We adapted and extended a previously published, dynamic, stochastic network model of HIV transmission dynamics, which was originally designed to elucidate racial disparities in HIV prevalence among MSM in Atlanta [30]. The original model comprised key aspects of HIV transmission dynamics among MSM, including the occurrence of condomless anal intercourse (CAI) and related HIV transmission probabilities, sexual partnership characteristics (eg, main or casual partnerships), HIV testing frequency, and HIV care seeking. In the original model, MSM possessed fixed (eg, race and circumcision status) and dynamic (eg, age and infection status) attributes. In addition, HIV-infected men possessed additional dynamic attributes (eg, diagnosis status, treatment status, infection stage, and plasma HIV RNA level). Consistent with prior studies [31,32], sexual contact networks used separable temporal exponential random graph models (STERGMs) [33], a flexible statistical framework for simulating partnership formation and dissolution across networks [34], facilitating one to match data on the complex cross-sectional network structure, as well as reported relational durations. We implemented STERGMs in the R package suite statnet [35] and EpiModel [36]. The specific parameters for the sexual behavior developed by the domain and city are presented in Appendix Table A1.

In the model, sexual contacts occurred on three networks, each of which shared the same set of nodes (people) but represented a different relationship type: main partners, casual partners, and one-time partners. Partnership formation depended on the following four predictors: partnership types (main, casual, or one-time partners), degree distribution (number of ongoing partners for each individual), age homophily (partners with similar age), and sexual role segregation (only those men who engaged in receptive anal sex could pair with men who engaged in exclusively insertive anal sex and vice versa). There was a constant relationship dissolution hazard for main and casual partnerships based on the median duration of each type (Multimedia Appendix 1, Table A1).

HIV progression followed both a natural trajectory of disease, in the absence of ART, and an ART-mediated trajectory [37]. In the absence of ART, HIV viral loads progressed in three stages: peak viremia during acute HIV infection (21 days); a set point viral load during the clinical latency (42 days); and a subsequent increase, resulting in AIDS and disease-induced mortality (728 days) [38]. In serodiscordant pairs, HIV transmission probabilities included those mediated by the viral load of the positive partner [39], condom use [40], the presence of the CCR5-Δ32 genetic allele [41,42], receptive versus insertive sexual position of the HIV-negative partner [31], and the circumcision status of an insertive HIV-negative partner [43]. After infection, men were assigned to three clinical care trajectories: those who never initiate treatment; those who initiate treatment and become partially suppressed; and those who initiate treatment and become entirely suppressed. The three trajectories exhibited different rates of infectiousness, HIV diagnosis, ART initiation, HIV viral suppression, and progression to AIDS and death to match empirical estimates of the prevalence of these states [44]. Furthermore, ART decreased the viral load and its associated transmission risk [4] and extended the life span [45].

We included PrEP use and adherence as additional features of the model. At any given time, 23.4% of HIV-negative MSM in the Seattle model and 11% of HIV-negative men in the Atlanta model were on PrEP according to Darcy Rao (oral communication, May 2017). If the proportion of HIV-negative MSM on PrEP decreased below the threshold coverage because of discontinuation or seroconversion, newly tested HIV-negative MSM were allowed to start PrEP. In addition, MSM on PrEP received a diagnostic HIV test at regular intervals (3 months). In fact, MSM who started PrEP were assigned a fixed adherence profile that reflected an average weekly dosage using data from the US PrEP Demo Project [46] weighted by race or ethnicity using methods from Jenness et al [32], which investigated the impact of the implementation of the US Centers for Disease Control and Prevention’s PrEP guidelines on the national HIV epidemic among MSM. For the Atlanta model, we assigned 21.1% of men as nonadherent (0 doses), 7.0% taking <2 doses/week, 10.0% taking 2-3 doses/week, and 61.9% taking ≥4 doses/week; for the Seattle model, we assigned 14.4% as nonadherent, 4.1% taking <2 doses/week, 5.3% taking 2-3 doses/week, and 76.2% taking ≥4 doses/week [32]. The probability of HIV acquisition per sex act was decreased according to the level of adherence. Little evidence for risk behavior changes among MSM while on PrEP was found in studies predating the development of this model [46-49]; thus, we focused on the PrEP coverage and adherence and did not model such behavior changes.

To investigate the possible impacts of HIV self-testing strategies on HIV epidemic dynamics in future models, we added more complex parameters describing clinic-based HIV testing behaviors to the original model to create a new baseline model. As existing patterns of the testing behavior vary among MSM, we conceptualized this baseline model with four tester types [50] (Table 1): (1) those who do not test in any setting (“never testers”); (2) those who test for HIV, but without a regular testing interval and without considering sexual episodes (eg, testing outreach at Pride festivals or when seeking medical care for a non-HIV or STD-related reason; “opportunistic-only testers”); (3) those who test for HIV regularly, irrespective of sexual behaviors (“regular testers”); and (4) those who test for HIV in response to a specific sexual episode (eg, CAI with a partner of unknown HIV serostatus; “risk-based testers”). Both regular and risk-based testers could also have an opportunity to become opportunistic testers and test outside of their regular testing interval or in the absence of a specific sexual episode, respectively, when opportunities were available. In addition, many public health agencies recommend different testing frequencies for MSM at higher versus lower risk for HIV acquisition [51-54], and evidence suggests that on an average, MSM at higher risk test more frequently [55-60]. Consequently, we stratified regular testers into high vs low anal intercourse (AI) frequency groups to allow for differential testing frequencies by risk.

The four categories of HIV tester types (Table 1) in the baseline model provide a framework to investigate the efficacy of different HIV self-testing scenarios for both Atlanta and Seattle. In the next stage of this research, we will implement two different self-testing intervention strategies: replacement testing and supplementary testing (Table 2). In the replacement testing scenarios, we will evaluate the proportion of HIV infections averted when HIVSTs replace clinic-based opportunistic tests, regular tests, and risk-based tests, respectively and simultaneously. In addition, we will assess the impact of replacing 25% and 50% of clinic-based tests with HIVSTs, assuming a 90-day window period (duration between when a person might have been exposed to HIV and when a test can give an accurate result) for self-tests [61].

We will also model the proportion of HIV infections averted when self-tests supplement clinic-based tests. In these scenarios, never testers and opportunistic-only testers take one or two supplementary HIVSTs randomly each year. Regular testers can supplement clinic-based tests with HIVSTs in two ways.

First, they can supplement clinic tests with one additional HIVST randomly during a year. Second, they can test more frequently (ie, shorter intertest interval) using both clinic tests and self-tests. For example, if a regular tester tests three times a year in a clinic, his intertest interval would be 120 days; if he supplements this with one self-test per year, his intertest interval would be 90 days, and he would have a 25% chance that each test would be a self-test. Risk-based testers supplement their clinic-based tests by increasing the probability of risk-based tests by 10% and 20%. For example, if a risk tester has a 40% chance of taking a clinic-based test after a risk event and self-testing increases the probability of risk-based testing by 10%, his likelihood of testing becomes 50% with a 40% chance of taking a clinic-based test and a 10% chance of self-testing.

We hypothesized that the impact of HIVST on MSM will differ in cities with different underlying patterns of HIV testing, access to HIV prevention and care, and epidemiological characteristics of MSM. King County (home to Seattle) is one of the first jurisdictions to reach the World Health Organization’s 90-90-90 goals [62] and has witnessed a rapid scale-up of PrEP [63]. HIV prevalence among MSM in Seattle is estimated to be 11% according to Dr Susan Buskin (personal communication, October 2017), and the rate of new HIV diagnoses has been declining over the last decade [64]. In contrast, the HIV prevalence among MSM in Atlanta is estimated to be much higher at 28% [65], with fewer MSM aware of their HIV infection status [66], exhibiting less access to PrEP and a more diverse population with significant disparities in HIV by race [67]. The data sources for parameterizing our model for each city are presented in Table 3, with additional detail in the Appendix Table A1. As the original model was structured to assess racial differences in the incidence, where race-stratified estimates were available, we used those estimates to create race-weighted composite estimates for the overall population in each city. Both HIV testing and network-based behavioral data were collected in a prospective cohort study [65] and an egocentric sexual network study [68] of MSM in Atlanta and cross-sectional surveys of MSM in Seattle [55,69].

We estimated parameters to characterize HIV testing behaviors in both Atlanta and Seattle, including the proportions of the four tester types (Table 4) and mean test intervals and test likelihood for opportunistic-only, regular, and risk-based testers (Table 5). Of note, these HIV testing parameters only apply to MSM who are not on PrEP (MSM on PrEP received a diagnostic HIV test at regular 3-month intervals). For Seattle, the proportions of the four tester types, the mean intervals between regular tests stratified by the frequency of AI, and the likelihood that opportunistic testers will seize a testing opportunity were estimated using data obtained from 361 HIV-negative and unknown-status MSM aged 18-39 years who participated in the Seattle Pride Survey [63] in 2013 and 2014 and reported living in Washington State. The Pride Survey is an annual convenience sample of self-identified MSM enrolled from along the Seattle Pride Parade route to complete a self-administered survey to monitor HIV risk behaviors and the uptake of treatment and prevention interventions. The 2013 and 2014 surveys included the following question: “How many HIV tests did you have in the last two years?” To calculate the mean interval in days between regular tests, we divided 2 years (730.5 days) by the mean number of HIV tests reported in the last 2 years among the participants reporting their last test as a “routine test,” stratified by the number of AI partners in the last year (0-2 vs 3+ partners). In addition, we calculated the likelihood that opportunistic-only testers will seize a testing opportunity by dividing the mean number of HIV tests reported in the last 2 years by the expected number of opportunities to test in a 2-year period (4 opportunities: 2 each year, based on expert opinion) among participants who reported the reason for their last test as something other than risk-based or routine.

For MSM in Atlanta, the proportions of the four tester types were estimated using data from the Man Project [68] and InvolveMENt [65]. The Man Project was a cross-sectional, chain-referral sexual network study among 314 MSM; however, InvolveMENt was a prospective cohort study among 803 black and white non-Hispanic MSM aged 18-39 years. Participants for both the studies completed self-administered computer-based questionnaires that assessed demographics as well as risk and prevention behaviors for both themselves and their most recent sex partners (up to the last 10 partners in the last 12 months for the Man Project and the last 5 partners in the previous 6 months for InvolveMENt). We evaluated the mean interval in days between regular tests using data from the PUMA Survey [70], an internet-based survey of MSM in the United States conducted from November 30, 2010 to December 19, 2010 (n=1251). Men who reported regularly testing for HIV were asked how often they tested (in months). Then, we calculated the mean number of months between regular tests, but unlike for the parameters of MSM in Seattle, we were unable to stratify this interval by the number of AI partners. Furthermore, we calculated the likelihood that opportunistic-only testers seized an opportunity from data collected in the Annual American Men’s Internet Survey of Behaviors of Men who have Sex with Men in the United States (AMIS) [7,69,71]. AMIS is an annual cross-sectional behavioral survey of MSM in the United States in which participants complete a Web-based survey that includes questions in the following domains: demographics, sexual behavior, HIV testing history, drug and alcohol use, and HIV prevention services exposure. As with the Seattle data, the likelihood was calculated among participants who self-reported living in Georgia and reported testing for reasons other than risk or routine by dividing the mean number of HIV tests reported among them in the last 2 years by the expected number of opportunities in that period.

Where local data for parameterization were unavailable for both cities, we used estimates from national Web-based surveys conducted by research teams involving members of our group. The likelihood of seizing a testing opportunity among regular and risk-based testers was estimated by calculating the proportion of individuals who reported currently testing on a regular schedule and reported that their last test was in response to an opportunity using data from the Internet Ethics and Incentives Study [7,37,69]. Specifically, to parameterize this model, we added questions to the 2016 cycle of AMIS [7,37,69] to ascertain the likelihood of testing following a risk event and the time from the risk event to test. Respondents were asked whether they tested in response to each of the following events: the last time they had CAI with a nonmain partner, the last time they had CAI with a serodiscordant partner, and the last time they started a new relationship. In addition, we calculated the likelihood of testing following each event as the proportion of individuals who reported testing in response to such an event among those who reported the event. Subsequently, men who reported that they last tested in response to CAI with a nonmain partner, CAI with a serodiscordant partner, or starting a new relationship were asked how many weeks following the event they tested. The time from event to test was calculated as the mean number of weeks for each type of event separately.

Using the above parameters, we simulated the sexual, vital, and epidemiological dynamics of HIV transmission among 10,000 MSM for 50 years using Seattle- and Atlanta-specific parameterizations and, at equilibrium, reproduced the epidemiological and demographic outcomes observed in Seattle and Atlanta, respectively. In addition, we calibrated the baseline models by varying the rate of AI within partnerships to closely match the estimates of HIV prevalence that were 28% in Atlanta and 11% in Seattle among MSM (Figure 1). We used a multiplier of 1.5 in Atlanta and 3.45 in Seattle to adjust the AI rate, which resulted in simulated epidemics equilibrating at 27.24% (95% CI: 27.79-28.35) in Atlanta and 11.55% (95% CI: 11.36-11.73) in Seattle. To select the multiplier, we varied the AI multiplier by 0.01 within preselected ranges of 1.45-1.55 and 3.4-3.5 for Atlanta and Seattle, respectively. Then, we identified the value that resulted in an average equilibrium HIV prevalence (from 100 simulations for each value for 50 years each) closest to the target estimates.

The next steps in our research will be to introduce each self-test scenario into the simulated populations and project epidemic outcomes over a 10-year time horizon. We will further investigate how different test sensitivities and detection windows affect the impact of HIVST.