HIV, transmitted drug resistance, and the paradox of preexposure prophylaxis

Abstract

The administration of antiretrovirals before HIV exposure to prevent infection (i.e., preexposure prophylaxis; PrEP) is under evaluation in clinical trials. Because PrEP is based on antiretrovirals, there is considerable concern that it could substantially increase transmitted resistance, particularly in resource-rich countries. Here we use a mathematical model to predict the effect of PrEP interventions on the HIV epidemic in the men-who-have-sex-with-men community in San Francisco. The model is calibrated using Monte Carlo filtering and analyzed by constructing nonlinear response hypersurfaces. We predict PrEP interventions could substantially reduce transmission but significantly increase the proportion of new infections caused by resistant strains. Two mechanisms can cause this increase. If risk compensation occurs, the proportion increases due to increasing transmission of resistant strains and decreasing transmission of wild-type strains. If risk behavior remains stable, the increase occurs because of reduced transmission of resistant strains coupled with an even greater reduction in transmission of wild-type strains. We define this as the paradox of PrEP (i.e., resistance appears to be increasing, but is actually decreasing). We determine this paradox is likely to occur if the efficacy of PrEP regimens against wild-type strains is greater than 30% and the relative efficacy against resistant strains is greater than 0.2 but less than the efficacy against wild-type. Our modeling shows, if risk behavior increases, that it is a valid concern that PrEP could significantly increase transmitted resistance. However, if risk behavior remains stable, we find the concern is unfounded and PrEP interventions are likely to decrease transmitted resistance.

The administration of antiretroviral drugs (ARVs) before HIV exposure to prevent infection (i.e., preexposure prophylaxis; PrEP) is currently under evaluation in clinical trials (1). The PrEP regimens under consideration are based on tenofovir (TDF) alone or in combination with emtricitabine (FTC). Results from phase III efficacy trials are expected in 2010 and several additional trials will begin soon (SI Appendix, Table S1) (2). The results from these trials are widely anticipated because, if PrEP is shown to be safe and effective, it will become an important biomedical intervention for controlling the HIV pandemic. A phase II study of TDF-based PrEP showed daily TDF in HIV-uninfected women to be safe (3). However, because PrEP is based on ARVs, there is concern that wide-scale usage could lead to a substantial increase in transmission of ARV-resistant strains (4). Such an increase would have significant clinical repercussions [as individuals infected with these strains would be limited in their future treatment options (5)], as well as exacerbate the difficulty of controlling the pandemic. In particular, increases in resistance in high-risk communities in resource-rich countries could cause major problems because, after two decades of using ARVs for treatment, the prevalence of transmitted resistance in these communities is already high (10–25%) (6–9). Furthermore, if individuals taking PrEP feel protected against infection and consequently increase their risky behavior (i.e., risk compensation occurs) (1, 10–12), transmitted resistance could potentially escalate. Here we present an innovative mathematical model that we use to predict the potential effects of PrEP interventions in a high-risk community with a high prevalence of transmitted resistance. Specifically, we investigate the potential effects of PrEP interventions in the men-who-have-sex-with-men (MSM) community in San Francisco. We predict the potential impact of PrEP interventions on reducing transmission and also use the model to address the following question: Could a PrEP intervention significantly increase transmitted resistance?

To address this question, we have developed a virologically complex mathematical model consisting of 72 equations; the equations and a detailed description of the model are given in SI Appendix, SI Text. We describe this as the PrEP intervention model. The model enables us to evaluate the effect of PrEP interventions on the transmission dynamics of both wild-type and ARV-resistant strains in a high-risk community where therapeutic treatment is available. A simplified schematic of the model is shown in Fig. 1. We assume, based on the available data, that wild-type strains are more transmissible (i.e., more fit) than resistant strains (13–15). The model includes susceptible individuals (S), individuals infected (I) with wild-type strains (blue) or with ARV-resistant strains (red), and individuals on treatment (T) (Fig. 1). In the model, infected individuals move through three stages of infection before the treatment stage: primary/acute infection, not yet eligible for treatment (i.e., CD4 count > 350 cells/μL), and eligible for treatment (i.e., CD4 ≤ 350 cells/μL) but not on treatment. Individuals not taking PrEP are represented by dotted circles or squares and individuals taking PrEP are represented by solid circles or squares (Fig. 1). In our theoretical framework, we model the emergence, reversion, and reemergence of resistant strains within an individual. Resistance can emerge in individuals who are infected with wild-type strains and taking PrEP or receiving treatment. Reversion of resistance can occur in individuals who develop resistance while taking PrEP (or during treatment) and then come off PrEP (or give up treatment); they revert, because wild-type strains outcompete the resistant strains in the absence of ARVs. Resistance can reemerge in individuals who develop resistance on PrEP, subsequently revert to wild-type, and then initiate treatment. Under these conditions, resistant strains can reemerge quickly, because they are maintained in reservoirs within the individual after reversion to wild-type has occurred. In the absence of PrEP interventions, the PrEP intervention model is similar in structure to the model described in ref. 16 (Materials and Methods).

Fig. 1.

Simplified flow diagram of the PrEP intervention model. The model includes susceptible individuals, infected untreated individuals, and individuals on therapeutic treatment. Susceptible individuals can be infected with wild-type (dark blue arrows) or resistant (red arrows) strains. Individuals not taking PrEP are represented by dotted circles or squares, and individuals taking PrEP are represented by solid circles or squares. Infected individuals can acquire resistance (thick red arrow) if prescribed PrEP before their infection is detectable or if they become infected on PrEP and continue taking PrEP. The model also includes the effect of therapeutic treatment with antiretrovirals and the development of resistance during therapeutic treatment (orange arrow). Resistant strains can revert to wild-type strains when the selection pressure of drug treatment is removed (light blue arrow).

The assumptions made to construct the PrEP intervention model, and the parameter ranges used to characterize PrEP regimens, are informed by data from preclinical studies of PrEP in the rhesus macaque model of simian-human immunodeficiency virus (SHIV)/simian immunodeficiency virus (SIV) infection (17–20) and a phase II study of PrEP in humans (3). The macaque studies have shown that PrEP can be highly effective in preventing infection; for example, the risk of SHIV infection in macaques receiving daily PrEP with FTC or Truvada was 3.8- and 7.8-fold, respectively, lower than in untreated macaques (17). However, macaques exposed to an SIV isolate carrying the TDF resistance mutation (K65R) were not protected by TDF, which suggests PrEP may be less effective against ARV-resistant viruses (19). Substantial reductions in viremia and blunted acute viremias (up to 2log₁₀ reduction) have been observed in a patient failing Truvada and in macaques failing PrEP with FTC, Truvada, or a CCR5 inhibitor (17, 18, 20–22). These results suggest that even when PrEP does not prevent infection it may, by reducing viral load and/or reducing CD4⁺ T-cell depletion, help preserve immune function that could attenuate the course of HIV infection (21). The results also imply that PrEP may be able to reduce infectivity in humans (by reducing viral load) (23) and could therefore indirectly reduce HIV transmission (24–27). The studies of PrEP in macaques have shown that resistance can emerge; for example, although the K65R mutation was not detected in macaques that failed Truvada (17), FTC resistance mutations (M184V/I) did emerge. However, FTC resistance mutations only emerged in two out of the six macaques that failed FTC or Truvada (17), and both of these macaques had high viral loads. Lower acute viremias in the other four macaques may have diminished their risk of acquiring resistance. These data suggest selection of resistance during PrEP may be less frequent than during treatment of established infections (17–19). The macaque studies also provide qualitative information on how drug resistance emerges, and how reversion to wild-type may occur. Macaques that failed PrEP were first infected with wild-type virus and only developed resistance after a few weeks (17). This is similar to how resistance is selected when an individual is receiving treatment (28). Rapid reversions of acquired TDF and FTC mutations have been observed in humans after stopping therapeutic treatment (29–31). Therefore, resistant viruses selected while on PrEP may also be rapidly outcompeted by the wild-type strains once the pressure of PrEP is removed.

To minimize the risk of resistance emergence, we assumed individuals in resource-rich countries will be tested for HIV infection before they are initially prescribed PrEP and each time their prescription is renewed. They will only be prescribed PrEP if they test negative for HIV infection. However, even under these conditions, some infected individuals could be on PrEP and at risk for developing resistance. This could occur for two reasons. First, individuals could become infected when they are taking PrEP (as PrEP is unlikely to be 100% effective) and remain at risk for developing resistance until they are retested to renew their prescription. Second, recently infected individuals could inadvertently be prescribed PrEP before their infection is detectable because current HIV tests do not detect very recent infection (32, 33). Hence, increasing testing frequency and/or reducing the length of the window period of an HIV test (i.e., the time period between infection and a positive test) will decrease the emergence of resistance. Fig. 2 illustrates how we model the emergence of resistance to PrEP as a function of the length of the window period and the frequency of testing. Individuals who are susceptible when they are first prescribed PrEP and become infected when taking PrEP are represented as gray squares (solid lines). They are at risk for developing resistance (shown as thick red arrows in Fig. 2) until they need to renew their prescription and are retested (shown as thin green arrows in Fig. 2). Very recently infected individuals (i.e., in phase A1 in our model; Fig. 2) can inadvertently be prescribed PrEP; they are represented by gray circles (solid lines). These individuals are at risk for developing resistance (shown as thick red arrows in Fig. 2) until they need to renew their prescription and are retested; at that point, their infection would be detected and they would be taken off PrEP (green arrows in Fig. 2). The testing frequency will therefore determine the length of time that an individual is at risk for developing resistance. When making our predictions, we varied testing frequency from every month to every 6 mo.

Fig. 2.

Simplified flow diagram representing disease progression, the window period of an HIV test, and testing frequency. The primary infection phase is split into two phases: (i) the phase where the infection is not detectable with HIV tests (phase A1) and (ii) the phase where the infection is detectable (phase A2). Susceptibles can go on and off PrEP. Infected individuals move through four stages of infection before treatment: phase A1, phase A2, not eligible for treatment (i.e., CD4 count > 350 cells/μL), and eligible for treatment (i.e., CD4 ≤ 350 cells/μL) but not on treatment. Infected individuals off PrEP (dotted circle) can inadvertently be prescribed PrEP (gray arrow) but only during a very short period after the infection has occurred (i.e., during phase A1). In contrast, infected individuals off PrEP (dotted circle) with detectable infection (i.e., in phase A2 or in not treatment-eligible phase) cannot be prescribed PrEP. Infected individuals who were inadvertently prescribed PrEP (solid circle) and individuals who were infected despite taking PrEP (solid square) can develop resistance (red arrow) as long as they are on PrEP. The testing frequency (or, equivalently, the length of the PrEP prescription) determines when infected individuals on PrEP will stop taking PrEP once the infection is detectable.

Before using the model to investigate the impact of PrEP interventions, we calibrated the model, using Monte Carlo filtering techniques (34), to reflect the current epidemiological conditions in the MSM community in San Francisco (Materials and Methods). Based on empirical data, the current prevalence of HIV is estimated to be ~27% (35), and ~16% of new infections are estimated to be due to resistant strains (6). After Monte Carlo filtering, we obtained an excellent fit to the empirical data; specifically, our simulations generated a prevalence of 27% [median value; interquartile range (IQR) 19–35%] and resulted in 16% (median value; IQR 11–21%) of new infections due to resistant strains. We used the filtered parameter set to simulate the model and to predict the potential effect of a PrEP intervention over a 10-y period. Because the characteristics of PrEP interventions and PrEP regimens are unknown, we used uncertainty and sensitivity analyses to evaluate their potential impact. To conduct these analyses, we specified ranges for experimental parameters that characterized PrEP interventions (e.g., coverage) or PrEP regimens (e.g., efficacy); ranges are listed in SI Appendix, Tables S2 and S3. The main experimental parameters for specifying PrEP regimens were: (i) efficacy in preventing infections with wild-type strains (range: 30–90%); (ii) relative efficacy in preventing infection with resistant strains (range: zero to half as efficient against resistant strains compared with wild-type); (iii) degree of PrEP-induced reduction of viremia during primary infection (range: no reduction to 2log₁₀); (iv) rate of emergence of resistance in infected individuals on PrEP (range: 10–99% per y); and (v) reversion rates of resistant strains (that were acquired when an individual was taking PrEP) to wild-type strains (range: 6 mo or less). We also assumed resistant strains acquired through sexual transmission could revert and that reversion would take at least 2 y, as has been observed in empirical studies (5, 36–38).

Results

The model predictions for the percentage reduction in transmission (due to wild-type plus resistant strains) after 10 y of PrEP use in the MSM community in San Francisco is shown in the form of response hypersurfaces in Fig. 3 A and B. Fig. 3A was generated under the assumption that risk behavior would remain stable, whereas Fig. 3B was generated assuming risk compensation would occur (i.e., risk behavior would increase). The response hypersurfaces are color-coded based on the degree of reduction in transmission; dark red corresponds to a 70% reduction in Fig. 3A and a 50% reduction in Fig. 3B. Taken together, the two hypersurfaces (Fig. 3 A and B) show the predicted effect of a PrEP intervention on reducing transmission as a function of coverage (i.e., the percentage of men in the MSM community who use PrEP), efficacy, and increases in risky behavior. Not surprisingly, a substantial number of infections would be prevented if a highly effective PrEP regimen is used, coverage is high, and risk behavior does not increase (Fig. 3A). However, our results show that risk compensation could significantly reduce the effectiveness of a PrEP intervention and—under certain conditions—even increase transmission (Fig. 3B). The black line in Fig. 3B delimits the threshold at which a PrEP intervention has no effect on reducing transmission; above the line, transmission increases and below the line transmission decreases. Surprisingly, our modeling shows a PrEP intervention could still have a significant effect on preventing infections even if risk behavior increased fairly substantially (Fig. 3B). For example, even if MSM completely gave up using condoms and increased their annual rate of acquiring new sex partners by 50%, a PrEP intervention could prevent 15% of infections over a decade (Fig. 3B). Only a very substantial increase in risk behavior (i.e., no condom use and more than a 70% increase in the rate of acquiring sex partners) after the introduction of a PrEP intervention would lead to an increase in transmission (Fig. 3B).

Fig. 3.

Nonlinear response surfaces, including interaction terms, were constructed from data generated by the PrEP intervention model. (A) Response surface of the percentage of cumulative infections prevented over 10 y after introducing PrEP assuming no increase in risk behavior as a function of the coverage of PrEP (SRC = 0.45, 95% CI = 0.42;0.47) versus the efficacy of PrEP against wild-type strains (SRC = 0.76, 95% CI = 0.74;0.78). (B) Response surface of the percentage of cumulative infections prevented over 10 y after introducing PrEP assuming risk compensation occurs as a function of the increase in the number of new sex partners per y (SRC = −0.47, 95% CI = −0.50;−0.45) versus decrease in the use of condoms (SRC = −0.19, 95% CI = −0.21;−0.17). The black line delimits the threshold at which a PrEP intervention has no effect on reducing transmission; above the line transmission increases, and below the line transmission decreases. (C) Response surface of the proportion of new infections due to resistant viruses 10 y after introducing PrEP assuming no increase in risk behavior as a function of the coverage of PrEP (SRC = 0.33, 95% CI = 0.31;0.35) versus the efficacy of PrEP against wild-type strains (SRC = 0.47, 95% CI = 0.45;0.49).

Viral load determines infectivity and individuals have the highest viral loads during primary infection (39, 40). Consequently, it has been suggested that PrEP regimens that reduce viral load during primary infection could indirectly contribute to reducing transmission. To assess the potential magnitude of such an effect, we calculated the percentage of new infections in the MSM community in San Francisco that are caused by individuals in the primary stage (technical details are in SI Appendix, SI Text). We found only a small fraction (6% median value; IQR 5–7%) of new infections were caused by individuals in the primary phase; this is because relatively few of the infected MSM were in this very infectious stage at any particular time. Consequently, our modeling showed that even if PrEP regimens reduced viremia during primary infection by as much as 2log₁₀, this would have a negligible effect on decreasing transmission, regardless of whether or not risk compensation occurred (SI Appendix, Fig. S1); standardized regression coefficients (SRCs) are given in SI Appendix, Tables S4 and S5. We note that it is possible that a PrEP-induced reduction in viremia during primary infection could have a significant effect on reducing incidence in other communities where primary infection is causing a large proportion of new infections. We also found that, whether or not risk behavior increased, neither the rate of emergence of resistance while on PrEP nor the testing frequency of individuals taking PrEP had a significant effect on increasing transmitted resistance (SI Appendix, Fig. S2 and SI Section 6); SRCs are given in SI Appendix, Tables S4 and S5.

Currently, ~16% of the new infections in the MSM community in San Francisco are due to resistant strains. Our modeling shows that a decade after a PrEP intervention is implemented, regardless of whether risk compensation occurs or not, over a third of new infections could be due to resistant strains. Specifically, the proportion of new infections due to resistant strains could increase from the current value of ~16% to either 35% (median value; IQR 26–43%) if risk behavior remains constant or to 38% (median value; IQR 29–48%) if risk compensation occurs. As efficacy and coverage increase, so does the proportion of new infections due to resistant strains (Fig. 3C) (SRCs are given in SI Appendix, Tables S4 and S5). Taken together, our results (Fig. 3 A and C) indicate that PrEP interventions that will be the most beneficial in terms of reducing the overall number of infections will also be the most detrimental in terms of increasing the proportion of new infections due to resistant strains. However, these results do not allow us to determine whether the number of new infections due to resistant strains is actually increasing or only appears to be increasing.

To predict whether PrEP could increase the number of new infections due to resistant strains, we calculated, for each simulation, a ratio for the absolute number of infections (ANI) in the presence and absence of a PrEP intervention. This ratio was calculated by dividing the predicted cumulative number of new infections (CNNI) in the decade after introducing PrEP by the predicted CNNI for the same time period assuming PrEP was not available. An ANI ratio < 1 signifies a PrEP intervention would decrease the CNNI, whereas an ANI ratio > 1 signifies a PrEP intervention would increase the CNNI. We calculated the ANI ratio for wild-type and resistant strains separately. Our modeling shows that the proportion of new infections due to resistant strains will always increase (Fig. 4, where Fig. 4A assumes risk compensation occurs and Fig. 4B assumes risk behavior remains stable). However, we find that the number of infections due to resistant strains could either increase (red data in Fig. 4 A and B) or decrease (black data in Fig. 4 A and B). We define the paradox of PrEP to occur when the proportion of new infections caused by resistant strains increases but the actual number of new infections due to resistant strains decreases.

Fig. 4.

Relationship between the proportion of new infections that are due to resistant viruses 10 y after introducing PrEP and the ANI ratio for resistant strains (A) assuming risk compensation occurs and (B) assuming no increase in risk behavior. DR, drug-resistant; TDR, transmitted drug resistance.

We find—if risk compensation occurs—that the proportion of infections caused by resistant strains will increase because of one of three mechanisms: (i) increased transmission of resistant strains and decreased transmission of wild-type strains (black data in Fig. 5A); (ii) increased transmission of wild-type strains coupled with an even greater increase in transmission of resistant strains (green data in Fig. 5A); and (iii) reduced transmission of resistant strains coupled with an even greater reduction in transmission of wild-type strains (blue data in Fig. 5A). Therefore, if risk behavior increases, the paradox of PrEP could occur (as shown by the blue data in Fig. 5A), but would be unlikely (it only occurred in 99 out of 1,089 simulations). In contrast, if risk behavior remains stable, we find the paradox of PrEP is likely to occur (it occurred in 805 out of 1,071 simulations and is shown by the blue data in Fig. 5B). The threshold conditions at which this paradox occurs are shown in Fig. 5C as a function of the efficacy of PrEP against wild-type strains and the relative efficacy against resistant strains; the threshold is delimited by the black line. We find that the paradox of PrEP is likely to occur if the efficacy of PrEP regimens in protecting against infection with wild-type strains is greater than 30% and the relative efficacy in protecting against infection with resistant strains is greater than 0.2 but less than the efficacy against wild-type (Fig. 5C). Our predictions show, if risk behavior remains stable, that the concern that PrEP interventions could lead to significant increases in transmission of resistant strains is unfounded. In fact, contrary to current expectations, we have found PrEP interventions are likely to decrease transmission of resistance.

Fig. 5.

Results from the PrEP intervention model. Scatterplots of the ANI ratio for resistant strains versus the ANI ratio for wild-type strains 10 y after introducing PrEP (A) assuming risk compensation occurs and (B) assuming no increase in risk behavior; dots are color-coded according to the values of the ANI ratios: blue if both ratios < 1; green if both ratios > 1; and black if the ANI ratio for resistant strains > 1 and the ANI ratio for wild-type strains < 1. (C) Response surface of the ANI ratio for resistant strains 10 y after introducing PrEP assuming no increase in risk behavior as a function of the efficacy of PrEP against wild-type strains (SRC = −0.30, 95% CI = −0.32;−0.28) versus the relative efficacy of PrEP (SRC = −0.81, 95% CI = −0.86;−0.83). The black line delimits the threshold at which a PrEP intervention would have no effect on reducing the number of resistant infections; to the right of the line the number of resistant infections decreases, and to the left of the line the number increases. (D) Response surface of the ANI ratio for resistant strains 10 y after introducing PrEP assuming risk compensation occurs as a function of the increase in the number of new sex partners per y (SRC = 0.62, 95% CI = 0.59;0.64) versus the percentage decrease in the use of condoms (SRC = 0.24, 95% CI = 0.21;0.27). The black line delimits the threshold at which a PrEP intervention would have no effect on increasing the number of resistant infections; below the line the number decreases, and above the line the number increases.

Our modeling shows, however, that if risk compensation occurs, PrEP interventions could significantly increase the number of infections due to resistant strains (Fig. 5D). The degree of increase will be determined by the degree of risk compensation, specifically the increase in the number of sex partners per year and/or the decrease in condom usage (Fig. 5D). The black line in Fig. 5D delimits the threshold conditions for the paradox of PrEP; below the line the number of resistant infections decreases, and above the line the number of resistant infections increases. Our results show that even a low level of risk compensation could increase the number of resistant infections (Fig. 5D), and a moderate increase in risky behavior could substantially increase the number of resistant infections (Fig. 5D). For example, a 40% increase in the number of partnerships per year and a 50% decrease in the use of condoms could increase the number of resistant infections by 50% (i.e., ANI ratio = 1.5) (Fig. 5D). If risk compensation occurs, our results show that it is a very valid concern that PrEP interventions could lead to significant increases in transmission of resistant strains. Consequently, it is essential to develop new regimens with high efficacy against resistant strains, and our results reinforce the importance of integrating PrEP with existing effective structural and behavioral prevention strategies.

Discussion

If the results from the phase III trials ending in 2010 show moderate to high efficacy, then PrEP interventions could be implemented in the near future in resource-rich countries. We have shown PrEP could significantly reduce transmission in the MSM community in San Francisco even if efficacy is only moderate, provided coverage is high and risk compensation does not occur. High coverage may be attainable: recent surveys indicate ~70% of MSM in California and in Massachusetts have stated they would be willing to take PrEP on a daily basis if it were proven safe and effective (41, 42); furthermore, MSM reporting risky behaviors were more likely to anticipate using PrEP (42). Although our quantitative results are specific to the MSM community in San Francisco, the qualitative insights we have gained are applicable to any high-risk community where treatment has been readily available for many years and current levels of transmitted resistance are already high.

Our modeling has shown that PrEP interventions will have complex effects on the transmission dynamics of HIV in resource-rich countries where resistant strains are already circulating. Specifically, we have found that PrEP interventions could increase or decrease transmission of resistant strains, and increase or decrease transmission of wild-type strains. We have predicted that the proportion of new infections caused by resistant strains is likely to rise substantially after the introduction of PrEP. This will indicate that there is a cause for concern regarding increasing resistance. However, our modeling has revealed several mechanisms can cause this increase. If risk compensation occurs, we have found the increase will most likely be the result of decreasing transmission of wild-type strains and increasing transmission of resistant strains. Hence, it will be a valid concern that PrEP interventions are increasing resistance. In contrast, we have found that if risk behavior remains stable, the concern is likely to be unfounded. Our modeling has shown that an increase in the proportion of new infections caused by resistant strains is likely to be the result of reduced transmission of resistant strains coupled with an even greater reduction in transmission of wild-type strains. Under these conditions, resistance would appear to be increasing, but would actually be decreasing. When PrEP interventions are implemented, public health officials should be prepared for the paradox of PrEP.

Materials and Methods

To predict the potential impact of PrEP interventions, we first modeled the current HIV epidemic in the MSM community in San Francisco. To do this, we used a model that one of us (S.B.) had published previously which specifies the transmission dynamics of wild-type and resistant strains in the presence of therapeutic programs (16). This model had been parameterized using epidemiological, clinical, and behavioral data to reflect the HIV epidemic in the MSM community in San Francisco (16). Consequently, we used the same parameter values in our current analysis as had been used in ref. 16. For completeness, we include these parameter values in the tables in SI Appendix, SI Text. SI Appendix, Table S6 lists demographic and behavioral parameters, SI Appendix, Tables S7–S9 list parameters that characterize the natural history of HIV infection, and SI Appendix, Table S10 lists parameters that characterize the current therapeutic programs and regimens in San Francisco.

Before modeling PrEP interventions, we calibrated the model using Monte Carlo filtering to reflect current epidemiological conditions in the MSM community in San Francisco. Before filtering, we sampled ranges of 46 of the model parameters 10,000 times using Latin hypercube sampling (43, 44). These parameter ranges are listed in SI Appendix, Tables S2, S3, and S6–S10. We used the 10,000 parameter sets to conduct 10,000 simulations and then calculated the HIV prevalence and level of transmitted drug resistance each simulation generated. To calibrate our model, we filtered these 10,000 simulations using HIV prevalence and level of transmitted drug resistance as filtering criteria. We used Kolmogorov–Smirnov tests to compare the distributions of the model's parameters before and after filtering, as Monte Carlo filtering reduces parameter space. The distribution of 14 of the 46 parameters was found to be statistically different after filtering (SI Appendix, Fig. S3). Filtering reduced the initial sample of 10,000 parameter sets to 1,071 for the analysis with no change in risk behavior (SI Appendix, Fig. S4) and from 10,000 to 1,089 for the analysis with risk compensation. For both analyses, the filtered parameter sets led to an HIV prevalence of 27% (median value; IQR 19–35%) and 16% (median value; IQR 11–21%) of new infections due to resistant strains.

We then expanded the model to include PrEP interventions. We used the expanded model to investigate characteristics of PrEP programs (e.g., coverage) and regimens (e.g., efficacy); model equations and technical details are in SI Appendix, SI Text. The filtered parameter sets were used in the PrEP intervention modeling. We conducted two analyses: one assuming risk behavior would remain stable after the introduction of PrEP and one allowing for risky behavior to increase (i.e., for risk compensation to occur). Risk compensation was modeled by increasing the rate of acquiring new sex partners and/or decreasing condom usage (technical details are in SI Appendix, SI Text).

We analyzed our results by calculating SRCs with their 95% confidence intervals (CIs) and fitting nonlinear response hypersurfaces (using multivariate regression) to our filtered simulated data; further details are in SI Appendix, SI Text.