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Objectives Papua New Guinea (PNG) has among the highest rates of sexually transmitted infections (STIs) globally and is committed to reducing their incidence. The Syphilis Interventions Towards Elimination (SITE) model was used to explore the expected impact and cost of alternative syphilis intervention scale-up scenarios. Methods SITE is a dynamical model of syphilis transmission among adults 15–49 years. Individuals are divided into nine groups based on sexual behaviour and into six stages of infection. The model was calibrated to PNG using data from routine surveillance, bio-behavioural surveys, research studies and program records. Inputs included syphilis prevalence, risk behaviours, intervention coverage and service delivery unit costs. Scenarios compared different interventions (clinical treatment, contact tracing, syphilis screening, and condom promotion) for incidence and cost per infection averted over 2021–2030. Results Increasing treatment coverage of symptomatic primary/secondary-stage syphilis cases from 25 to 35% in 2020 to 60% from 2023 onwards reduced estimated incidence over 2021–2030 by 55%, compared to a scenario assuming constant coverage at 2019–2020 levels. The introduction of contact tracing in 2020, assuming 0.4 contacts per symptomatic person treated, reduced incidence over 2021–2030 by 10%. Increasing screening coverage by 20–30 percentage points from the 2019–2020 level reduced incidence over 2021–2030 by 3–16% depending on the target population. Scaling-up clinical, symptom-driven treatment and contact tracing had the lowest cost per infection averted, followed by condom promotion and periodic screening of female sex workers and men who have sex with men. Conclusions PNG could considerably reduce its syphilis burden by scaling-up clinical treatment and contact tracing alongside targeted behavioural risk reduction interventions. SITE is a useful tool countries can apply to inform national STI programming and resource allocation.

Summary Background The COVID-19 pandemic could lead to disruptions to provision of HIV services for people living with HIV and those at risk of acquiring HIV in sub-Saharan Africa, where UNAIDS estimated that more than two-thirds of the approximately 38 million people living with HIV resided in 2018. We aimed to predict the potential effects of such disruptions on HIV-related deaths and new infections in sub-Saharan Africa. Methods In this modelling study, we used five well described models of HIV epidemics (Goals, Optima HIV, HIV Synthesis, an Imperial College London model, and Epidemiological MODeling software [EMOD]) to estimate the effect of various potential disruptions to HIV prevention, testing, and treatment services on HIV-related deaths and new infections in sub-Saharan Africa lasting 6 months over 1 year from April 1, 2020. We considered scenarios in which disruptions affected 20%, 50%, and 100% of the population. Findings A 6-month interruption of supply of antiretroviral therapy (ART) drugs across 50% of the population of people living with HIV who are on treatment would be expected to lead to a 1·63 times (median across models; range 1·39–1·87) increase in HIV-related deaths over a 1-year period compared with no disruption. In sub-Saharan Africa, this increase amounts to a median excess of HIV deaths, across all model estimates, of 296 000 (range 229 023–420 000) if such a high level of disruption occurred. Interruption of ART would increase mother-to-child transmission of HIV by approximately 1·6 times. Although an interruption in the supply of ART drugs would have the largest impact of any potential disruptions, effects of poorer clinical care due to overstretched health facilities, interruptions of supply of other drugs such as co-trimoxazole, and suspension of HIV testing would all have a substantial effect on population-level mortality (up to a 1·06 times increase in HIV-related deaths over a 1-year period due to disruptions affecting 50% of the population compared with no disruption). Interruption to condom supplies and peer education would make populations more susceptible to increases in HIV incidence, although physical distancing measures could lead to reductions in risky sexual behaviour (up to 1·19 times increase in new HIV infections over a 1-year period if 50% of people are affected). Interpretation During the COVID-19 pandemic, the primary priority for governments, donors, suppliers, and communities should focus on maintaining uninterrupted supply of ART drugs for people with HIV to avoid additional HIV-related deaths. The provision of other HIV prevention measures is also important to prevent any increase in HIV incidence. Funding Bill & Melinda Gates Foundation.

Background UNAIDS has established new program targets for 2025 to achieve the goal of eliminating AIDS as a public health threat by 2030. This study reports on efforts to use mathematical models to estimate the impact of achieving those targets. Methods and findings We simulated the impact of achieving the targets at country level using the Goals model, a mathematical simulation model of HIV epidemic dynamics that includes the impact of prevention and treatment interventions. For 77 high-burden countries, we fit the model to surveillance and survey data for 1970 to 2020 and then projected the impact of achieving the targets for the period 2019 to 2030. Results from these 77 countries were extrapolated to produce estimates for 96 others. Goals model results were checked by comparing against projections done with the Optima HIV model and the AIDS Epidemic Model (AEM) for selected countries. We included estimates of the impact of societal enablers (access to justice and law reform, stigma and discrimination elimination, and gender equality) and the impact of Coronavirus Disease 2019 (COVID-19). Results show that achieving the 2025 targets would reduce new annual infections by 83% (71% to 86% across regions) and AIDS-related deaths by 78% (67% to 81% across regions) by 2025 compared to 2010. Lack of progress on societal enablers could endanger these achievements and result in as many as 2.6 million (44%) cumulative additional new HIV infections and 440,000 (54%) more AIDS-related deaths between 2020 and 2030 compared to full achievement of all targets. COVID-19–related disruptions could increase new HIV infections and AIDS-related deaths by 10% in the next 2 years, but targets could still be achieved by 2025. Study limitations include the reliance on self-reports for most data on behaviors, the use of intervention effect sizes from published studies that may overstate intervention impacts outside of controlled study settings, and the use of proxy countries to estimate the impact in countries with fewer than 4,000 annual HIV infections. Conclusions The new targets for 2025 build on the progress made since 2010 and represent ambitious short-term goals. Achieving these targets would bring us close to the goals of reducing new HIV infections and AIDS-related deaths by 90% between 2010 and 2030. By 2025, global new infections and AIDS deaths would drop to 4.4 and 3.9 per 100,000 population, and the number of people living with HIV (PLHIV) would be declining. There would be 32 million people on treatment, and they would need continuing support for their lifetime. Incidence for the total global population would be below 0.15% everywhere. The number of PLHIV would start declining by 2023., John Stover and co-workers assess the potential health impacts of UNAIDS’ HIV/AIDS targets., Author summary Why was this study done? The previous UNAIDS strategic plan expired in 2020, creating a need for a new plan to guide efforts for the next 5 years. Modeling contributed to the development of the new plan by assessing the epidemiological impact of proposed intervention coverage targets and estimating the financial resources needed to achieve them. What did the researchers do and find? We applied mathematical simulation models to 77 high HIV burden countries to examine the effects of the proposed intervention coverage targets on trends in new HIV infections and AIDS-related deaths. The results were extended to a total of 173 countries to provide a comprehensive global analysis. Results show that achieving the 2025 targets would reduce new annual infections by 83% (71% to 86% across regions) and AIDS-related deaths by 78% (67% to 81% across regions) by 2025 compared to 2010. Progress on societal enablers (access to justice, prevention of stigma and discrimination, and prevention of gender-based violence [GBV]) is essential to achieve these targets. Coronavirus Disease 2019 (COVID-19)–related disruptions could increase new HIV infections and AIDS-related deaths in the short term, but targets could still be achieved by 2025. What do these findings mean? Although global efforts have failed to achieve the ambitious 2020 targets, it is still possible to achieve the 2030 goal of eliminating AIDS as a public health threat. Many of the 2025 intervention coverage targets have already been achieved in some settings. Additional effort is required to accelerate progress in all countries and in all populations.

Funder: Joint United Nations Programme on HIV/AIDS; Id: http://dx.doi.org/10.13039/501100018734, Introduction: HIV planning requires granular estimates for the number of people living with HIV (PLHIV), antiretroviral treatment (ART) coverage and unmet need, and new HIV infections by district, or equivalent subnational administrative level. We developed a Bayesian small‐area estimation model, called Naomi, to estimate these quantities stratified by subnational administrative units, sex, and five‐year age groups. Methods: Small‐area regressions for HIV prevalence, ART coverage and HIV incidence were jointly calibrated using subnational household survey data on all three indicators, routine antenatal service delivery data on HIV prevalence and ART coverage among pregnant women, and service delivery data on the number of PLHIV receiving ART. Incidence was modelled by district‐level HIV prevalence and ART coverage. Model outputs of counts and rates for each indicator were aggregated to multiple geographic and demographic stratifications of interest. The model was estimated in an empirical Bayes framework, furnishing probabilistic uncertainty ranges for all output indicators. Example results were presented using data from Malawi during 2016–2018. Results: Adult HIV prevalence in September 2018 ranged from 3.2% to 17.1% across Malawi's districts and was higher in southern districts and in metropolitan areas. ART coverage was more homogenous, ranging from 75% to 82%. The largest number of PLHIV was among ages 35 to 39 for both women and men, while the most untreated PLHIV were among ages 25 to 29 for women and 30 to 34 for men. Relative uncertainty was larger for the untreated PLHIV than the number on ART or total PLHIV. Among clients receiving ART at facilities in Lilongwe city, an estimated 71% (95% CI, 61% to 79%) resided in Lilongwe city, 20% (14% to 27%) in Lilongwe district outside the metropolis, and 9% (6% to 12%) in neighbouring Dowa district. Thirty‐eight percent (26% to 50%) of Lilongwe rural residents and 39% (27% to 50%) of Dowa residents received treatment at facilities in Lilongwe city. Conclusions: The Naomi model synthesizes multiple subnational data sources to furnish estimates of key indicators for HIV programme planning, resource allocation, and target setting. Further model development to meet evolving HIV policy priorities and programme need should be accompanied by continued strengthening and understanding of routine health system data.

Introduction The Case Surveillance and Vital Registration (CSAVR) model within Spectrum estimates HIV incidence trends from surveillance data on numbers of new HIV diagnoses and HIV‐related deaths. This article describes developments of the CSAVR tool to more flexibly model diagnosis rates over time, estimate incidence patterns by sex and age group and by key population group. Methods We modelled HIV diagnosis rate trends as a mixture of three factors, including temporal and opportunistic infection components. The tool was expanded to estimate incidence rate ratios by sex and age for countries with disaggregated reporting of new HIV diagnoses and AIDS deaths, and to account for information on key populations such as men who have sex with men (MSM), males who inject drugs (MWID), female sex workers (FSW) and females who inject drugs (FWID). We used a Bayesian framework to calibrate the tool in 71 high‐income or low‐HIV burden countries. Results Across countries, an estimated median 89% (interquartile range [IQR]: 78%–96%) of HIV‐positive adults knew their status in 2019. Mean CD4 counts at diagnosis were stable over time, with a median of 456 cells/μl (IQR: 391–508) across countries in 2019. In European countries reporting new HIV diagnoses among key populations, median estimated proportions of males that are MSM and MWID was 1.3% (IQR: 0.9%–2.0%) and 0.56% (IQR: 0.51%–0.64%), respectively. The median estimated proportions of females that are FSW and FWID were 0.36% (IQR: 0.27%–0.45%) and 0.14 (IQR: 0.13%–0.15%), respectively. HIV incidence per 100 person‐years increased among MSM, with median estimates reaching 0.43 (IQR: 0.29–1.73) in 2019, but remained stable in MWID, FSW and FWID, at around 0.12 (IQR: 0.04–1.9), 0.09 (IQR: 0.06–0.69) and 0.13% (IQR: 0.08%–0.91%) in 2019, respectively. Knowledge of HIV status among HIV‐positive adults gradually increased since the early 1990s to exceed 75% in more than 75% of countries in 2019 among each key population. Conclusions CSAVR offers an approach to using routine surveillance and vital registration data to estimate and project trends in both HIV incidence and knowledge of HIV status.

Introduction The Spectrum/AIM model is used by national HIV programs and UNAIDS to prepare annual estimates of key HIV indicators. This article describes key updates to paediatric and adult models for the 2021 round of HIV estimates. Methods Potential updates to Spectrum arise due to newly available data, new analyses of existing data, and the need for new issues to be addressed. Updates are guided by experts through the UNAIDS Reference Group on Estimates, Modelling and Projections. Changes are tested and assessed for impact before being accepted into the final model. Results Spectrum tracks children living with HIV by CD4% for ages 0–4 and CD4 count for ages 5–14. Data from IeDEA treatment sites have been used to map the transition from CD4% to CD4 count at age 5. Breastfeeding patterns in sub‐Saharan Africa have been updated with the latest survey data and estimates of continuation on antiretroviral therapy (ART) with breastfeeding have been revised based on recent studies. Model assumptions about the CD4 counts of people who drop out of ART have been revised to account for CD4 count increases while on treatment. If available, monthly data on numbers on ART can now be used to estimate the effects of COVID‐19‐related disruptions during 2020. Conclusions These changes are intended to provide more accurate estimates of HIV burden. The effects of these changes on paediatric indicators are small except in countries with new surveys that might have updated patterns of breastfeeding. Changes to the adult model have little effect on total new infections. AIDS‐related deaths will be somewhat lower in countries that have data on ART drop out but might be increased by HIV care disruptions due to COVID‐19. The updated model uses newly available data to improve the estimation of paediatric and adult HIV indicators.

Supplemental Digital Content is available in the text, Objective: The Joint United Nations Programme on HIV/AIDS-supported Spectrum software package is used by most countries worldwide to monitor the HIV epidemic. In Spectrum, HIV incidence trends among adults (aged 15–49 years) are derived by either fitting to seroprevalence surveillance and survey data or generating curves consistent with case surveillance and vital registration data, such as historical trends in the number of newly diagnosed infections or AIDS-related deaths. This article describes development and application of the case surveillance and vital registration (CSAVR) tool for the 2019 estimate round. Methods: Incidence in CSAVR is either estimated directly using single logistic, double logistic, or spline functions, or indirectly via the ‘r-logistic’ model, which represents the (log-transformed) per-capita transmission rate using a logistic function. The propensity to get diagnosed is assumed to be monotonic, following a Gamma cumulative distribution function and proportional to mortality as a function of time since infection. Model parameters are estimated from a combination of historical surveillance data on newly reported HIV cases, mean CD4+ at HIV diagnosis and estimates of AIDS-related deaths from vital registration systems. Bayesian calibration is used to identify the best fitting incidence trend and uncertainty bounds. Results: We used CSAVR to estimate HIV incidence, number of new diagnoses, mean CD4+ at diagnosis and the proportion undiagnosed in 31 European, Latin American, Middle Eastern, and Asian-Pacific countries. The spline model appeared to provide the best fit in most countries (45%), followed by the r-logistic (25%), double logistic (25%), and single logistic models. The proportion of HIV-positive people who knew their status increased from about 0.31 [interquartile range (IQR): 0.10–0.45] in 1990 to about 0.77 (IQR: 0.50–0.89) in 2017. The mean CD4+ at diagnosis appeared to be stable, at around 410 cells/μl (IQR: 224–567) in 1990 and 373 cells/μl (IQR: 174–475) by 2017. Conclusion: Robust case surveillance and vital registration data are routinely available in many middle-income and high-income countries while HIV seroprevalence surveillance and survey data may be scarce. In these countries, CSAVR offers a simpler, improved approach to estimating and projecting trends in both HIV incidence and knowledge of HIV status.

Supplemental Digital Content is available in the text, Objectives: Improve models for estimating HIV epidemic trends in sub-Saharan Africa (SSA). Design: Mathematical epidemic model fit to national HIV survey and ANC sentinel surveillance (ANC-SS) data. Methods: We modified EPP to incorporate age and sex stratification (EPP-ASM) to more accurately capture the shifting demographics of maturing HIV epidemics. Secondly, we developed a new functional form for the HIV transmission rate, termed ‘r-hybrid’, which combines a four-parameter logistic function for the initial epidemic growth, peak, and decline followed by a first-order random walk for recent trends after epidemic stabilization. We fitted the r-hybrid model along with previously developed r-spline and r-trend models to HIV prevalence data from household surveys and ANC-SS in 177 regions in 34 SSA countries. We used leave-one-out cross validation with household survey HIV prevalence to compare model predictions. Results: The r-hybrid and r-spline models typically provided similar HIV prevalence trends, but sometimes qualitatively different assessments of recent incidence trends because of different structural assumptions about the HIV transmission rate. The r-hybrid model had the lowest average continuous ranked probability score, indicating the best model predictions. Coverage of 95% posterior predictive intervals was 91.5% for the r-hybrid model, versus 87.2 and 85.5% for r-spline and r-trend, respectively. Conclusion: The EPP-ASM and r-hybrid models improve consistency of EPP and Spectrum, improve the epidemiological assumptions underpinning recent HIV incidence estimates, and improve estimates and short-term projections of HIV prevalence trends. Countries that use general population survey and ANC-SS data to estimate HIV epidemic trends should consider using these tools.

Supplemental Digital Content is available in the text, Background: The Spectrum/AIM model is used by national programs and UNAIDS to prepare annual estimates of the status of the HIV epidemic in 170 countries. The model and assumptions are updated regularly under the guidance of the UNAIDS Reference Group on Estimates, Modelling and Projections in response to new data, studies and program needs. This article describes the most recent updates for the 2018 round of estimates. Methods: New data on AIDS-related mortality from Europe and Brazil have been used to update mortality rates of those not on antiretroviral therapy (ART). Household survey data and new studies of pregnant women, mothers, and children have been used to improve estimates of the number of HIV-positive pregnant and breastfeeding women and pediatric ART initiation. New tools to estimate geographic variation in HIV prevalence have been used to prepare district estimates of key indicators. Results: The 2018 version of Spectrum includes: new estimates of non-ART AIDS-related mortality by CD4+ count that depend on ART coverage; a procedure to estimate country-specific patterns of HIV incidence by age by fitting to prevalence by age from household surveys; an updated estimate of postpartum transmission with ART started before pregnancy of 0.023% per month; an updated estimate of retention on treatment at delivery of 80% for all women on ART; a somewhat older pattern of ART initiation by age that has 26% of new pediatric patients initiating ART at 10–14 years of age, 18% at 2–4 years of age, and 26% at 5–9 years of age; and a new tool for estimating key HIV indicators at the district level. Conclusion: The new methods and data implemented in the 2018 version of Spectrum allow national programs more flexibility in describing their programs and are intended to improve the estimates of adult mortality and pediatric HIV indicators.

Introduction Model‐based estimates of key HIV indicators depend on past epidemic trends that are derived based on assumptions about HIV disease progression and mortality in the absence of antiretroviral treatment (ART). Population‐based HIV Impact Assessment (PHIA) household surveys conducted between 2015 and 2018 found substantial numbers of respondents living with untreated HIV infection. CD4 cell counts measured in these individuals provide novel information to estimate HIV disease progression and mortality rates off ART. Methods We used Bayesian multi‐parameter evidence synthesis to combine data on (1) cross‐sectional CD4 cell counts among untreated adults living with HIV from 10 PHIA surveys, (2) survival after HIV seroconversion in East African seroconverter cohorts, (3) post‐seroconversion CD4 counts and (4) mortality rates by CD4 count predominantly from European, North American and Australian seroconverter cohorts. We used incremental mixture importance sampling to estimate HIV natural history and ART uptake parameters used in the Spectrum software. We validated modelled trends in CD4 count at ART initiation against ART initiator cohorts in sub‐Saharan Africa. Results Median untreated HIV survival decreased with increasing age at seroconversion, from 12.5 years [95% credible interval (CrI): 12.1–12.7] at ages 15–24 to 7.2 years (95% CrI: 7.1–7.7) at ages 45–54. Older age was associated with lower initial CD4 counts, faster CD4 count decline and higher HIV‐related mortality rates. Our estimates suggested a weaker association between ART uptake and HIV‐related mortality rates than previously assumed in Spectrum. Modelled CD4 counts in untreated people living with HIV matched recent household survey data well, though some intercountry variation in frequencies of CD4 counts above 500 cells/mm3 was not explained. Trends in CD4 counts at ART initiation were comparable to data from ART initiator cohorts. An alternate model that stratified progression and mortality rates by sex did not improve model fit appreciably. Conclusions Synthesis of multiple data sources results in similar overall survival as previous Spectrum parameter assumptions but implies more rapid progression and longer survival in lower CD4 categories. New natural history parameter values improve consistency of model estimates with recent cross‐sectional CD4 data and trends in CD4 counts at ART initiation.

Background: Preexposure prophylaxis (PrEP) with tenofovir and emtricitabine can prevent new HIV-1 infections, but there is a concern that use of PrEP could increase HIV drug resistance resulting in loss of treatment options. We compared standardized outcomes from three independent mathematical models simulating the impact of PrEP on HIV transmission and drug resistance in sub-Saharan African countries. Methods: All models assume that people using PrEP receive an HIV test every 3-6 months. The models vary in structure and parameter choices for PrEP coverage, effectiveness of PrEP (at different adherence levels) and the rate with which HIV drug resistance emerges and is transmitted. Results: Themodels predict that the use of PrEP in conjunction with antiretroviral therapy will result in a lower prevalence of HIVthanwhen only antiretroviral therapy is used.With or without PrEP, all models suggest that HIV drug resistance will increase over the next 20 years due to antiretroviral therapy. PrEP will increase the absolute prevalence of drug resistance in the total population by less than 0.5%andamongst infected individuals by at most 7%. Twenty years after the introduction of PrEP, the majority of drug-resistant infections is due to antiretroviral therapy (50-63% across models), whereas 40-50% will be due to transmission of drug resistance, and less than 4% to the use of PrEP. Conclusion: HIV drug resistance resulting from antiretroviral therapy is predicted to far exceed that resulting from PrEP. Concern over drug resistance should not be a reason to limit the use of PrEP.

SummaryWe applied a simulation model of HIV to analyze the effects of 3 and 6-month disruptions in health services as a result of COVID-19. We found that disruptions to primary prevention programs (male circumcision, behavior change programs, condom distribution) would have small but transitory effects on new infections that might be more than offset by reductions in commercial and multi-partner sex due to lock downs. However, if COVID-19 leads to disruptions in ART services the impacts on mortality could be severe, doubling or tripling the estimated number of HIV deaths in 2020.

Introduction Oral pre‐exposure prophylaxis (PrEP) provision is a priority intervention for high HIV prevalence settings and populations at substantial risk of HIV acquisition. This mathematical modelling analysis estimated the impact, cost and cost‐effectiveness of scaling up oral PrEP in 13 countries. Methods We projected the impact and cost‐effectiveness of oral PrEP between 2018 and 2030 using a combination of the Incidence Patterns Model and the Goals model. We created four PrEP rollout scenarios involving three priority populations—female sex workers (FSWs), serodiscordant couples (SDCs) and adolescent girls and young women (AGYW)—both with and without geographic prioritization. We applied the model to 13 countries (Eswatini, Ethiopia, Haiti, Kenya, Lesotho, Mozambique, Namibia, Nigeria, Tanzania, Uganda, Zambia and Zimbabwe). The base case assumed achievement of the Joint United Nations Programme on HIV/AIDS 90‐90‐90 antiretroviral therapy targets, 90% male circumcision coverage by 2020 and 90% efficacy and adherence levels for oral PrEP. Results In the scenarios we examined, oral PrEP averted 3% to 8% of HIV infections across the 13 countries between 2018 and 2030. For all but three countries, more than 50% of the HIV infections averted by oral PrEP in the scenarios we examined could be obtained by rollout to FSWs and SDCs alone. For several countries, expanding oral PrEP to include medium‐risk AGYW in all regions greatly increased the impact. The efficiency and impact benefits of geographic prioritization of rollout to AGYW varied across countries. Variations in cost‐effectiveness across countries reflected differences in HIV incidence and expected variations in unit cost. For most countries, rolling out oral PrEP to FSWs, SDCs and geographically prioritized AGYW was not projected to have a substantial impact on the supply chain for antiretroviral drugs. Conclusions These modelling results can inform prioritization, target‐setting and other decisions related to oral PrEP scale‐up within combination prevention programmes. We caution against extensive use given limitations in cost data and implementation approaches. This analysis highlights some of the immediate challenges facing countries—for example, trade‐offs between overall impact and cost‐effectiveness—and emphasizes the need to improve data availability and risk assessment tools to help countries make informed decisions.

Introduction A vaginal ring containing dapivirine is effective for HIV prevention as pre‐exposure prophylaxis (PrEP). We evaluated the potential epidemiological impact and cost‐effectiveness of dapivirine vaginal ring PrEP among 22‐ to 45‐year‐old women in KwaZulu‐Natal, South Africa. Methods Using mathematical modelling, we studied dapivirine vaginal ring PrEP implementation, either unprioritized, or prioritized based on HIV incidence (≥3% per year), age (22 to 29 years) or female sex worker status, alongside the implementation of voluntary medical male circumcision and antiretroviral therapy scaled‐up to UNAIDS Fast‐Track targets. Outcomes over the intervention (2019 to 2030) and lifetime horizons included cumulative HIV infections, life‐years lived, costs and cost‐effectiveness. We assessed the incremental cost‐effectiveness ratios against the revealed willingness to pay ($500) and the standard (2017 per capita gross domestic product; $6161) cost‐effectiveness thresholds for South Africa. Results Compared to a reference scenario without PrEP, implementation of dapivirine vaginal ring PrEP, assuming 56% effectiveness and covering 50% of 22 to 29‐year‐old or high‐incidence women, prevented 10% or 11% of infections by 2030 respectively. Equivalent, unprioritized coverage (30%) prevented fewer infections (7%), whereas 50% coverage of female sex workers had the least impact (4%). Drug resistance attributable to PrEP was modest (2% to 4% of people living with drug‐resistant HIV). Over the lifetime horizon, dapivirine PrEP implementation among female sex workers was cost‐saving, whereas incidence‐based PrEP cost $1898 per life‐year gained, relative to PrEP among female sex workers and $989 versus the reference scenario. In a scenario of 37% PrEP effectiveness, PrEP had less impact, but prioritization to female sex workers remained cost‐saving. In uncertainty analysis, female sex worker PrEP was consistently cost‐saving; and over the lifetime horizon, PrEP cost less than $6161 per life‐year gained in over 99% of simulations, whereas incidence‐ and age‐based PrEP cost below $500 per life‐year gained in 61% and 49% of simulations respectively. PrEP adherence and efficacy, and the effectiveness of antiretroviral therapy for HIV prevention, were the principal drivers of uncertainty in the cost‐effectiveness of PrEP. Conclusions Dapivirine vaginal ring PrEP would be cost‐saving in KwaZulu‐Natal if prioritized to female sex workers. PrEP's impact on HIV prevention would be increased, with potential affordability, if prioritized to women by age or incidence.

Background Tenofovir-containing regimens comprise the preferred first-line antiretroviral therapy (ART) in many countries including South Africa, where utilization of second-line regimens is limited. Considerable HIV drug resistance has occurred among persons failing tenofovir-containing first-line ART. We evaluated drug resistance at the population level using mathematical modeling. Setting Heterosexual HIV epidemic in KwaZulu-Natal, South Africa. Methods We constructed a stochastic individual-based model and simulated scenarios of ART implementation, either CD4-based (threshold < 500 cells/mL) or Fast-track (81% coverage by 2020), with consideration of major drug-associated mutations (M184V, K65R and non-nucleoside reverse transcriptase inhibitor (NNRTI)). Using base case and uncertainty analyses, we assessed (majority) drug resistance levels. Results By 2030, the median total resistance (proportion of HIV-infected persons with drug resistance) is predicted to reach 31.4% (interquartile range (IQR): 16.5%-50.2%) with CD4-based ART, decreasing to 14.5% (IQR: 7.7%-25.8%) with Fast-track implementation. In both scenarios, we find comparably high prevalence (~80%) of acquired NNRTI-associated, M184V and K65R mutations. Over 48% of individuals with acquired resistance harbor dual, 44% triple and 7% just single drug mutations. Drug-resistant HIV is predicted to comprise 40% (IQR: 27%-50%) of incident infections, while 70% of prevalent transmitted resistance is NNRTI-associated. At 2018, the projected total resistance is 15% (IQR: 7.5%-25%), with 18% (IQR: 13%-24%) of incident infections from transmitted drug-resistant HIV. Conclusions WHO-recommended preferred first-line ART could lead to substantial drug resistance. Effective surveillance of HIV drug resistance and utilization of second-line as well as alternative first-line regimens is crucial.

(See the editorial commentary by Celum et al on pages 189–91) Oral antiretroviral (ARV) pre-exposure prophylaxis (PrEP) is a new biomedical intervention against human immunodeficiency virus (HIV) transmission with proven efficacy [1–3]. There is concern, however, about the potential emergence and spread of HIV drug resistance arising from the rollout of PrEP, particularly in resource-constrained settings, where antiretroviral therapy (ART) options are limited [4]. This concern is amplified by the possibility that the same ARVs will be used for both ART and PrEP. The combination of 2 nucleoside reverse-transcriptase inhibitors, tenofovir (TDF) and lamivudine or emtricitabine (3TC or FTC, respectively), with 1 nonnucleoside reverse-transcriptase inhibitor (NNRTI), efavirenz or nevirapine, is the World Health Organization–recommended first-line ART regimen in several countries worldwide, including South Africa [4], and TDF or TDF + FTC have shown efficacy in HIV prevention trials [1–3]. Thus far, only 9 drug-resistant cases have been observed among clinical trial participants on PrEP, most of whom had unrecognized acute infection at enrollment. However, clinical trials of PrEP are not designed to address the population-level and/or long-term epidemiological impact of PrEP, including consequences of drug resistance. We therefore used a mathematical model [5] to examine the potential impact of orally administered overlapping and nonoverlapping PrEP and ART on HIV transmission and drug resistance in South Africa.

BACKGROUND: Long-acting injectable antiretrovirals such as rilpivirine (RPV) could promote adherence to preexposure prophylaxis (PrEP) for human immunodeficiency virus (HIV) prevention. However the cost-effectiveness of injectable PrEP is unclear. METHODS: We constructed a dynamic model of the heterosexual HIV epidemic in KwaZulu-Natal South Africa and analyzed scenarios of RPV PrEP scale-up for combination HIV prevention in comparison with a reference scenario without PrEP. We estimated new HIV infections life-years and costs and incremental cost-effectiveness ratios (ICERs) over 10-year and lifetime horizons assuming a societal perspective. RESULTS: Compared with no PrEP unprioritized scale-up of RVP PrEP covering 2.5%-15% of adults prevented up to 9% of new infections over 10 years. HIV prevention doubled (17%) when the same coverage was prioritized to 20- to 29-year-old women costing $10 880-$19 213 per infection prevented. Prioritization of PrEP to 80% of individuals at highest behavioral risk achieved comparable prevention (4%-8%) at

Injectable antiretrovirals including non-nucleoside reverse transcriptase inhibitors are being evaluated for pre-exposure prophylaxis for HIV prevention. Mathematical modeling suggests that injectable pre-exposure prophylaxis among KwaZulu-Natal's at-risk populations could have substantial preventive impact but may increase drug resistance unless highly effective., Background. A long-acting injectable formulation of rilpivirine (RPV), under investigation as antiretroviral pre-exposure prophylaxis (PrEP), may facilitate PrEP adherence. In contrast, cross-resistance between RPV and nonnucleoside reverse-transcriptase inhibitors comprising first-line antiretroviral therapy (ART) could promote human immunodeficiency virus (HIV) drug resistance and reduce PrEP's effectiveness. Methods. We use novel mathematical modeling of different RPV PrEP scale-up strategies in KwaZulu-Natal, South Africa, to investigate their effects on HIV prevention and drug resistance, compared with a reference scenario without PrEP. Results. Pre-exposure prophylaxis scale-up modestly increases the proportion of prevalent drug-resistant infections, from 33% to ≤37%. The change in the number of prevalent drug-resistant infections depends on the interplay between PrEP factors (coverage, efficacy, delivery reliability, and scale-up strategy) and the level of cross-resistance between PrEP and ART. An optimistic scenario of 70% effective RPV PrEP (90% efficacious and 80% reliable delivery), among women aged 20–29 years, prevents 17% of cumulative infections over 10 years while decreasing prevalent resistance; however, prevention decreases and resistance increases with more conservative assumptions. Uncertainty analysis assuming 40%–70% cross-resistance prevalence predicts an increase in prevalent resistance unless PrEP's effectiveness exceeds 90%. Conclusions. Prioritized scale-up of injectable PrEP among women in KwaZulu-Natal could reduce HIV infections, but suboptimal effectiveness could promote the spread of drug resistance.

Classical scheduling abstractions such as deadlines and priorities do not readily capture the complex timing semantics found in many real-time cyber-physical systems. Time utility functions provide a necessarily richer description of timing semantics, but designing utility-aware scheduling policies using them is an open research problem. In particular, scheduling design that optimizes expected utility accrual is needed for real-time cyber-physical domains. In this paper we design scheduling policies that optimize expected utility accrual for cyber-physical systems with periodic, non-preemptable tasks that run with stochastic duration. These policies are derived by solving a Markov Decision Process formulation of the scheduling problem. We use this formulation to demonstrate that our technique improves on existing heuristic utility accrual scheduling policies.

Open soft real-time systems, such as mobile robots, must respond adaptively to varying operating conditions, while balancing the need to perform multiple mission specific tasks against the requirement that those tasks complete in a timely manner. Setting and enforcing a utilization target for shared resources is a key mechanism for achieving this behavior. However, because of the uncertainty and non-preempt ability of some tasks, key assumptions of classical scheduling approaches do not hold. In previous work we presented foundational methods for generating task scheduling policies to enforce proportional resource utilization for open soft real-time systems with these properties. However, these methods scale exponentially in the number of tasks, limiting their practical applicability.In this paper, we present a novel parameterized scheduling policy that scales our technique to a much wider range of systems. These policies can represent geometric features of the scheduling policies produced by our earlier methods, but only require a number of parameters that is quadratic in the number of tasks. We provide empirical evidence that the best of these policies are competitive with exact solution methods in small problems, and significantly outperform heuristic methods in larger ones.

Open soft real-time systems, such as mobile robots, experience unpredictable interactions with their environments and yet must respond both adaptively and with reasonable temporal predictability. New scheduling approaches are needed to address the demands of such systems, in which many of the assumptions made by traditional real-time scheduling theory do not hold. In previous work we established foundations for a scheduling policy design and verification approach for open soft real-time systems, that can use different decision models, e.g., a Markov decision process (MDP), to capture the nuances of their scheduling semantics.However, several important refinements to the preliminary techniques developed in that work are needed to make the approach applicable in practice. This paper makes three main contributions to the state of the art in scheduling open soft real-time systems: (1) it defines a novel representation of the scheduling state space that is both more compact and more expressive than the model defined in our previous work; (2) it exploits regular structure of that representation to allow efficient verification of properties involving both discrete and continuous system state variables under specific scheduling policies; and (3) it removes the unnecessary use of a time horizon in our previous approach, thus allowing the more precise specification and enforcement of a wider range of scheduling policies for open soft real-time systems.

Scheduling the execution of multiple concurrent tasks on shared resources such as CPUs and network links is essential to ensuring the reliable operation of many autonomic systems. Well-known techniques such as rate-monotonic scheduling can offer rigorous timing and preemption guarantees, but only under assumptions (i.e. a fixed set of tasks with well-known execution times and invocation rates) that do not hold in many autonomic systems. New hierarchical scheduling techniques are better suited to enforce the more flexible execution constraints and enforcement mechanisms that are required for autonomic systems, but a rigorous and efficient foundation for verifying and enforcing concurrency and timing guarantees is still needed for these approaches. This paper summarises our previous work on addressing these challenges, on Markov decision process-based scheduling policy design and on wrapping repeated structure of the scheduling state spaces involved into a more efficient model, and presents a new algorithm called expanding state policy iteration (ESPI), that allows us to compute the optimal policy for a wrapped state model.