Wrote the paper: ULA.Model formulation: ULA JWM. Model analyses: ULA. Computer programming and multivariate sensitivity analyses at the Pittsburgh Supercomputing Center: GH AWW. Interpreted results and edited the manuscript: JWM.
John W. Mellors reports that he is a consultant to Gilead Sciences, Merck, and RFS Pharmaceuticals, has received grant support from Merck, and owns share options in RFS Pharmaceuticals. This does not alter the authors' adherence to all the PLoS ONE policies on sharing data and materials.
The potential for emergence and spread of HIV drug resistance from rollout of antiretroviral (ARV) pre-exposure prophylaxis (PrEP) is an important public health concern. We investigated determinants of HIV drug resistance prevalence after PrEP implementation through mathematical modeling.
A model incorporating heterogeneity in age, gender, sexual activity, HIV infection status, stage of disease, PrEP coverage/discontinuation, and HIV drug susceptibility, was designed to simulate the impact of PrEP on HIV prevention and drug resistance in a sub-Saharan epidemic.
Analyses suggest that the prevalence of HIV drug resistance is influenced most by the extent and duration of inadvertent PrEP use in individuals already infected with HIV. Other key factors affecting drug resistance prevalence include the persistence time of transmitted resistance and the duration of inadvertent PrEP use in individuals who become infected on PrEP. From uncertainty analysis, the median overall prevalence of drug resistance at 10 years was predicted to be 9.2% (interquartile range 6.9%–12.2%). An optimistic scenario of 75% PrEP efficacy, 60% coverage of the susceptible population, and 5% inadvertent PrEP use predicts a rise in HIV drug resistance prevalence to only 2.5% after 10 years. By contrast, in a pessimistic scenario of 25% PrEP efficacy, 15% population coverage, and 25% inadvertent PrEP use, resistance prevalence increased to over 40%.
Inadvertent PrEP use in previously-infected individuals is the major determinant of HIV drug resistance prevalence arising from PrEP. Both the rate and duration of inadvertent PrEP use are key factors. PrEP rollout programs should include routine monitoring of HIV infection status to limit the spread of drug resistance.
Antiretroviral (ARV) pre-exposure prophylaxis (PrEP) is a promising HIV prevention strategy
We have developed and analyzed a population model of heterosexual HIV transmission and disease progression to assess the impact of PrEP implementation
For the present work, we extended our published model
PARAMETER | UNIT | SENSITIVITY | SCENARIO | REFERENCE | ||
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Fraction of individuals enrolled into PrEP (coverage) | per year | 0.15–0.60 | 0.60 | 0.30 | 0.15 | Assumption |
Time period to achieve target coverage | year | 1–10 | 1 | 5 | 10 | Assumption |
Efficacy of PrEP against sensitive virus (ξ) | - | 0.25–0.75 | 0.75 | 0.50 | 0.25 | Assumption |
(Relative) Efficacy of PrEP against resistant virus (ξR = ι |
- | 0.00–0.25 |
0.25 |
0.125 |
0 |
Assumption |
Adherence (θ) | - | 0.25–0.75 | 0.75 | 0.50 | 0.25 | Assumption |
PrEP discontinuation rate in susceptible individuals | per year | 0.05–0.25 | 0.05 | 0.10 | 0.25 | Assumption |
Duration of inadvertent PrEP use in those who become infected on PrEP | year | 0.5–3 | 0.5 | 1 | 3 | Assumption |
Rate of inadvertent PrEP uptake in previously-infected individuals | per year | 0.05–0.25 | 0.05 | 0.10 | 0.25 | Assumption |
Duration of inadvertent PrEP use in previously-infected individuals | year | 0.5–3 | 0.5 | 1 | 3 | Assumption |
Time to development of acquired resistance in inadvertent PrEP users who become infected on PrEP (t1) | year | 0.167–0.5 | 0.5 | 0.25 | 0.167 |
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Rate of development of acquired resistance in inadvertent PrEP users who become infected on PrEP | per year | derived | −LN(1−0.99 |
−LN(1−0.99 |
−LN(1−0.99 |
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Time to development of acquired resistance in inadvertent PrEP users who are previously infected (t2) | year | 0.083–0.25 | 0.25 | 0.125 | 0.083 | |
Rate of development of acquired resistance in inadvertent PrEP users who are previously infected | per year | derived | −LN(1−0.99 |
−LN(1−0.99 |
−LN(1−0.99 |
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Infectivity of donor with transmitted resistance |
per act | 0.5–1.0 |
0.5 | 0.75 | 1 | |
Infectivity of donor with acquired resistance |
per act | 0.5–1.0 |
0.5 | 0.75 | 1 | |
Probability of transmission of resistant versus sensitive virus from donor with transmitted resistance | - | 0.75–1.0 | 0.75 | 0.9 | 1 | |
Probability of transmission of resistant versus sensitive virus from a donor with acquired resistance | - | 0.5–1.0 | 0.5 | 0.75 | 1 | |
Probability of transmission of resistant versus sensitive virus from a donor with wild-type or reverted to wild-type virus to a recipient on PrEP | - | 0.01–0.25 | 0.01 | 0.05 | 0.25 | Assumption |
Persistence time of transmitted resistance in recipients not on PrEP | year | 1–5 | 1 | 2 | 5 | |
Persistence time of transmitted resistance in recipients after PrEP discontinuation | year | 1–5 | 1 | 2 | 5 | |
Persistence time of acquired resistance after PrEP discontinuation | year | 0.083–1 | 0.083 | 0.5 | 1 | |
Factor increase in rates of sexual partnership change of individuals, both susceptible and infected, while on PrEP (i.e., risk compensation) | - | 1.0–2.0 | 1.0–2.0 | 1.0–2.0 | 1.0–2.0 | Assumption |
HIV disease progression
HIV infectivity and disease progression
*Relative to infectivity (per sex act probability of transmission) of donor with wild-type virus based on stage of infection, γΩ
Latin Hypercube Sampling (uniform distribution).
Our model represents the transmission of HIV as a Poisson process
We sub-classified HIV-infected individuals based on their PrEP status (naïve, on PrEP or off PrEP), HIV drug susceptibility (drug-sensitive or drug-resistant), type of drug resistance (transmitted or acquired), and virus population dynamics of drug-resistant HIV (persistence of resistance or reversion of resistance, the latter either from genetic reversion of virus to wild-type or overgrowth of resistant virus by wild-type virus) into 22 different HIV drug susceptibility strata (
HIV Donor | HIV Recipient | |||
Case | PrEP Status | Majority Variant | PrEP Status | Transmitted Variant |
1 | − | Wild-type | − | Sensitive |
2 | + | Wild-type | − | Sensitive |
3 | − | Wild-type | + | Sensitive |
4 | − | Wild-type | + | Resistant |
5 | + | Wild-type | + | Sensitive |
6 | + | Wild-type | + | Resistant |
7 | − | Acquired Resistant | − | Sensitive |
8 | − | Acquired Resistant | − | Resistant |
9 | − | Acquired Resistant | + | Sensitive |
10 | − | Acquired Resistant | + | Resistant |
11 | + | Acquired Resistant | − | Sensitive |
12 | + | Acquired Resistant | − | Resistant |
13 | + | Acquired Resistant | + | Sensitive |
14 | + | Acquired Resistant | + | Resistant |
15 | − | Transmitted Resistant | − | Sensitive |
16 | − | Transmitted Resistant | − | Resistant |
17 | − | Transmitted Resistant | + | Sensitive |
18 | − | Transmitted Resistant | + | Resistant |
19 | + | Transmitted Resistant | − | Sensitive |
20 | + | Transmitted Resistant | − | Resistant |
21 | + | Transmitted Resistant | + | Sensitive |
22 | + | Transmitted Resistant | + | Resistant |
23 | − | Reverted to Wild-type | − | Sensitive |
24 | − | Reverted to Wild-type | + | Sensitive |
25 | − | Reverted to Wild-type | + | Resistant |
The model's dynamical behavior was investigated using numerical methods. The key model outputs were: i) HIV incidence; ii) HIV prevalence; iii) cumulative new HIV infections; iv) proportion of cumulative new infections with transmitted resistance; v) overall prevalence of HIV drug resistance (transmitted plus acquired); vi) prevalence of transmitted resistance; and vii) prevalence of acquired resistance. PrEP was introduced (once daily oral dosing of a single antiretroviral drug, e.g. tenofovir disoproxil fumarate) at endemic equilibrium when HIV prevalence in sexually active adults (15–49 year-olds) was approximately 20%. We made comparisons between the epidemics with and without PrEP at each simulation time-step over a 10 year interval after PrEP introduction.
We performed sensitivity analyses
The impact of PrEP was next determined by simulating three different scenarios: optimistic, realistic and pessimistic (
Our mathematical model stratifies the study population by gender, age, sexual activity level, PrEP use, HIV infection status, disease stage and HIV drug susceptibility (
Model Input |
Model Output | |||
Cumulative New Infections Prevented | Prevalence of Overall Resistance |
Prevalence of Transmitted Resistance |
Prevalence of Acquired Resistance |
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PrEP Coverage | 0.52 (26.9) | |||
Adherence | 0.49 (24.0) | |||
Efficacy of PrEP against sensitive virus | 0.42 (17.5) | |||
Infectivity of individuals with acquired resistance | −0.32 (9.9) | |||
PrEP discontinuation rate in susceptible individuals | −0.23 (5.4) | |||
Duration of inadvertent PrEP use in pre-infected individuals | 0.62 (38.8) | 0.32 (10.2) | 0.74 (54.1) | |
Rate of inadvertent PrEP uptake in pre-infected individuals | 0.34 (11.7) | 0.32 (10.5) | 0.27 (7.5) | |
Duration of inadvertent PrEP use in post-infected individuals | 0.30 (9.2) | 0.32 (10.0) | ||
Persistence time of transmitted resistance | 0.28 (7.6) | 0.53 (28.0) | ||
Persistence time of acquired resistance | 0.25 (6.0) |
*Parameters that contribute 5% or more of the variance in the model outcome are shown (SRRC2≥0.05). The reported coefficients were significant with a p-value≤0.05.
Of the total variance in the predicted outcome explained by the regression model. The respective R2 values were: 0.91 (cumulative infections prevented); 0.85 (overall prevalence of resistance); 0.89 (prevalence of transmitted resistance); 0.85 (prevalence of acquired resistance); and 0.89 (resistant cumulative infections).
Proportion of cases with drug-resistant infection in the infected population.
By contrast, the overall prevalence of drug resistance was influenced most by the duration of inadvertent PrEP use (SRRC = 0.62) and the rate of PrEP uptake (SRRC = 0.34) in previously-infected individuals. Together these two parameters explained 50.5% of the variance in overall prevalence of resistance after 10 years. Not surprisingly, the prevalence of transmitted resistance after 10 years was most influenced by the persistence time of transmitted resistance (SRRC = 0.53), explaining 28% of the variance. The rate of PrEP uptake and duration of inadvertent use in previously-infected individuals (SRRC = 0.32) explained another 10.5% and 10.2% of variance in transmitted resistance, respectively. The prevalence of acquired resistance was most sensitive to the duration of inadvertent PrEP use (SRRC = 0.74) and its rate of uptake (SRRC = 0.27) in previously-infected individuals; together these parameters explained 61.6% of the variance in the prevalence of acquired resistance after 10 years. Likewise, the rate (SRRC = 0.40) and duration (SRRC = 0.36) of inadvertent PrEP use in previously-infected individuals were most influential for the proportion of cumulative new infections with transmitted resistance, explaining 28.8% of the variance in this outcome (data not shown). Factors influencing the prevalence of drug resistance when risk compensation was assumed were similar to the above (data not shown).
Panel A shows overall prevalence of HIV drug resistance and Panel B shows cumulative new HIV infections prevented.
For each time point, results of 10,000 simulations are shown as a box-and-whisker plot; representing the median, upper and lower quartiles, and maximum and minimum values.
Non-Targeted | Targeted-by-Age | Targeted-by-Gender | Targeted-by-Activity | |||||||||
O | R | P | O | R | P | O | R | P | O | R | P | |
Overall prevalence |
2.5% | 9.9% | 42.3% | 2.4% | 9.7% | 42.4% | 2.1% | 9.3% | 42.3% | 1.9% | 9.2% | 42.5% |
Prevalence |
0.4% | 2.9% | 27.1% | 0.3% | 2.7% | 27.0% | 0.2% | 2.5% | 26.9% | 0.2% | 2.5% | 26.9% |
Prevalence |
2.2% | 7.0% | 15.2% | 2.1% | 7.0% | 15.4% | 1.9% | 6.8% | 15.5% | 1.7% | 6.6% | 15.6% |
Cumulative new infections prevented | 30.3% | 6.6% | 0.2% | 17.5% | 4.5% | 0.1% | 18.5% | 4.6% | 0.1% | 8.0% | 3.0% | 0.0% |
Resistant cumulative infections |
2.2% | 8.3% | 40.3% | 1.5% | 7.4% | 39.9% | 1.3% | 7.0% | 39.7% | 1.3% | 7.1% | 39.7% |
Decline in HIV prevalence | 26.2% | 6.0% | 0.2% | 16.6% | 4.2% | 0.1% | 16.2% | 4.2% | 0.1% | 7.1% | 2.7% | 0.0% |
Decline in HIV incidence | 32.3% | 7.4% | 0.2% | 25.4% | 6.0% | 0.1% | 20.2% | 5.3% | 0.1% | 8.6% | 3.2% | 0.0% |
*Proportion of cases with drug-resistant infection in the infected population.
Proportion of cumulative new infections with transmitted resistance.
For each scenario, the largest decrease in infections was achieved with the non-targeted strategy and the smallest decrease with the targeted-by-activity strategy (
Univariate sensitivity analyses of resistance prevalence confirmed that the most important factors affecting resistance prevalence were the rate and duration of use of inadvertent PrEP in previously-infected individuals. When no inadvertent PrEP use in previously infected individuals was assumed, there was a major decline in the prevalence of drug resistance (
Panel A shows overall prevalence of HIV drug resistance and Panel B shows cumulative new HIV infections prevented.
Using the targeted-by-gender strategy (PrEP targeted to female population), more infections were prevented in women compared to men. These findings were generally robust (data not shown) to single and multiple changes in the model's key structural assumptions including those related to balance in the supply and demand of sexual partnerships in the population over time
Data from animal studies show that orally administered antiretrovirals can prevent infection of macaques by simian immunodeficiency virus
The current model represents a significant refinement of our earlier version in terms of model structure, parameter assignment and scenario design
Notwithstanding model improvements, sensitivity analyses of infections prevented confirm our earlier findings of the impact of PrEP on HIV prevention
The results of our scenario analyses provide important insight into potential emergence of HIV drug resistance after PrEP implementation. The non-targeted optimistic and realistic scenarios predicted low to moderate prevalence of drug resistance (2.5% and 9.9% respectively) along with high to moderate decreases in cumulative infections (30.3% and 6.6%, respectively). Uncertainty analysis also predicted moderate levels of overall drug resistance. With targeted optimistic and realistic scenarios, the prevalence of resistance was modestly reduced with considerable erosion (up to 70%) of infections prevented. The prevalence of drug resistance rose to over 40% in the pessimistic scenarios with minimal reduction in HIV infections. Sensitivity analyses showed that the key driver of this negative outcome was the high level of inadvertent PrEP use in the already infected population. When the pessimistic scenarios were re-simulated excluding PrEP use in previously-infected individuals, the prevalence of resistance decreased to 4.5%.
There are some important limitations of our current model structure and the assumptions within it. The precise quantitative detail of our predictions will be affected by variations in the sexual activity patterns of different populations, for which data are very limited, especially on sexual mixing patterns. However, we employed a well-established template of sexual behavior
The actual impact of PrEP on drug resistance will depend on the PrEP agent or agents used as well as the biological, behavioral and viral characteristics of the HIV-infected population. Although we do not model a specific PrEP agent, we used resistance-related input estimates that would be expected for a single antiretroviral drug used for PrEP such as tenofovir disoproxil fumarate
We excluded from our analyses the impact of antiretroviral therapy for infected persons and various other influences on transmission (e.g. STDs, circumcision and condom use). These and other refinements will be addressed in future work. Nevertheless, the important conclusion for our modeling is that the spread of HIV drug resistance could be mitigated by limiting inadvertent PrEP exposure in already infected individuals. To accomplish this, PrEP implementation programs would need to be tightly coupled with HIV testing of individuals who are candidates for PrEP and monitoring of PrEP recipients for HIV infection and drug resistance.
Model Equations and Details.
(DOC)