Hyperbolic Hexagons and Algebraic Curves in Genus 3

One of the consequences of the uniformization theorem of Koebe and Poincaré is that any smooth complex algebraic curve C of genus g > 1 is conformally equivalent to H/G, where G ⊂ PSL2(R) is a Fuchsian group and is naturally endowed with a hyperbolic metric. Conversely, any compact hyperbolic surface is isomorphic to an algebraic curve. Hence any curve of genus g > 1 may be described in two ways, either by an equation or by a Fuchsian grou

The population impact of herpes simplex virus type 2 (HSV-2) vaccination on the incidence of HSV-2, HIV and genital ulcer disease in South Africa: a mathematical modelling study

BACKGROUND: Evidence suggests HSV-2 infection increases HIV acquisition risk and HIV/HSV-2 coinfection increases transmission risk of both infections. We analysed the potential impact of HSV-2 vaccination in South Africa, a high HIV/HSV-2 prevalence setting. METHODS: We adapted a dynamic HIV transmission model for South Africa to incorporate HSV-2, including synergistic effects with HIV, to evaluate the impact of: (i) cohort vaccination of 9-year-olds with a prophylactic vaccine that reduces HSV-2 susceptibility; (ii) vaccination of symptomatically HSV-2-infected individuals with a therapeutic vaccine that reduces HSV shedding. FINDINGS: An 80% efficacious prophylactic vaccine offering lifetime protection with 80% uptake could reduce HSV-2 and HIV incidence by 84.1% (95% Credibility Interval: 81.2-86.0) and 65.4% (56.5-71.6) after 40 years, respectively. This reduces to 57.4% (53.6-60.7) and 42.1% (34.1-48.1) if efficacy is 50%, 56.1% (53.4-58.3) and 41.5% (34.2-46.9) if uptake is 40%, and 29.4% (26.0-31.9) and 24.4% (19.0-28.7) if protection lasts 10 years. An 80% efficacious therapeutic vaccine offering lifetime protection with 40% coverage among symptomatic individuals could reduce HSV-2 and HIV incidence by 29.6% (21.8-40.9) and 26.4% (18.5-23.2) after 40 years, respectively. This reduces to 18.8% (13.7-26.4) and 16.9% (11.7-25.3) if efficacy is 50%, 9.7% (7.0-14.0) and 8.6% (5.8-13.4) if coverage is 20%, and 5.4% (3.8-8.0) and 5.5% (3.7-8.6) if protection lasts 2 years. INTERPRETATION: Prophylactic and therapeutic vaccines offer promising approaches for reducing HSV-2 burden and could have important impact on HIV in South Africa and other high prevalence settings. FUNDING: WHO, NIAID

Empirical validation of the UNAIDS Spectrum model for subnational HIV estimates: case-study of children and adults in Manicaland, Zimbabwe

Background: More cost-effective HIV control may be achieved by targeting geographical areas with high infection rates. The AIDS Impact model of Spectrum – used routinely to produce national HIV estimates – could provide the required subnational estimates but is rarely validated with empirical data, even at a national level. Design: The validity of the Spectrum model estimates were compared to empirical estimates. Methods: Antenatal surveillance and population survey data from a population HIV cohort study in Manicaland, east Zimbabwe, were input into Spectrum 5.441 to create a simulation representative of the cohort population. Model and empirical estimates were compared for key demographic and epidemiological outcomes. Alternative scenarios for data availability were examined and sensitivity analyses were conducted for model assumptions considered important for subnational estimates. Results: Spectrum estimates generally agreed with observed data but HIV incidence estimates were higher than empirical estimates while estimates of early age all-cause adult mortality were lower. Child HIV prevalence estimates matched well with the survey prevalence among children. Estimated paternal orphanhood was lower than empirical estimates. Including observations from earlier in the epidemic did not improve the HIV incidence model fit. Migration had little effect on observed discrepancies - possibly because the model ignores differences in HIV prevalence between migrants and residents. Conclusions: The Spectrum model, using subnational surveillance and population data, provided reasonable subnational estimates although some discrepancies were noted. Differences in HIV prevalence between migrants and residents may need to be captured in the model if applied to subnational epidemics

The association between heterosexual anal intercourse and HIV acquisition in three prospective cohorts of women

The extent to which receptive anal intercourse (RAI) increases the HIV acquisition risk of women compared to receptive vaginal intercourse (RVI) is poorly understood. We evaluated RAI practice over time and its association with HIV incidence during three prospective HIV cohorts of women: RV217, MTN-003 (VOICE), and HVTN 907. At baseline, 16% (RV 217), 18% (VOICE) of women reported RAI in the past 3 months and 27% (HVTN 907) in the past 6 months, with RAI declining during follow-up by around 3-fold. HIV incidence in the three cohorts was positively associated with reporting RAI at baseline, albeit not always significantly. The adjusted hazard rate ratios for potential confounders (aHR) were 1.1 (95% Confidence interval: 0.8-1.5) for VOICE and 3.3 (1.6-6.8) for RV 217, whereas the ratio of cumulative HIV incidence by RAI practice was 1.9 (0.6-6.0) for HVTN 907. For VOICE, the estimated magnitude of association increased slightly when using a time-varying RAI exposure definition (aHR = 1.2; 0.9-1.6), and for women reporting RAI at every follow-up survey (aHR = 2.0 (1.3-3.1)), though not for women reporting higher RAI frequency (> 30% acts being RAI vs. no RAI in the past 3 months; aHR = 0.7 (0.4-1.1)). Findings indicated precise estimation of the RAI/HIV association, following multiple RVI/RAI exposures, is sensitive to RAI exposure definition, which remain imperfectly measured. Information on RAI practices, RAI/RVI frequency, and condom use should be more systematically and precisely recorded and reported in studies looking at sexual behaviors and HIV seroconversions; standardized measures would aid comparability across geographies and over time

Can HIV self-testing reach first-time testers? A telephone survey among self-test end users in Côte d'Ivoire, Mali, and Senegal

BACKGROUND: Coverage of HIV testing remains sub-optimal in West Africa. Between 2019 and 2022, the ATLAS program distributed ~400 000 oral HIV self-tests (HIVST) in Côte d'Ivoire, Mali, and Senegal, prioritising female sex workers (FSW) and men having sex with men (MSM), and relying on secondary redistribution of HIVST to partners, peers and clients to reach individuals not tested through conventional testing. This study assesses the proportion of first-time testers among HIVST users and the associated factors. METHODS: A phone-based survey was implemented among HIVST users recruited using dedicated leaflets inviting them to anonymously call a free phone number. We collected socio-demographics, sexual behaviours, HIV testing history, HIVST use, and satisfaction with HIVST. We reported the proportion of first-time testers and computed associated factors using logistic regression. RESULTS: Between March and June 2021, 2 615 participants were recruited for 50 940 distributed HIVST (participation rate: 5.1%). Among participants, 30% received their HIVST kit through secondary distribution (from a friend, sexual partner, family member, or colleague). The proportion who had never tested for HIV before HIVST (first-time testers) was 41%. The main factors associated with being a first-time tester were sex, age group, education level, condom use, and secondary distribution. A higher proportion was observed among those aged 24 years or less (55% vs 32% for 25-34, aOR: 0.37 [95%CI: 0.30-0.44], and 26% for 35 years or more, aOR: 0.28 [0.21-0.37]); those less educated (48% for none/primary education vs 45% for secondary education, aOR: 0.60 [0.47-0.77], and 29% for higher education, aOR: 0.33 [0.25-0.44]). A lower proportion was observed among women (37% vs 43%, aOR: 0.49 [0.40-0.60]); those reporting always using a condom over the last year (36% vs 51% for those reporting never using them, aOR: 2.02 [1.59-2.56]); and those who received their HISVST kit through primary distribution (39% vs 46% for secondary distribution, aOR: 1.32 [1.08-1.60]). CONCLUSION: ATLAS HIVST strategy, including secondary distribution, successfully reached a significant proportion of first-time testers. HIVST has the potential to reach underserved populations and contribute to the expansion of HIV testing services in West Africa

Modelling the Effects of Population Structure on Childhood Disease: The Case of Varicella

Realistic, individual-based models based on detailed census data are increasingly used to study disease transmission. Whether the rich structure of such models improves predictions is debated. This is studied here for the spread of varicella, a childhood disease, in a realistic population of children where infection occurs in the household, at school, or in the community at large. A methodology is first presented for simulating households with births and aging. Transmission probabilities were fitted for schools and community, which reproduced the overall cumulative incidence of varicella over the age range of 0–11 years old

What Proportion of Female Sex Workers Practise anal Intercourse and How Frequently? A Systematic Review and Meta-analysis.

HIV is more efficiently acquired during receptive anal intercourse (AI) compared to vaginal intercourse (VI) and may contribute substantially to female sex workers' (FSW) high HIV burden. We aim to determine how common and frequent AI is among FSW globally. We searched PubMed, Embase and PsycINFO for studies reporting the proportion of FSW practising AI (prevalence) and/or the number of AI acts (frequency) worldwide from 01/1980 to 10/2018. We assessed the influence of participant and study characteristics on AI prevalence (e.g. continent, study year and interview method) through sub-group analysis. Of 15,830 identified studies, 131 were included. Nearly all (N = 128) reported AI prevalence and few frequency (N = 13), over various recall periods. Most studies used face-to-face interviews (N = 111). Pooled prevalences varied little by recall period (lifetime: 15.7% 95%CI 12.2-19.3%, N = 30, I2 = 99%; past month: 16.2% 95%CI 10.8-21.6%, N = 18, I2 = 99%). The pooled proportion of FSW reporting < 100% condom use tended to be non-significantly higher during AI compared to during VI (e.g. any unprotected VI: 19.1% 95%CI 1.7-36.4, N = 5 and any unprotected AI: 46.4% 95%CI 9.1-83.6, N = 5 in the past week). Across all study participants, between 2.4 and 15.9% (N = 6) of all intercourse acts (AI and VI) were anal. Neither AI prevalence nor frequency varied substantially by any participant or study characteristics. Although varied, AI among FSW is generally common, inconsistently protected with condoms and practiced sufficiently frequently to contribute substantially to HIV acquisition in this risk group. Interventions to address barriers to condom use are needed

Comparison of empirically derived and model-based estimates of key population HIV incidence and the distribution of new infections by population group in sub-Saharan Africa

Background: The distribution of new HIV infections among key populations, including female sex workers (FSWs), gay men and other men who have sex with men (MSM), and people who inject drugs (PWID) are essential information to guide an HIV response, but data are limited in sub-Saharan Africa (SSA). We analyzed empirically derived and mathematical model-based estimates of HIV incidence among key populations and compared with the Joint United Nations Programme on HIV/AIDS (UNAIDS) estimates.Methods: We estimated HIV incidence among FSW and MSM in SSA by combining meta-analyses of empirical key population HIV incidence relative to the total population incidence with key population size estimates (KPSE) and HIV prevalence. Dynamic HIV transmission model estimates of HIV incidence and percentage of new infections among key populations were extracted from 94 country applications of 9 mathematical models. We compared these with UNAIDS-reported distribution of new infections, implied key population HIV incidence and incidence-to-prevalence ratios.Results: Across SSA, empirical FSW HIV incidence was 8.6-fold (95% confidence interval: 5.7 to 12.9) higher than total population female 15–39 year incidence, and MSM HIV incidence was 41.8-fold (95% confidence interval: 21.9 to 79.6) male 15–29 year incidence. Combined with KPSE, these implied 12% of new HIV infections in 2021 were among FSW and MSM (5% and 7% respectively). In sensitivity analysis varying KPSE proportions within 95% uncertainty range, the proportion of new infections among FSW and MSM was between 9% and 19%. Insufficient data were available to estimate PWID incidence rate ratios. Across 94 models, median proportion of new infections among FSW, MSM, and PWID was 6.4% (interquartile range 3.2%–11.7%), both much lower than the 25% reported by UNAIDS.Conclusion: Empirically derived and model-based estimates of HIV incidence confirm dramatically higher HIV risk among key populations in SSA. Estimated proportions of new infections among key populations in 2021 were sensitive to population size assumptions and were substantially lower than estimates reported by UNAIDS.</div

Estimating the effect of HIV on cervical cancer elimination in South Africa: comparative modelling of the impact of vaccination and screening

Background In 2020, the World Health Organization (WHO) launched its initiative to eliminate cervical cancer as a public health problem. To inform global efforts for countries with high HIV and cervical cancer burden, we assessed the impact of human papillomavirus (HPV) vaccination and cervical cancer screening and treatment in South Africa, on cervical cancer and the potential for achieving elimination before 2120, considering faster HPV disease progression and higher cervical cancer risk among women living with HIV(WLHIV) and HIV interventions. Methods Three independent transmission-dynamic models simulating HIV and HPV infections and disease progression were used to predict the impact on cervical cancer incidence of three scenarios for all women: 1) girls' vaccination (9–14 years old), 2) girls' vaccination plus 1 lifetime cervical screen (at 35 years), and 3) girls’ vaccination plus 2 lifetime cervical screens (at 35 and 45 years) and three enhanced scenarios for WLHIV: 4) vaccination of young WLHIV aged 15–24 years, 5) three-yearly cervical screening of WLHIV aged 15–49 years, or 6) both. Vaccination assumed 90% coverage and 100% lifetime protection with the nonavalent vaccine (against HPV-16/18/31/33/45/52/58). Cervical cancer screening assumed HPV testing with uptake increasing from 45% (2023), 70% (2030) to 90% (2045+). We also assumed that UNAIDS 90-90-90 HIV treatment and 70% male circumcision targets are reached by 2030. We examined three elimination thresholds: age-standardised cervical cancer incidence rates below 4 or 10 per 100,000 women-years, and >85% reduction in cervical cancer incidence rate. We conducted sensitivity analyses and presented the median age-standardised predictions of outcomes of the three models (minimum–maximum across models). Findings Girls' vaccination could reduce age-standardised cervical cancer incidence from a median of 47.6 (40.9–79.2) in 2020 to 4.5 (3.2–6.3) per 100,000 women-years by 2120, averting on average ∼4% and ∼46% of age-standardised cumulative cervical cancer cases over 25 and 100 years, respectively, compared to the basecase. Adding 2 lifetime screens helped achieve elimination over the century among all women (2120 cervical cancer incidence: 3.6 (1.9–3.6) per 100,000 women-years), but not among WLHIV (10.8 (5.3–11.6)), and averted more cumulative cancer cases overall (∼45% over 25 years and ∼61% over 100 years compared to basecase) than girls' vaccination alone. Adding three-yearly cervical screening among WLHIV (to girls' vaccination and 2 lifetime cervical screens) further reduced age-standardised cervical cancer incidence to 3.3 (1.8–3.6) per 100,000 women-years overall and to 5.2 (3.9–8.5) among WLHIV by 2120 and averted on average 12–13% additional cumulative cancer cases among all women and 21–24% among WLHIV than girls’ vaccination and 2 lifetime cervical screens over 25 years or longer. Long-term vaccine protection and using the nonavalent vaccine was required for elimination. Interpretation High HPV vaccination coverage of girls and 2 lifetime cervical screens could eliminate cervical cancer among women overall in South Africa by the end of the century and substantially decrease cases among all women and WLHIV over the short and medium term. Cervical cancer elimination in WLHIV would likely require enhanced prevention strategies for WLHIV. Screening of WLHIV remains an important strategy to reduce incidence and alleviate disparities in cervical cancer burden between women with and without HIV, despite HIV interventions scale-up. Funding World Health Organization. National Cancer Institute, National Institutes of Health. MRC Centre for Global Infectious Disease Analysis, UK Medical Research Council. National Institute of Child Health and Human Development research. Cancer Association of South Africa. Canadian Institutes of Health Research and the Fonds de recherche du Québec – Santé research