Figures
Abstract
Objective
To project the HIV/AIDS epidemics among men who have sex with men (MSM) under different combinations of HIV testing and linkage to care (TLC) interventions including antiretroviral therapy (ART) in Beijing, China.
Methods
Using a mathematical model to fit prevalence estimates from 2000–2010, we projected trends in HIV prevalence and incidence during 2011–2020 under five scenarios: (S1) current intervention levels by averaging 2000–2010 coverage; (S2) increased ART coverage with current TLC; (S3) increased TLC/ART coverage; (S4) increased condom use; and (S5) increased TLC/ART plus increased condom use.
Results
The basic reproduction number based upon the current level of interventions is significantly higher than 1 ( confidence interval (CI), 1.83–2.35), suggesting that the HIV epidemic will continue to increase to 2020. Compared to the 2010 prevalence of 7.8%, the projected HIV prevalence in 2020 for the five prevention scenarios will be: (S1) Current coverage: 21.4% (95% CI, 9.9–31.7%); (S2) Increased ART: 19.9% (95% CI, 9.9–28.4%); (S3) Increased TLC/ART: 14.5% (95% CI, 7.0–23.8%); (S4) Increased condom use: 13.0% (95% CI, 9.8–28.4%); and (S5) Increased TLC/ART and condom use: 8.7% (95% CI, 5.4–11.5%). HIV epidemic will continue to rise (
) for S1–S4 even with hyperbolic coverage in the sensitivity analysis, and is expected to decline (
) for S5.
Citation: Lou J, Blevins M, Ruan Y, Vermund SH, Tang S, Webb GF, et al. (2014) Modeling the Impact on HIV Incidence of Combination Prevention Strategies among Men Who Have Sex with Men in Beijing, China. PLoS ONE 9(3): e90985. https://doi.org/10.1371/journal.pone.0090985
Editor: Harry Zhang, Old Dominion University, United States of America
Received: October 17, 2013; Accepted: February 5, 2014; Published: March 13, 2014
Copyright: © 2014 Lou et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: Research reported in this publication was mainly supported by the National Institute Of Allergy And Infectious Diseases of the National Institutes of Health under Award Numbers R01AI094562 and R34AI091446. This study was also in part sponsored by grants from the Natural Science Foundation of China (grants #11271246 & 11331009), the International Development Research Center of Canada (grant #104519-010) and Chinese State Key Laboratory for Infectious Disease Develop Grant (grant # 2012SKLID103). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
More than 30 years have passed since the first HIV case was reported among men who have sex with men (MSM) [1]. MSM contribute to the majority of new cases in the Americas, Western Europe, Oceania, and much of Asia [2]. Of the 780,000 people living with HIV/AIDS in China, 17.4% were infected through homosexual contacts in 2011, rising from 11.0% in 2007 and 7.3% in 2005 [3]. A recent survey among 47,231 MSM from 61 Chinese cities showed an overall prevalence of 4.9% [4]. The unrelenting HIV burden among MSM suggests that HIV intervention remains an urgent priority. One promising concept is the expansion of HIV testing and linkage to care (TLC) including antiretroviral therapy (ART), so that a much higher proportion of infected men know their HIV status and undergo ART, thereby reducing their infectiousness to others [5], [6], [7], [8], [9].
China has implemented several aggressive public health programs in the past decade, including routine HIV testing and risk reduction interventions for high risk populations and free ART for HIV-infected treatment-eligible individuals [10]. These programs curtailed HIV transmission through unhygienic plasma collection and injecting drug use, and reduced mortality among HIV-infected patients [11], [12], [13]; however, no programs have reversed the rising HIV epidemic among Chinese MSM [14], [15]. A recently published mathematic model estimated that a four-fold increase in testing rates may prevent 42,000 new HIV infections among all at-risk groups in China over 5 years [16]. A few mathematical models evaluated independent or joint impacts of HIV testing, risk reduction intervention and ART among MSM [17], [18], [19], [20], [21], [22], [23], [24], but these studies were mainly from the Americas, Western Europe, and Australia, where the HIV epidemics have been long established among MSM, and none from regions with a rapidly rising HIV epidemic among MSM. ART may not have the same protection against HIV transmission in homosexual contacts as in heterosexual contacts due to biological and behavioral differences in infectiousness/susceptibility or differences in co-factor frequency [25]. Furthermore, the effectiveness of combined TLC intervention packages may be contingent on the epidemiological context [26].
In this study, we modeled the dynamics of the HIV/AIDS epidemic among MSM in China's capital city, Beijing, which is representative of most Chinese urban areas [4]. We simulated HIV prevalence from 2000–2010 based on the coverage and intensity of existing public health programs including uptake of HIV testing, linkage to HIV care (e.g. risk reduction), ART and condom use. Further, we made projections for the HIV epidemic beyond 2010 under various intervention scenarios. We then examined the robustness of model predictions based on different underlying assumptions in sensitivity analyses.
Methods
We used a compartmental ordinary differential equations model for simulating and projecting the HIV epidemic among MSM in Beijing. Instead of the bilinear incidence [27], [28], [29] and the standard incidence models [5], [8], [9], we used Bernoulli processes to describe the probability of HIV transmission [30]. Bernoulli processes can more accurately describe the HIV transmission network among MSM by giving consideration for multiple sexual partners, type of sexual partner (i.e., regular or casual), differential condom use, and probability of transmission by preferred anal sex position (i.e., receptive or insertive). Substance abuse is rare among MSM in Beijing; therefore, injecting drug use is unlikely to contribute substantially to HIV transmission [31],[32],[33]. Additionally, some Chinese MSM may have female sexual partners, but these female partners generally do not have risky behavior and are unlikely to transmit disease to male partners [34]. Therefore, we only considered HIV transmission as a result of homosexual contact; we implicitly assumed there is no other route of transmission [31], [33], [35]. We also assumed that the age of active homosexual intercourse ranges from 18–60 years among Chinese MSM [36].
Model structure
Receipt of HIV testing and risk reduction services may change the risk of HIV transmission among MSM. Thus, we divided the study population into three mutually exclusive sub-populations: those who are not testing for HIV (Non-testing), those who are testing but not reducing their risk of infection/transmission (Testing), and those who are testing and reducing their risk of infection/transmission (Risk reduction). The population was further compartmentalized by infection status and disease status (or eligibility for ART treatment). According to Chinese national ART guidelines [37], patients with CD4+ T cell count <350 cells/µL are eligible for ART treatment.
Figure 1 shows the schematic diagram of our compartmental model structure. In this model we assumed that uninfected MSM enter the model as susceptible () (these MSM could be local Beijing residents who turn 18 years old, or those who migrate from other areas to Beijing). Some who receive HIV testing may test negative (
), and then a proportion of those HIV-negative men are linked to care and receive risk reduction intervention provided by public health programs in Beijing (
). The subscripts
refer to the non-testing, testing, and risk reduction, respectively.
The top row of compartments show uninfected MSM who are Susceptible to HIV infection. They are divided into Non-testers, Testers, and testers who received Risk reduction and linkage-to-care interventions. The bottom two rows representing two stages of disease contain an additional compartment—Infected individuals. Stage 1 is CD4+ cell count <350/µL while stage 2 is CD4+ ≥350/µL. The last column of compartments shows HIV-infected individuals who have initiated Antiretroviral therapy. is the recruitment rate per year into the MSM population in Beijing. They are local HIV- MSM who turn 18 years old, or those from other areas who immigrate to Beijing. Horizontal movement is parameterized by rates of testing (
), rates of linkage to care (
), rates of ART initiation (
), and rates of ART failure or dropout (
). Movement from Susceptible to Infected (
) is the HIV transmission rate. It is estimated from multiple parameters including condom use, insertive/receptive intercourse, regular/casual partner encounter, CD4 count, and reductions in infectivity due to TLC or ART. The natural removal rate (
) represents death, being older than 60 years, or migration out of Beijing. The rate of disease progression is different for HIV-infected individuals on ART (
) or not on ART (
).
Upon infection, individuals move from susceptible into infected status, and the latter is further divided into two infection stages: CD4 count ≥350/µL ( and
) and CD4 count <350/µL (
and
). Flow is unidirectional from susceptible status to infection stage 1 and then 2, as without ART, an HIV-infected individual is unlikely to experience immunological recovery. A proportion of infected MSM (
or
) receive ART (
or
); these compartments are bidirectional due to attrition or adherence to ART and decline or improvement of immunological status.
The key to quantifying HIV incidence among MSM in Beijing is specifying the time-dependent HIV transmission rate, . Multiplying the number of susceptible MSM by this transmission rate gives the frequency of new infections. Since MSM in Beijing often have multiple sexual partners, we classified them as regular partners (RP) and casual partners (CP), because they typically have different risk profiles [32], [35]. We also classified sexual behaviors of MSM as insertive or receptive anal intercourse (AI) with different HIV transmission probabilities per sex act [8]. We investigated the relationship between per-act and per-partner AI transmission probabilities for a given number of sex acts using the Bernoulli process assuming independence of risk for each sex act within a partnership [38], [39]. Parameter notation and descriptions are provided in Table 1; initial conditions and parameter values are described later.
Using the Bernoulli process model of HIV transmission during a given number of sex acts, the non-infection probability by infected regular sexual partners through receptive AI and insertive AI (
) under condom-use rate
can be described as:
(1)where r is the proportion of sex acts which are insertive AI and θ is the single act transmission probability, and
and
are the mean number of sex acts and condom use rates with superscripts r (above) or c (not shown) denoting regular or casual sex partnerships, respectively.
The HIV transmission rate is defined as:(2)where
is the effective contact rate for all MSM N at time t with
(3)
The definitions for parameters in the equation (3) are described in Table 1.
From this model, we calculated the basic reproduction number () [40].
is the number of secondary cases produced by a typical HIV-infected MSM during his entire period of infectiousness in a demographically steady susceptible population. Calculating
is critical to determine whether HIV will increase, stabilize, or decline among the MSM population in Beijing.
Data source and estimation
To simulate the HIV prevalence rates during 2000–2010 among MSM in Beijing, we used data from local HIV surveillance systems and published studies [31], [32], [33], [35], [41]. As these data were summary statistics, and did not include any identifiers that could link the data to individual subjects in the local HIV surveillance systems or participants from the published studies, consent was waived and the mathematical modeling protocol was approved by the institutional review boards of the National Center for AIDS/STD Control and Prevention of Chinese Center for Disease Control and Prevention and Vanderbilt University.
We employed a Metropolis-Hastings algorithm to carry out extensive Markov-chain Monte-Carlo simulations for estimating the mean values of some unknown parameters [42], including yearly recruitment rate (or number of new members into the pool of the study population each year), risk-reduction rate of healthy MSM (during 2000–2010), relative infectiousness of risk-reduction to non-testing subgroups, the per-act probability of unprotected insertive or receptive anal intercourse resulting in an infection, and the relative infectiousness ratio of HIV positive MSM in the infection stages 2 to 1 (see Figure 1). The algorithm ran for 1,000,000 iterations, and we adapted the proposal distribution after 500,000 iterations using Geweke's method to assess convergence [42].
Initial conditions.
The earliest HIV prevalence data among MSM in Beijing were available for 2000. The observed HIV prevalence rates among MSM in Beijing during 2000–2010 were: 1.2% in 2000 [41], 3.2% in 2005 [32], 4.8% in 2006 [32], 5.1% in 2007 [32], 6.5% in 2008 [31], [33], 6.8% in 2009 [35], and 7.8% in 2010 [43]. In order to set the initial conditions, we had to estimate the target population of MSM living in Beijing in 2000. According the national census in 2000, there were 14 million of people living in Beijing. We assumed half of them were male and 3% of males in Beijing in 2000 were MSM, of which half lived in the city. The testing rate in 2010 was very low (assumed 0.125%). Also, we assumed there was no risk reduction intervention in 2000, as the burgeoning HIV epidemic in MSM did not receive attention from Chinese public health programs at that time [44]. For these non-testing HIV-positive MSM, we assumed one-third were in infection stage 1 (CD4 count≥350/µL) and two-thirds were in the infection stage 2 (CD4 count <350/µL). Also, we assumed that there was no ART available for MSM in 2000. The resulting parameter values for the initial conditions are shown in Table 1.
Progression.
With an 18 year average age of sexual debut, we considered a natural removal rate per year which corresponds to an average of 42 years of sexual activity and non-AIDS mortality (). The recruitment rate per year into HIV-negative MSM population was estimated to range from 2–6.4% of the total population [8] giving the recruitment rate (
) (Table 1). The progression duration from HIV infection to AIDS is 10–12 years in the absence of treatment and may increase by additional 8–12 years with ART [5], [45], [46]. We used estimated disease progression rates being an average duration of 5.6 years without ART (therefore,
), and 11.2 years with ART (
) [5]. We also performed sensitivity analyses for a range of disease progression rates.
Sex and condom use.
We estimated condom use rate and frequency of AI based on three cohort studies among MSM in Beijing [31], [32], [47] and one meta-analysis among Chinese MSM [34]. Table 1 shows condom use rates for insertive and receptive AI ( and
) ranging from 30.7%–41.4% [34] and the average frequency of AI with regular and casual sexual partners (
and
) ranging from 18.2–36.6 [31], [32], [47].
Transmission.
Relative infectiousness of HIV-infected MSM (MSM+) who receive HIV testing versus non-testing was defined as the ratio of high risk behavior of testing MSM+ to that of non-testing MSM+. The rationale is that HIV testing (and counseling) may lead to change of risky behaviors, such as reduction in sexual encounters or increasing condom use, or both. Based on risky behaviors among MSM+ from three cohort studies [31], [32], [42], we calculated the relative infectiousness ratio (; 13.8/18.6) (Table 1). We assumed that non-testing MSM did not have different risk behaviors by HIV status (as they are unaware of their status) and simulated the effect of risk reduction intervention to non-testing MSM (
). The conservative estimate for the relative infectiousness among MSM+ who are on ART versus non-ART (
) was based on evidence that ART can reduce HIV transmission by 60% [48].
The per-act risk of HIV transmission through unprotected receptive AI ranged from 0.008–0.028, while the risk through insertive AI ranged from 0.0006–0.0019 [8]. The estimated proportion of practicing receptive anal sex among MSM ranged from 0.4–0.5 while the proportion of practicing insertive sex ranged from 0.5–0.6 [8], and we estimated the proportion of insertive versus receptive sex acts as 0.56 (Table 1).
Intervention uptake.
The average testing rate for MSM during 2001–2010 was estimated to be 9% [49]. The linkage rates for HIV-positive MSM ranged from 17% to 85% with a mean rate of 33% [49]. The ART initiation rates were estimated to be 1.8% and 53% among MSM whose CD4 counts are ≥350/µL and <350/µL, respectively [49].
Hypothetical scenarios
We used the model to project HIV prevalence and incidence trends during 2011–2020 under five different scenarios:
- Maintaining the coverage of interventions as they were (i.e., average coverage during 2000–2010): ART coverage (
and
), condom use (
and
), HIV testing (
), and linkage to care (
) [31], [32], [34], [47], [49].
- Increased ART coverage only (
and
).
- Increased TLC/ART, but no increased condom use (
).
- Increased condom use only (
and
).
- Increased TLC/ART (
) and condom use (
and
).
In S4–S5, we assumed that condom use doubled since 2000.
Sensitivity analysis
Finally, we performed sensitivity analyses to assess the robustness of the model results. First, by perturbing individual parameters, we investigated their influence on estimates of . Second, we estimated uncertainty ranges for model parameters based on literature reviews (Table 1) and randomly sampled 20,000 parameter sets over these uncertainty ranges using a Latin Hypercube Sampling design [50], [51] to derive a frequency distribution for R0. Analyses were performed using Matlab computer software (MATLAB 7.7, The MathWorks Inc., Natick, MA, 2008); analysis scripts and supplemental materials are available online (http://biostat.mc.vanderbilt.edu/ArchivedAnalyses).
Results
Using parameter values summarized in Table 1, our model produces a best-fit curve to historical HIV prevalence rates among MSM in Beijing during 2000–2010 (Figure 2A). The basic reproduction number in 2010 is (95% confidence interval (CI), 1.83–2.35). Because
, if the epidemic assumptions remain unchanged from 2010, the HIV prevalence is expected to substantially increase among MSM in Beijing. Using this best-fit model of HIV transmission during 2000–2010, we project HIV prevalence for the next ten years (until 2020) under five different scenarios. The HIV prevalence is 7.8% in 2010. If there is no change in the coverage of interventions or maintaining the average level during 2000–2010 (Figure 2, line 1), then the HIV prevalence is estimated to increase to 21.4% (95%CI, 9.9–31.7%) (Figure 2A, line 1), with an incidence rate of 3.1% (95%CI, 1.0–5.1%) by 2020 (Figure 2B, line 1). By increasing the coverage of ART among MSM+ who are linked to risk reduction (Figure 2, line 2), we expect a modest improvement in lowering HIV prevalence (19.9%; 95%CI, 9.9–28.4%) and incidence (2.6%; 95%CI, 0.8–4.6%). If TLC and ART coverage increases (Figure 2, line 3), the projected HIV prevalence and incidence will be 14.5% (95%CI, 7.0–23.8%) and 1.4% (95%CI, 0.2–3.3%). If MSM increase condom use only (Figure 2, line 4), then HIV prevalence and incidence will be 13.0% (95%CI, 9.8–28.4%) and 1.5% (95%CI, 0.8–4.6%), respectively. Bundling increased TLC/ART with increased condom use (Figure 2, line 5) may result in an HIV prevalence of 8.7% (95%CI, 5.4–11.5%) and an incidence of 0.5% (95%CI, 0.1–0.9%) by 2020. It is important to note that only this bundled HIV intervention strategy is likely to have an
and eventually result in HIV eradication in this population.
(A) effect on HIV prevalence; (B) effect on HIV incidence.
We performed simple sensitivity analyses for intervention and transmission parameters. First, we analyzed the influence of the six intervention parameters (testing and linkage to risk reduction) on the prevalence during 2000–2020 (Table S1). The parameters related to HIV testing () have the greatest influence on the estimates of
. In particular, the partial rank correlation coefficient (PRCC) values range from −0.98 to −0.59, indicating that
decreases for higher testing rates. Similarly, the parameters related to HIV linkage to risk reduction (l) also impact
. PRCC ranged from −0.44 to −0.14, indicating that
decreases for a higher linkage rate. Figure 3 shows two contour plots of
under different HIV testing or linkage to risk reduction among MSM+ while condom use remains at the average level during 2000–2010. Even if all MSM+ are tested (testing rate = 100%) or are linked to risk reduction (RR rate = 100%) without increasing condom use, the reproduction number remains above the epidemic threshold (
).
(A) Under the different coverage rates of HIV testing intervention; (B) Under the different coverage rates of HIV risk reduction (RR) intervention.
Second, we analyzed the influence of the relative infectiousness of MSM+ on ART versus non-ART (varying 0.01–0.4) and that of MSM+ with CD4 counts <350/µL versus ≥350/µL (varying 0.5–5.0). In all perturbations for relative infectiousness, endures.
Third, we found that is sustained if MSM increase condom use but the coverage of TLC interventions remains at the average level during 2000–2010.
Fourth, we varied the average duration of disease progression without ART from 3.7–11.1 years and with ART from 7.4–22.2 years. The median is 2.11 and consistently greater than 1.
In extensive sensitivity analyses, 20,000 parameter sets were randomly sampled from corresponding uncertainty ranges (Table S2). The distribution of is skewed to the right with mean 1.93 (standard deviation: 0.82) and median 1.82 (interquartile range: 1.36–2.42). A small percentage (11.4%) of estimates falls below the epidemic threshold (
). Relative infectiousness of RR to non-testing MSM+, transmission probability of unprotected receptive AI, and relative infectiousness of MSM+ on ART to non-ART are the three most influential parameters with PRCC equaling to 0.95, 0.90 and 0.71, respectively.
Discussion
Combination testing and treatment intervention packages have been considered as a promising strategy for HIV prevention among MSM in recent years [52]. We explored the effects of TLC/ART, along with condom use, for the emerging HIV epidemic among Chinese MSM [4], [53]. Our projections predicted that with the current level of services HIV prevalence among MSM in Beijing will almost triple from 7.8% in 2010 to 21.4% by 2020. Expansion of ART coverage in the current continuum of care among MSM+ would only lead to a moderate reduction of this rising trend, though enhanced TLC interventions plus increased ART coverage will further reduce incident HIV infections. Only with a combination of increased condom use and a higher TLC/ART coverage might HIV epidemic be expected to decline. Hence, promoting safer sex education and risk reduction counseling service to increase condom use is crucial for HIV prevention among Chinese MSM, even in the context of expanded TLC and ART.
As observational studies and the HPTN 052 randomized controlled trial have demonstrated the effectiveness of ART for reducing heterosexual HIV transmission [54], [55], [56], [57], [58], treatment as prevention has been advocated as a strategy for HIV prevention among MSM [59]. However, the impact may vary by epidemic scenarios [21]. In settings with a long-standing epidemic like San Francisco, TLC with ART expansion may reduce the HIV epidemic [52]. Our model is less optimistic that ART interventions alone will succeed in substantial prevention reduction. The HIV epidemic among Chinese MSM is relatively recent [44], and the majority of cases may still be in earlier stages of disease, and therefore have not received ART [13]. We use local public health data such as ART coverage rates for estimating the parameters in the mathematical models; therefore our modeling results likely reflect what is actually happening in Beijing. A comparable example is that in the HPTN 052 trial earlier ART treatment reduced heterosexual transmission by 96% [7], while among 38,862 Chinese serodiscordant couples the rate of transmission was only reduced by 26% in the first year of treatment and the reduction lost statistical significance in subsequent years [60]. The former result comes from a controlled trial setting while the later one is from a real-world public health setting. Our model projections are consistent with the study in the United Kingdom where increased condom use was more likely to drive down HIV incidence than high ART coverage [20].
Increasing coverage of HIV testing may lead MSM+ in Beijing to reduce risky behaviors, notably the use of condoms; partner reduction interventions and serosorting (i.e., MSM of the same HIV status) interventions could conceivably have a similar benefit, but we did not model these factors. Based on our model, HIV prevalence will continue to increase, as fewer MSM+ die and fall out of transmission networks. The impact of HIV testing is largely dependent on how those infected MSM with known status reduce their risk behaviors, particularly practicing anal sex without condom use. Given that only a fraction of HIV-infected men know their status, are eligible for ART, and successfully negotiate the system to adhere to ART, increased condom use is a crucial element in the combined interventions for reducing the epidemic.
The limitation of our mathematical model is a simplification of the real world epidemic. Like other models, we balance parsimony and reality. For example, we assumed that all linked MSM+ receive risk reduction. This is consistent with Chinese HIV testing protocol that all MSM+ are expected to receive risk reduction counseling. However, in reality, the quality of counseling may vary by clinic and client. Because some counseling may not lead to behavioral changes, we considered condom use as an independent factor in our model. Although model parameters are carefully specified using the available literature, they may not reflect the current realities among Beijing MSM. For example for scenario 3, we assumed increasing HIV testing from 9% to 25%; increasing the linkage rate to risk reduction education from 19% to 50% among HIV-uninfected MSM and from 33% to 75% among HIV-infected MSM; increasing ART coverage from 1.8% to 25% among HIV-infected MSM whose CD4+ cell count ≥350/µL and from 53% to 75% among those with CD4 count <350/µL. The magnitude of these assumed increases in coverage are based on our best estimations of how well the public health system could do, in the view of local HIV/AIDS experts (including authors YR, XH, HL and YS as well as non-author experts from local centers for disease control). However, we performed extensive sensitivity analyses by varying input parameters and found that our findings are robust to reasonable perturbations.
No scenario can result in a substantial decline in HIV epidemic by 2020 among Chinese MSM, except the bundled package of transmission prevention strategies including increased TLC/ART and condom use. Simulations show that TLC alone has some impact for HIV reduction, but far less than increasing condom use. Our model suggests that increasing condom use must be a component of combination intervention packages to achieve significant reduction in HIV incidence.
Supporting Information
Table S1.
Partial Rank Correlation Coefficients for R0.
https://doi.org/10.1371/journal.pone.0090985.s001
(DOCX)
Table S2.
Sensitivity analysis of reproduction number R0.
https://doi.org/10.1371/journal.pone.0090985.s002
(DOC)
Author Contributions
Conceived and designed the experiments: JL YR SHV YS HZQ. Performed the experiments: JL MB GFW BES HZQ. Analyzed the data: JL ST. Contributed reagents/materials/analysis tools: JL YR XH HL. Wrote the paper: JL YR SHV YS HZQ. All authors revised the manuscript.
References
- 1. US Centers for Disease Control and Prevention (1981) Pneumocystis pneumonia–Los Angeles. MMWR Morbidity and mortality weekly report 30: 250–252.
- 2. Beyrer C, Baral SD, van Griensven F, Goodreau SM, Chariyalertsak S, et al. (2012) Global epidemiology of HIV infection in men who have sex with men. Lancet 380: 367–377.
- 3.
Ministry of Health in People's Republic of China, Joint United Nations Programme on HIV/AIDS, World Health Organization (2011) 2011 Estimates for the HIV/AIDS Epidemic in China. Beijing, China.
- 4.
Wu Z, Xu J, Liu E, Mao Y, Xiao Y, et al.. (2013) HIV and Syphilis Prevalence Among Men Who Have Sex With Men: A Cross-Sectional Survey of 61 Cities in China. Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.
- 5. Granich RM, Gilks CF, Dye C, De Cock KM, Williams BG (2009) Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. Lancet 373: 48–57.
- 6. Vernazza PL, Gilliam BL, Flepp M, Dyer JR, Frank AC, et al. (1997) Effect of antiviral treatment on the shedding of HIV-1 in semen. AIDS 11: 1249–1254.
- 7. Cohen MS, Chen YQ, McCauley M, Gamble T, Hosseinipour MC, et al. (2011) Prevention of HIV-1 infection with early antiretroviral therapy. The New England journal of medicine 365: 493–505.
- 8. Lima VD, Johnston K, Hogg RS, Levy AR, Harrigan PR, et al. (2008) Expanded access to highly active antiretroviral therapy: a potentially powerful strategy to curb the growth of the HIV epidemic. J Infect Dis 198: 59–67.
- 9. Cremin I, Alsallaq R, Dybul M, Piot P, Garnett G, et al. (2013) The new role of antiretrovirals in combination HIV prevention: a mathematical modelling analysis. Aids 27: 447–458.
- 10. Wu Z, Sullivan SG, Wang Y, Rotheram-Borus MJ, Detels R (2007) Evolution of China's response to HIV/AIDS. Lancet 369: 679–690.
- 11. Qian HZ, Vermund SH, Kaslow RA, Coffey CS, Chamot E, et al. (2006) Co-infection with HIV and hepatitis C virus in former plasma/blood donors: challenge for patient care in rural China. Aids 20: 1429–1435.
- 12. Lu L, Jia M, Ma Y, Yang L, Chen Z, et al. (2008) The changing face of HIV in China. Nature 455: 609–611.
- 13. Zhang F, Dou Z, Ma Y, Zhang Y, Zhao Y, et al. (2011) Effect of earlier initiation of antiretroviral treatment and increased treatment coverage on HIV-related mortality in China: a national observational cohort study. The Lancet infectious diseases 11: 516–524.
- 14. Ye S, Xiao Y, Jin C, Cassell H, Blevins M, et al. (2012) Effectiveness of integrated HIV prevention interventions among Chinese men who have sex with men: evaluation of a 16-city public health program. PloS one 7: e50873.
- 15. Li HM, Peng RR, Li J, Yin YP, Wang B, et al. (2011) HIV incidence among men who have sex with men in China: a meta-analysis of published studies. PloS one 6: e23431.
- 16. Zhang L, Gray RT, Wilson DP (2012) Modelling the epidemiological impact of scaling up HIV testing and antiretroviral treatment in China. Sexual health 9: 261–271.
- 17. Ahlgren DJ, Gorny MK, Stein AC (1990) Model-based optimization of infectivity parameters: a study of the early epidemic in San Francisco. Journal of acquired immune deficiency syndromes 3: 631–643.
- 18. Jacquez JA, Koopman JS, Simon CP, Longini IM Jr (1994) Role of the primary infection in epidemics of HIV infection in gay cohorts. Journal of acquired immune deficiency syndromes 7: 1169–1184.
- 19. Tan WY, Xiang Z (1999) The state-space model of the HIV epidemic with variable infection in the homosexual populations. J Stat Plan Inference 78: 71–87.
- 20. Phillips AN, Cambiano V, Nakagawa F, Brown AE, Lampe F, et al. (2013) Increased HIV incidence in men who have sex with men despite high levels of ART-induced viral suppression: analysis of an extensively documented epidemic. PloS one 8: e55312.
- 21. Wirtz AL, Walker DG, Bollinger L, Sifakis F, Baral S, et al. (2013) Modelling the impact of HIV prevention and treatment for men who have sex with men on HIV epidemic trajectories in low- and middle-income countries. International journal of STD & AIDS
- 22. van Sighem A, Vidondo B, Glass TR, Bucher HC, Vernazza P, et al. (2012) Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study. PloS one 7: e44819.
- 23. Wilson DP, Hoare A, Regan DG, Law MG (2009) Importance of promoting HIV testing for preventing secondary transmissions: modelling the Australian HIV epidemic among men who have sex with men. Sexual health 6: 19–33.
- 24. Supervie V, Garcia-Lerma JG, Heneine W, Blower S (2010) HIV, transmitted drug resistance, and the paradox of preexposure prophylaxis. Proceedings of the National Academy of Sciences of the United States of America 107: 12381–12386.
- 25. Muessig KE, Smith MK, Powers KA, Lo YR, Burns DN, et al. (2012) Does ART prevent HIV transmission among MSM? AIDS 26: 2267–2273.
- 26. Dodd PJ, Garnett GP, Hallett TB (2010) Examining the promise of HIV elimination by ‘test and treat’ in hyperendemic settings. AIDS 24: 729–735.
- 27. Agusto FB, Gumel AB (2013) Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains. Math Biosci 243: 147–162.
- 28. Buonomo B, Vargas-De-Leon C (2012) Global stability for an HIV-1 infection model including an eclipse stage of infected cells. Journal of Mathematical Analysis and Applications 385: 709–720.
- 29. Wang JJ, Zhang JZ, Jin Z (2010) Analysis of an SIR model with bilinear incidence rate. Nonlinear Analysis-Real World Applications 11: 2390–2402.
- 30. Baggaley RF, White RG, Boily MC (2010) HIV transmission risk through anal intercourse: systematic review, meta-analysis and implications for HIV prevention. Int J Epidemiol 39: 1048–1063.
- 31. Zhou ZH, Li SM, Liu YJ, Jiang SL, Zhang XX, et al. (2010) [Study on the relationship between behavioral factors, psychological status and HIV infection among men who have sex with men in Beijing.]. Zhonghua Liu Xing Bing Xue Za Zhi 31: 273–276.
- 32. Ruan Y, Luo F, Jia Y, Li X, Li Q, et al. (2009) Risk factors for syphilis and prevalence of HIV, hepatitis B and C among men who have sex with men in Beijing, China: implications for HIV prevention. AIDS Behav 13: 663–670.
- 33. Xu J, Han DL, Liu Z, Ma XY, Wang LL, et al. (2010) [The prevalence of HIV infection and the risk factors among MSM in 4 cities, China]. Zhonghua Yu Fang Yi Xue Za Zhi 44: 975–980.
- 34. Chow EP, Wilson DP, Zhang L (2012) Patterns of condom use among men who have sex with men in China: a systematic review and meta-analysis. AIDS and Behavior 16: 653–663.
- 35. Fan S, Lu H, Ma X, Sun Y, He X, et al. (2012) Behavioral and serologic survey of men who have sex with men in Beijing, China: implication for HIV intervention. AIDS Patient Care STDS 26: 148–155.
- 36. Li D-l, Liang H-Y, Yang Y (2008) A Survey of Initial and Factors of Homosexual Intercourse Among Men Who Have Sex With Men. Journal of Preventive Medicine Information 6: 008.
- 37. Ma Y, Zhang F, Zhao Y, Zang C, Zhao D, et al. (2010) Cohort profile: the Chinese national free antiretroviral treatment cohort. International journal of epidemiology 39: 973–979.
- 38. Røttingen J-A, Garnett GP (2002) The epidemiological and control implications of HIV transmission probabilities within partnerships. Sexually transmitted diseases 29: 818–827.
- 39. Wilson DP, Law MG, Grulich AE, Cooper DA, Kaldor JM (2008) Relation between HIV viral load and infectiousness: a model-based analysis. The Lancet 372: 314–320.
- 40. Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences 180: 29–48.
- 41. Liu H, Liu Y, Xiao Y (2001) A survey on knowledge, attitude, belief and practice related to HIV/AIDS among MSM. J China AIDS/STD Prevent Control 7: 289–291.
- 42. Haario H, Laine M, Mira A, Saksman E (2006) DRAM: efficient adaptive MCMC. Statistics and Computing 16: 339–354.
- 43. Li X, Lu H, Raymond HF, Sun Y, Jia Y, et al. (2012) Untested and undiagnosed: barriers to HIV testing among men who have sex with men, Beijing, China. Sexually transmitted infections 88: 187–193.
- 44. Qian HZ, Vermund SH, Wang N (2005) Risk of HIV/AIDS in China: subpopulations of special importance. Sex Transm Infect 81: 442–447.
- 45. Vardavas R, Blower S (2007) The emergence of HIV transmitted resistance in Botswana:“when will the WHO detection threshold be exceeded?”. PLoS One 2: e152.
- 46. Johnson LF, Dorrington RE (2006) Modelling the demographic impact of HIV/AIDS in South Africa and the likely impact of interventions. Demographic Research 14: 541–574.
- 47. Yu M-R, Li S-M, Yan L (2011) HIV testing and its influence factors among men who have sex with men in Beijing. Chinese Journal of Public Health 10: 011.
- 48. Porco TC, Martin JN, Page-Shafer KA, Cheng A, Charlebois E, et al. (2004) Decline in HIV infectivity following the introduction of highly active antiretroviral therapy. AIDS (London, England) 18: 81.
- 49.
CDC C (2010) Annual Report on HIV/AIDS in Beijing.
- 50. Hoare A, Regan DG, Wilson DP (2008) Theoretical Biology and Medical Modelling. Theoretical Biology and Medical Modelling 5: 4.
- 51. Helton JC, Iman RL, Brown JB (1985) Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides. Ecological modelling 28: 243–278.
- 52. Velasco-Hernandez JX, Gershengorn HB, Blower SM (2002) Could widespread use of combination antiretroviral therapy eradicate HIV epidemics? The Lancet infectious diseases 2: 487–493.
- 53. Tucker JD, Wong FY, Nehl EJ, Zhang F (2012) HIV testing and care systems focused on sexually transmitted HIV in China. Sexually transmitted infections 88: 116–119.
- 54. Bunnell R, Ekwaru JP, Solberg P, Wamai N, Bikaako-Kajura W, et al. (2006) Changes in sexual behavior and risk of HIV transmission after antiretroviral therapy and prevention interventions in rural Uganda. AIDS 20: 85–92.
- 55. Del Romero J, Castilla J, Hernando V, Rodriguez C, Garcia S (2010) Combined antiretroviral treatment and heterosexual transmission of HIV-1: cross sectional and prospective cohort study. BMJ 340: c2205.
- 56. Donnell D, Baeten JM, Kiarie J, Thomas KK, Stevens W, et al. (2010) Heterosexual HIV-1 transmission after initiation of antiretroviral therapy: a prospective cohort analysis. Lancet 375: 2092–2098.
- 57.
Sullivan P, Kayitenkore K, Chomba E, Karita E, Mwananyanda L, et al.. (2010) Reduction of HIV transmission risk while prescribed anti-retroviral therapy (ARVT): Misclassification of ARVT status as a methodological issue [abstract]. In: AIDS Res Hum Retroviruses, editor. AIDS Vaccine 2010; 28 Sept–1 Oct 2010. Atlanta, Georgia, US.
- 58. Wang L, Zeng G, Luo J, Duo S, Xing G, et al. (2010) HIV transmission risk among serodiscordant couples: a retrospective study of former plasma donors in Henan, China. J Acquir Immune Defic Syndr 55: 232–238.
- 59. Sullivan PS, Carballo-Dieguez A, Coates T, Goodreau SM, McGowan I, et al. (2012) Successes and challenges of HIV prevention in men who have sex with men. Lancet 380: 388–399.
- 60. Jia Z, Ruan Y, Li Q, Xie P, Li P, et al. (2012) Antiretroviral therapy to prevent HIV transmission in serodiscordant couples in China (2003–11): a national observational cohort study. Lancet