Model overview

To project HIV transmission dynamics among MSM in the Netherlands, the developed agent-based model captures three types of processes: demographic dynamics, sexual network dynamics, and HIV disease progression and transmission dynamics. The demographic dynamics include the entrance of new individuals into the population, aging, and the exit of individuals from the population due to background mortality or cessation of sexual activity. The sexual network dynamics capture steady (long-term, non-overlapping with other steady partnerships) and non-steady (short-term, with the potential for concurrency) sexual partnerships that form and dissolve dynamically. HIV disease progression and transmission capture the natural history of HIV infection, and current practices of HIV care and prevention in the Netherlands, such as the cascade of care and pre-exposure prophylaxis (PrEP). The model accounts for importation of HIV infections from outside of the Netherlands, either as a result of residents of the Netherlands acquiring HIV while traveling abroad or due to individuals immigrating to the Netherlands with an existing infection. The simulation advances one day at a time.

Demography

The modeled population consisted of 25,000 individuals, scaled down from an estimated MSM population in the Netherlands of 200,000–300,000 individuals [12]. We considered sexually active individuals between 15 and 75 years of age. Individuals enter the population at the age of 15 years, age as the simulation advances, and exit the population once they reach 75 years. They can also leave the population as a result of background age-dependent mortality.

Sexual network dynamics

In the context of MSM, anal intercourse (AI) is the predominant mode of transmission [13]. We model HIV transmission through AI in steady and non-steady sexual partnerships. Individuals can enter new partnerships, and existing partnerships can dissolve. A steady partnership is a long-term partnership. Individuals can have at most one steady partner at a time. All individuals in the population have the same propensity to enter a steady partnership. The term non-steady partnership designates all other partnerships where AI can take place. Non-steady partnerships are short-term and may be concurrent with other partnerships, both steady and non-steady. The propensity to enter new non-steady partnerships is an intrinsic property of an individual and depends on age and on being in a steady partnership. This property may change as individuals age, or when their steady-partner state changes. The formation of both types of partnerships is influenced by the effects of age and HIV status on selecting a partner, referred to as age assortativity and serosorting, respectively.

HIV dynamics

We use a standard HIV framework for modeling the natural history of HIV infection, which is viewed as the sequence of early, chronic, and AIDS infection stages. In our study, we adopt an approach similar to that by Dijkstra et al. [9], where early infection lasts, on average, 89 days. This duration aligns with the cumulative duration of the first five stages of infection in the Fiebig classification [14] that delineates substages of early infection corresponding to distinct levels of HIV viremia, antibody seroconversion responses, and sensitivity of diagnostic methods needed to detect HIV infection. After an infection has occurred, individuals who acquired HIV progress through the early infection stage. Subsequently, individuals enter the chronic infection stage, which is an extended period where the potential to transmit HIV remains approximately constant and significantly lower than in the early infection stage. Once the chronic infection stage has concluded, individuals enter the AIDS stage, which we further divide into early and late AIDS stages. The early AIDS stage is characterized by an increased probability of transmitting HIV via AI compared to the chronic stage and additional mortality due to AIDS. Finally, a rare occurrence in the Netherlands, individuals who survive the early AIDS stage enter the late AIDS stage. This stage is characterized by a rapid rise in viral load, cessation of sexual activity, and increased mortality relative to the early AIDS stage.

Baseline care and prevention

The model captures the current routine HIV care and prevention programs in the Netherlands, including diagnosis-treatment-suppression cascade and PrEP. Since September 2019, PrEP can be obtained through the national PrEP program and via a prescription from general practitioners. We model continuous PrEP use, resulting in a substantial reduction in the likelihood of HIV acquisition during anal intercourse with individuals with HIV. We approximate the eligibility criteria for PrEP by considering the number of sexual partners in the past 6 months. The rates of enrollment in and exit from the PrEP program are calibrated so that, following the initial years of the PrEP rollout, 5% of the population is using PrEP. Individuals who acquire HIV may be diagnosed, subsequently initiate ART, and eventually achieve viral suppression, rendering them effectively incapable of transmitting HIV. A fraction of individuals may discontinue ART or experience ART failure, returning to a state with an unsuppressed viral load. For simplicity, we assume that these individuals can be offered ART again. We do not explicitly simulate testing or account for differences in testing rates across various individual characteristics. Instead, we model diagnosis rates, which are dependent on the stage of infection.

Importation of HIV infections from outside of the Netherlands

To capture importation of HIV infections arising outside of the transmission network within the Netherlands, we assign a positive HIV status to a proportion of individuals who enter the population. Individuals with HIV can enter the population either aware or unaware of their status. The rate of entrance of individuals who know their HIV status is extrapolated using the Stichting HIV monitoring (SHM) reported data for years 2017-2022 [1,15–20], according to which about approximately 95% of incoming individuals who know their HIV status, have initiated ART treatment, and have a suppressed viral load. We model that these individuals continue ART treatment in the Netherlands. The annual number of individuals who either acquire HIV infection abroad or immigrate to the Netherlands with existing HIV infection and do not know their status cannot be estimated directly from the data, and thus we conflated these two sources of new HIV infections arising from outside of the Netherlands into a single parameter. The distribution for this parameter was estimated through the calibration process.

HIV transmission within partnerships

HIV transmission between two sexual partners via AI depends on the HIV infection stage of the partner with HIV, the effective sexual contact rate between the two partners, and the use of PrEP. The effective sexual contact rate can be further broken down into the frequency of AI acts and the probability of condom use during these acts. Condom use depends on the type of partnership and on PrEP use by individuals in the partnership and results from reconciling the personal, age-dependent preferences of individuals. We model condom use as constant for the entire duration of the partnership. The frequency of AI acts differs per type of partnership, with everyone modeled as having the same preference for the frequency of AI. Finally, based on existing evidence [21], we model that the effective sexual contact rates in serodiscordant partnerships where the partner with HIV is diagnosed are reduced compared to the baseline level of partnerships with unknown HIV status. We assumed the reduction to be by a factor of 2.

Model parametrization and calibration

To accurately project HIV transmission dynamics in the MSM population in the Netherlands, we use available data to set model parameter values. Most parameter values are determined through direct calculation, known as parametrization, whereas others are derived by adjusting the model outputs to fit available data, a method called calibration. This approach is used for parameters that are particularly difficult to measure directly, such as the probability of transmission by an individual with chronic HIV infection during condomless AI.We estimate diagnosis rates of individuals at various stages of HIV infection, by calibrating the model to the annual distribution of infection stages at time of diagnosis, reported by SHM. In this way we ensure that the model accurately reproduces the pattern of diagnosis rates in MSM in the Netherlands. To set parameters relevant to sexual network dynamics and sexual behavior within partnerships, either through the direct calculation from data or via the calibration process, we use data collected from several sexual network/behavior surveys among MSM in the Netherlands, i.e., the cross-sectional European MSM Internet Survey 2017 (EMIS-2017) [22], the longitudinal Amsterdam Cohort Studies (ACS) [23], and the cross-sectional Amsterdam MSM Network study [24,25]. To estimate HIV transmission dynamics, we use HIV surveillance data for MSM in the Netherlands [1,15–20,26] and estimates from the literature [27–29]. Employing parametrization and calibration procedures, we obtain the 100 parameter sets for which the distance between the median of the model simulation and the HIV surveillance estimate/data [1] was minimized and which were used to produce the analyses. For the selected parameter sets, the simulation median always falls within the estimate of the confidence interval for the data. For a comprehensive description of parameter estimation, consult the S1 Appendix.

Model scenarios

In all scenarios, at the beginning of the simulation the population age structure is seeded using the state of the male population in 2014. We initiate HIV dynamics using the population distribution in the cascade of care in 2016 [15] and allow it to progress until 2023. Depending on the modeled scenario, an intervention is then initiated and run for 10 years starting in 2023. We simulate the following scenarios:

1. Baseline scenario. No additional interventions are modeled, except for the PrEP program and the cascade of care using the standard of care in 2016, wherein ART initiation increasingly occurred soon after HIV diagnosis.
2. Intervention scenario. An intervention that facilitates an increased diagnosis for individuals with early HIV infection and immediate ART initiation would start in 2023. We considered scenarios with the following specifications:
   1. Maximum impact scenario. In this scenario, we simulate that every individual, whether with newly acquired HIV infection or with HIV infection acquired within the previous 6 months, begins ART right at the point of HIV acquisition or at the start of the intervention, whichever comes first. We achieve this by setting the diagnosis rates high enough to ensure immediate ART initiation for all eligible individuals upon HIV acquisition or with the intervention’s initiation. Although this scenario may not be realistic, examining its outcomes helps us understand the maximum potential impact of the intervention which combines increased diagnosis in individuals with early HIV infection with immediate initiation of ART.
   2. Accelerated diagnosis in individuals with early HIV infection. In this scenario, we explore incremental increases in the diagnosis rate for individuals with early HIV infection, combined with immediate initiation of ART. Ultimately, we aim to identify the sufficient increase rate of the diagnosis rate in order to approach the maximum impact of the intervention. The diagnosis rates are increased relative to the baseline level by factors of 2, 4, 8, 16, and 32. At the baseline, 22% of individuals with newly acquired HIV are diagnosed during the early infection stage. As the diagnosis rates increase incrementally, the proportions of diagnosed individuals rise to 39%, 62%, 86%, 98% and 100%, respectively.
   3. Accelerated diagnosis in individuals who acquired HIV within the previous 6 months. This scenario captures the effect of an intervention that causes an increase in diagnosis rates not only in individuals with early HIV infection as in (b) but also in individuals who have entered the chronic HIV infection but have acquired HIV within the previous 6 months. Similarly, the diagnosis rate is increased (i.e., 2, 4, 8, 16, and 32-fold) compared to the baseline diagnosis rate, and individuals initiate ART on the same day. At the baseline, 36% of individuals who acquired HIV are diagnosed during the first 6 months of infection. As the diagnosis rates increase incrementally, the proportions of diagnosed individuals rise to 60%, 84%, 97%, 99.99%, and 100%, respectively.

Model outcomes

To evaluate the intervention impact, we considered the annual numbers of new HIV infections and new HIV diagnoses, the cumulative number of new HIV infections averted and reduction in HIV diagnoses, as well as the distribution of the annual number of new HIV diagnoses by the duration between HIV acquisition and diagnosis. To facilitate comparison between the data and model outputs, we report the latter by adapting the classification used by SHM in the annual reports. This classification stratifies stage of HIV infection at diagnosis as 0-6 months, 6-12 months, more than 12 months. The cumulative number of new HIV infections averted and reduction in HIV diagnoses were calculated over 10 years starting from the intervention implementation on 1 January 2023. For each scenario, we generated 20 trajectories for each of 100 parameter sets obtained through the calibration process. We summarized the distribution of the model outputs by calculating median of measurements over 20 trajectories for each parameter set and subsequently presenting the outputs as medians and 95-th quantile interval (95-th QI) of measurements over 100 parameter sets.

Sensitivity analyses

We investigated the contribution of immediate initiation of ART on the impact of the intervention on HIV transmission dynamics. We also have considered an impact of the intervention which may increase diagnosis rates in individuals whose history of HIV infection exceeds 6 months but is shorter than one year. The full description of the sensitivity analyses is provided in the Subsections Sensitivity to parameter perturbation and Immediate initiation of ART in Section Additional Analyses in S2 Appendix.

Model fit

The model fit to key data statistics of interest is shown in Fig 1. There was strong agreement between the model outputs and the data, namely the SHM estimate of the annual numbers of new HIV infections (Fig 1a) and new HIV diagnoses (Fig 1b). The model estimates of the proportions of individuals who received an HIV diagnosis within the first 6 and between 6 and 12 months following HIV acquisition marginally exceeded the data estimates (Fig 1c).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Model fit to the HIV surveillance data and SHM-provided estimates among MSM in the Netherlands.

a Newly acquired HIV infections, b newly diagnosed HIV infections, and c distribution of the number of new HIV diagnoses by the duration between HIV acquisition and diagnosis for MSM, as estimated in the model and reported by SHM in the Netherlands. In a and b, the red dots connected by the dashed line depict the baseline model output. For the data, the large grey stars and the bars denote the median estimates and the confidence intervals, respectively. For the model outputs, the large red dots and the bars denote the median estimates and the 95-th QI, respectively. In c, the bar chart colors correspond to the time between HIV acquisition and diagnosis. For each year, bars with saturated colors and solid borders on the left correspond to the data, while the bars with less saturated colors and dashed borders on the right correspond to the model output.

https://doi.org/10.1371/journal.pcbi.1012055.g001

Maximum impact of the intervention

The comparison of the baseline model scenario with the maximum impact scenario is shown in Figs 2 and 3. Specifically, we examined the annual numbers of new HIV infections (Fig 2a) and new HIV diagnoses (Fig 2b). Furthermore, we assessed the distribution of the annual number of new HIV diagnoses by the duration between HIV acquisition and diagnosis to evaluate the intervention’s time frame of efficiency (Fig 3). New HIV infections. Our analyses indicated that in the context of continually decreasing low annual numbers of new HIV infections, as observed among MSM in the Netherlands, an intervention facilitating increased diagnosis of individuals with early HIV infection combined with immediate initiation of ART can further expedite this downward trend (Fig 2a). The effects of such intervention can become noticeable as early as the first year after implementation. In the baseline scenario, we anticipate the median annual number of new HIV infections to decline from 128 (95-th QI: 94–161) in 2023 to 81 (95-th QI: 46–138) in 2032. In the maximum impact scenario, we expect the median annual number of new HIV infections to decrease from 108 (95-th QI: 83–137) in 2023 to 55 (95-th QI: 31–96) in 2032, resulting in a cumulative decrease of 298 (95-th QI: 162–451) over 10 years. Despite the fact that all individuals who newly acquire HIV are diagnosed almost immediately, onward transmission may still occur in the model due to undiagnosed individuals with chronic HIV infection remaining undiagnosed and undiagnosed HIV infections imported from abroad. Furthermore, individuals who experience ART failure or drop out from ART programme may transmit HIV until the time when they achieve a suppressed viral load again.

New HIV diagnoses. The analysis of the annual number of new diagnoses (Fig 2b) indicated that, in the maximum impact scenario, there will be a sharp increase in the median number of newly diagnosed HIV infections from 166 (IQR: 139–202) at baseline to 235 (186–280) in the year following the start of the intervention. However, the number of HIV diagnoses is expected to decrease to the baseline scenario level within the first two years of the intervention onset and subsequently drop significantly below it by the third year. This drastic decrease in newly diagnosed HIV infections signifies an overall reduction in HIV transmission induced by the intervention. In the maximum impact scenario, the model predicted a decrease in the cumulative number of diagnoses of 182 (95-th QI: 77–315) over 10 years.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Model predictions for the maximum impact intervention.

(a) Newly acquired HIV infections and (b) newly diagnosed HIV infections in the baseline and maximum impact model scenarios. The red dots connected by the dashed line depicts the baseline scenario without additional diagnosis of individuals with early infection. The black triangles connected by a solid line depict the maximum expected impact of an intervention where individuals with early infection are diagnosed immediately after HIV acquisition and start ART immediately at the time point of receiving the diagnosis. The dynamics are summarized by the median estimates (circles and triangles) and the IQ (bars).

https://doi.org/10.1371/journal.pcbi.1012055.g002

Distribution of new HIV diagnoses by the duration between HIV acquisition and diagnosis. To analyze the window of efficiency of the maximum impact intervention, we examined the distribution of new HIV diagnoses by the duration between HIV acquisition and the time of diagnosis (Fig 3). In the baseline scenario, our model predicted that the majority of individuals continue to be diagnosed more than 12 months after HIV acquisition (Fig 3a). For the maximum impact intervention, the number and proportion of diagnoses in individuals with early HIV infection increased drastically in the first three years of the intervention (Fig 3b) and continued the exceed baseline levels in the subsequent years. Specifically, over the first three years, in the baseline scenario, a median of 80 (95-th QI: 44–132) out of 422 (95-th QI: 296-564) new diagnoses were in individuals who acquired HIV within the previous 6 months. In the maximum impact scenario, a median of 206 (95-th QI: 128–292) out of 458 (95-th QI: 320–616) individuals were expected to receive a diagnosis within the first 6 months following HIV acquisition. In both baseline and maximum impact scenarios, the number of new diagnoses in individuals infected in the first 6 months following HIV acquisition stabilizes towards the end of the time horizon with median 20 (95-th QI: 8–36) and 24 (95-th QI: 16–60), respectively.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Distribution of new HIV diagnoses by the duration between HIV acquisition and diagnosis.

(a) The baseline scenario without an increase in the diagnosis rate of individuals with early infection. (b) The maximum impact intervention combines immediate diagnosis following acquisition of HIV combined with immediate ART initiation. Bar chart colors correspond to the duration between HIV acquisition and the time of diagnosis.

https://doi.org/10.1371/journal.pcbi.1012055.g003

Attaining maximum impact

To identify the increase that results in a reduction (relative to the baseline) of the number of new HIV infections comparable to that of the maximum impact intervention we investigated a range of diagnosis rates for individuals with early HIV infection (Fig 4). Additionally, we considered the impact of an extended intervention, where the diagnosis rate is increased in all individuals who acquired HIV infection within the previous 6 months. To perform these analyses, we calculated the cumulative number of averted HIV infections (Fig 4a) and diagnoses (Fig 4b) over 10 years.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Impact of the intervention across different scenarios.

(a) Cumulative number averted of HIV infections and (b) cumulative HIV diagnoses over 10 years. Yellow squares and blue triangles correspond to the intervention where the diagnosis rate is increased, compared to the baseline, in individuals with early HIV infection or those who acquired HIV within the previous 6 months, respectively. The black dots mark the maximum impact scenario.

https://doi.org/10.1371/journal.pcbi.1012055.g004

Accelerated diagnosis in individuals infected with early HIV infection. A 2-fold increase in the diagnosis rate of individuals with early HIV infection led to 80 (95-th QI: -32–195) total infections averted in 10 years, with 31 (95-th QI -234–334) of which were averted in the first five years (Fig 4a). An 8-fold increase in the diagnosis rate of early infections reduced the median cumulative infections to 216 (95-th QI: 75–338). The 8-fold increase had a more immediate impact than the 2-fold increase, with 95 (95-th QI: -155–417) infections averted in the first five years. A 16-fold increase resulted in 247 (95-th QI: 122–398) total infections averted, 114 (95-th QI: -123–450) of which occurred in the first five years. Finally, a 32-fold increase in the diagnosis rate resulted in 269 (95-th QI: 148-400) infections averted. However, this outcome is not proximate to the maximum impact of the intervention [i.e., 298 (95-th QI: 162–451) infections averted]. Notably, in the first five years, the number of infections averted in the 32-increase intervention was almost equal to the 16-fold increase intervention [i.e., 114 (95-th QI: -123–450) vs. 128 (95-th QI: -100–435) cumulative infections, respectively]. The trends we observed in the decrease in the cumulative number of new HIV infections were respectively reflected in the cumulative number of new HIV diagnoses (Fig 4b). Thus, an intervention that accelerates diagnosis in individuals with early HIV infection should aim for a sufficiently high increase in the diagnosis rate. However, once this threshold is reached, no additional benefit can be attained through further increases. Instead, consideration should be given to an additional expansion of the intervention involving a larger group of MSM with undiagnosed HIV infection.

Accelerated diagnosis in individuals infected within the previous 6 months. To identify such expansion, we investigated the outcomes of an intervention with an increased diagnosis rate in individuals who acquired HIV within the previous 6 months. We observed that this intervention yields a larger number of infections averted (Fig 4a, blue triangles) throughout the range of increases in the diagnosis rate that we considered. For a 16-fold or larger increase in the diagnosis rate, in individuals who acquired HIV within the previous 6 months predicted to result in 282 (95-th QI: 147–408) infections averted. Also, expansion of the intervention to individuals who acquired HIV infection within the last 6 months requires a lower increase in diagnosis rate, i.e. 8 times, yields comparable outcomes to the intervention that captures only individuals with AEHI but requires an increase of 32 times, with 256 (95-th QI: 122–411) and 269 (95-th QI: 147–400) infections averted. Finally, the increase of the diagnosis rate by a factor of 8, in the intervention with scope extending to individuals who acquired HIV in the last 6 months results in the largest absolute decrease in the number of diagnoses (median of 37).

For the full tabulation of scenarios’ outcomes as presented on Fig 4 please refer to Section Complete statement of the results for incremental increases in diagnosis rate in Supplementary Materials 1.

Sensitivity analyses

We explored the contribution of ART immediately after receiving an HIV diagnosis on the impact of the intervention. Repeating the analysis from the previous section, we examined the 10-year trends in both new HIV infections and diagnoses across various diagnosis rates among individuals with early HIV infection and those infected in the last 6 months. This time, individuals diagnosed through the intervention were assumed to start ART at the same rate as those identified via routine testing. Our findings suggest that, in our study context, under conditions similar to the contemporary Netherlands, when the increase in diagnosis rates is small, the added benefit of immediate ART initiation on reducing HIV incidence is not substantial beyond the impact of accelerated diagnosis. However, with larger increases in diagnosis rates, the immediate initiation of ART can result in averting a significant number of new HIV infections. However, even for large increases in the diagnosis rate, the contribution of ART is significantly smaller than that of the accelerated diagnosis.

Finally, we investigated whether expanding the scope of the intervention to include individuals who acquired HIV within the last 12 months would yield further benefits. We assumed an equal diagnosis rate for individuals infected between 6 and 12 months prior and those infected within the previous 6 months. Our projections show that this scenario could result in further reductions in the number of HIV infections and diagnoses. The most substantial improvement relative to the 6-months intervention is expected for a smaller increases in the diagnosis rate (2- and 4-fold), with diminishing returns for larger diagnosis rates. In contrast, when considering reduction in the cumulative number of HIV diagnoses, a progressive increase in the diagnosis rate, results in comparable gains across different rates. It is important to note that while the increase in diagnosis rates is multiplicative, the cumulative reduction in the number of HIV diagnoses is additive.

The detailed analyses are provided in the Subsections Immediate initiation of ART and Increase in the scope of the intervention in Section Additional Analyses in S2 Appendix.