacts due to heterogeneity in infectiousness). This approach represents one approximation; it is imperfect because individuals do become infected several years into the described studies. No matter how transmission rates are estimated, a wide variety of point estimates are received, with per-partnership rates exhibiting a particularly high variance. This is due to factors such as differences in lengths of the studies, differences in coital frequencies, differences in the fraction of study participants who report perfect condom usage, and small sample sizes, as well as different biological transmission rates. Because of this, the most recent studies—all African—prefer per-partnership-year or per-coital act transmission rates, which this study follows.

If only a partial reduction in transmission rates is achieved, using biology to treat the epidemic is less effective. Reducing transmission rates by 12.5% (50% of what is feasible) reduces the multiplier by 1 (available from the author).

These transmission rate numbers are justified by the review in Cohen et al. (2007), which also suggests that the true transmission rate under treatment is likely closer to the 0 estimate than the 50% of latent rates; the durations of treatment are meant to provide a fairly broad range given the availability and institutional constraints in Africa.

Results are not presented because the large number of assumptions renders them fairly speculative. In particular, there is little research on the natural course of infection, which would result from a window of treatment early in the infection. Implications for drug-resistant strains may also be severe and quite negative, but they are beyond the scope of this analysis.

Adolescent girls in rural Kenya have been shown to respond to information on relative risks of different partners by changing their sexual behavior (Dupas 2011), so this message of targeted risk seems likely to be one to which individuals respond.