Our findings suggest that the epidemic in Zimbabwe is very close to the persistence threshold—small changes in either behavior or infectivity may be enough to push it into eventual extinction. Differences as small as the interpretation of stage-specific infectivity used by researchers working with the same underlying source data were sufficient to push the transmission dynamics across that threshold, while a slight increase of 6% in the number of active partnerships might be enough to ensure persistence at prevalence >10%. Both of these suggest that measurement error, in both biological and behavioral parameters, may play a significant role in the projections from epidemic models in Zimbabwe. This uncertainty should be acknowledged in simulation studies; much more attention should be paid to both the validity and reliability of the biological and behavioral measures, and to the accurate representation of all elements of the transmission system.
The one finding for which there is very little uncertainty comes from our counterfactual scenarios: both concurrency and the peak in acute infection are needed for epidemic persistence of HIV in this population at this point. Neither alone is sufficient. While some of the other scenarios only generate one persistent epidemic for every 10 or 100 tries, both counterfactuals failed to generate a single epidemic in 1,000 tries, which strongly suggests these scenarios lack epidemic potential. This is a qualitative difference. Only a small fraction of infections directly stemmed from acute index cases, but eliminating this peak infection window makes the epidemic unsustainable. The same is true for concurrent partnerships; eliminating concurrency, while keeping the same number of total partners, partnership durations, and coital frequencies, and the same peak infection window, leads to epidemic extinction. The joint impacts of concurrency and acute infection, long the subject of speculation, are clearly confirmed here.
Our estimates of the fraction of infections associated with the acute-stage do not always match the original published estimates. Hollingsworth et al. [12
] estimate 31%, and Abu-Raddad and Longini [11
] estimate ~5–13% of transmissions stem from acute-stage infections at equilibrium. Using their infectivity profiles, we estimate about 20% for the Hollingsworth scenario and 11% for the Abu-Raddad scenario. Pinkerton [10
] estimates that 89.1% of the transmissions during the first 20 months of infection occur in the acute phase; our model estimates 76% using Pinkerton’s parameters. Since we are using the same infectivity parameters as these studies in each comparison, the differences in our estimates must stem from other components of our models.
With respect to these papers, the critical difference is the way we model behavior. Our behavioral model is different in two important ways. First, our transmission network parameters are estimated from data on a single population. This is not the case for the models used in other studies. Parameters in those models are taken from a number of different populations, in order to meet the input needs of the simulation setup given the constraints of empirical datasets. There are real differences in behavior within and between the populations of sub-Saharan Africa that make this mixed input approach hard to defend. Restricting behavioral inputs to a single population does limit generalization, especially to “sub-Saharan Africa.” But in return, it strongly increases the validity of inferences to the population of interest. Second, our model accurately represents the observed timing and sequence of multiple partnerships (both concurrent and sequential), and the distinctions between types of partners. This is also not the case in the other models. The recent paper by Eaton et al. [14
] that included a stylized version of concurrency and used the Hollingsworth infectivity estimates, by contrast, show similar results to ours. They find that 16–28% of infections are attributable to the acute phase at equilibrium across a range of concurrency levels. Both our study and theirs examine a “no concurrency” counterfactual scenario, and both find that it makes a qualitative difference in the epidemic outcome: in this population, it is not possible to sustain an epidemic without concurrency, if the empirical distribution of the number and types of partnerships is represented with fidelity.
This has an important implication for using models to understand the epidemiology of HIV in Africa: details matter, but some details matter more than others. In order to match observed epidemic trajectories, previous modeling studies that have not explicitly represented concurrency have had to posit absurdly high rates of partner accumulation. One example from a widely cited study has to assume that the average
male and female in the population of Yaoundé, Cameroon has 221 lifetime partners, and 7% have an average of 2,870 partners, each relationship at least 1 week long, over 35 sexually-active years [11
]. In another widely cited study, the average person in “sub-Saharan Africa” (male and female both) is assumed to have 120 partners over their lifetime, and the top 10% of both sexes have 723 partners over 40 years, each with 25 sex acts or more [52
]. These are not extreme examples of model assumptions; they are typical for models that do not explicitly represent concurrency. Behavioral patterns like this are not found in general heterosexual populations anywhere, but they are apparently necessary, in the absence of concurrency, to generate realistic epidemics. One reason is that the mathematics underlying these examples implicitly assumes that a partnership can only transmit if it is serodiscordant at its outset, and not if it becomes serodiscordant during its course. The profound disconnect between these types of assumptions and empirical data has been criticized [53
], and has been used to argue for the importance of non-sexual transmission routes in Africa [54
]. Our modeling approach suggests a different interpretation. Consistent with other emerging studies [14
], we find that far fewer partners are necessary to generate substantial HIV epidemics—when concurrency is explicitly measured and modeled. While this provides strong support for the role of sexual transmission of HIV, we suspect that the massive exaggeration of the number of partners in these other models is bound to lead to artifacts in their primary findings. This suggests it would be worth going back to re-evaluate the validity of the findings from key modeling studies in the past decade.
Our model also has many assumptions and limitations that must be kept in mind when making inferences. Our model excluded people who had never had sex (19.9% of the original study sample), as well as commercial sexual contacts. Each would affect our equilibrium prevalence estimates, though in opposite directions. Including the not-yet-sexually-active population would lower HIV prevalence estimates somewhat; if we chose to model them as a distinct, permanent class, as is sometime done, then the new estimates would simply be 80.1% of the values previously estimated. Including commercial contacts would, of course, raise prevalence estimates. Our data were drawn from young adults, and inference should be focused on this subpopulation. We did not consider additional network structuring induced by geographic mixing, nor mixing by age or other exogenous demographic or social variables. Our modeling framework can represent these, but our goal here was more limited. We assumed that deaths were balanced with new arrivals due to limitations on the ERGM framework that were in place when we began this research; these limitations are now lifted [42
], enabling future work to explore the interactions of vital dynamics and relational structure in more detail. We did not consider variation in circumcision status or co-infection with STDs or other infections. Neither STD treatment nor circumcision was needed to push our epidemic into extinction in this study, but their absence may help to keep transmission marginally above the reproductive threshold in the population. Our empirical estimates of concurrency are subject to several sources of measurement error. Some may lead to overestimates (e.g., our selecting the month with highest prevalence), others to underestimates (e.g. social desirability bias in self-reported sexual behavior data). Our sensitivity analyses suggest these could well be important for accurate inference. Our estimates of stage-specific transmission probabilities and coital frequency are based on data from a single study, and are also subject to measurement error (this limitation applies to all other published studies on this topic as well). There is uncertainty in the duration and magnitude of the acute infection window, and in coital frequency during late-stage AIDS. For these limitations, the sensitivity analyses we conduct on transmission probabilities gives some intuition regarding the impact on model outcomes.
Finally, our models do not accurately reproduce the rapid rise in prevalence that was observed in Zimbabwe, from the low single digits in the early 1980s to around 20% in the early 2000s; they took well over a century to achieve equilibrium prevalence when starting from two initially infected cases. This would be a serious limitation if we were trying to replicate the original epidemic trajectory. However, that was not our goal. Rather, time in our model simply represents a “burn-in” period required to determine the equilibrium conditions implied if the behavior observed in our data had and always will be present. Reproducing the original trajectory would require an accurate model of behavior in the pre-1980 period, for which we have no data at all, let alone the type of egocentric network data needed to accurately represent concurrency. There is evidence from the longitudinal cohort study in Manicaland that risky behavior declined from 1998 to 2003, with reductions in both casual partners and concurrency, especially among men [45
]. But this is nearly two decades after the start of the epidemic. It is worth noting that Eaton et al., using the 1998–2000 Manicaland data, also find that while the final prevalence in their simulated epidemics is in a realistic range (9–23%, depending on the level of concurrency), it takes 50–100 years to reach these levels, even though they start with a much higher fraction of infections (1%, 100 males and 100 females). They draw the conclusion that something other than concurrency must have caused the early explosive epidemic growth. Since their models use behavioral data collected 20 years after the epidemic began, this inference cannot really be drawn. Unfortunately, we will never have the data we need to answer this question empirically. What we can do now, in the absence of data, is to use this modeling framework to identify the sexual behavior conditions under which a major epidemic could
unfold in one or two decades. This is an important topic for future research.
Despite these limitations, we believe our findings have important implications for HIV prevention. Logic dictates that a short acute infection window depends on either rapid serial partner acquisition or concurrency to generate epidemic persistence. These patterns of relational timing vary widely among populations in which HIV is spread, but concurrency is the only plausible driver in generalized epidemics. Of the two necessary components for persistence that we found here—peak infection and concurrency—concurrency is something we can address now. And it may be all we need to address, especially in populations that are, as Zimbabwe seems to be, close to the threshold for epidemic persistence. A vaccine only needs to achieve the critical coverage level for herd immunity to kick in, and in this sense, concurrency reduction will function as a behavioral vaccine. We eliminated concurrency in our counterfactual scenario for clarity, but elimination, like 100% vaccine coverage, is not necessary. Using their stylized version of concurrency, Eaton et al. found that rates of concurrency of 4% and below could not sustain an epidemic at the partnership acquisition rates reported in Zimbabwe in 2000. Better models, and better data will help to bracket the target level of concurrency reduction needed to confer herd immunity, but this is a very good start. It is important to recognize that the target level will be population-specific; it depends on the distribution of partnership duration, and gender-specific partnering patterns, so it will be an empirical question for each case. Estimates of this concurrency reduction target are a key component to “knowing your epidemic” and for developing the right prevention package.