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H. Strietz proved in 1975 that the minimum size of a generating set of the partition lattice Part(n) on the n-element set (n ≥ 4) equals 4. This classical result forms the foundation for this study. Strietz's results have been echoed by L. Zádori (1983), who gave a new elegant proof confirming the outcome. Several studies have indeed emerged henceforth concerning four-element generating sets of partition lattices. More recently more studies have presented the approach for the lower bounds on the number λ(n) of the four-element generating sets of Part(n) and statistical approach to λ(n) for small values of n. Also, G. Czédli and the present author have recently proved that certain direct products of partition lattices are also 4-generated. In a recent paper, G. Czédli has shown that this result has connection with information theory. On this basis, here we give a lower bound on the number ν(n) of 4-element generating sets of the direct product Part(n) × Part(n + 1) for n ≥ 7 using the results from previous studies. For n = 1, . . . , 5, we use a computer-aided approach; it gives exact values for n = 1, 2, 3, 4 but we need a statistical method for n = 5.

The world currently has a profusion of intergovernmental organizations charged with various public functions previously reserved for states. The operations of these organizations affect the ordinary lives of individual citizens in the member states. Yet these organizations are not legitimate, based on the standard expected of a democratic state government. This article joins the chorus demanding the legitimization of international organizations that perform public functions, taking into account their peculiar circumstances and nature, and with specific reference to the East African Community. It sets out criteria for assessing legitimacy and examines the organs, functions and administration of the East African Community against those criteria. It argues that, as presently established and structured, the East African Community seriously lacks legitimacy. There is therefore an urgent need for reform, to avoid this body becoming yet another statistic of moribund regional integration schemes in Africa. [ABSTRACT FROM AUTHOR]

Background: The World Health Organization recommends a single-dose human papillomavirus (HPV) vaccination schedule for girls and boys to accelerate progress toward cervical cancer elimination. We applied the Theoretical Framework of Acceptability (TFA) within the context of HPV vaccination to assess the acceptability of a single-dose schedule among health-care professionals in Kenya., Methods: A REDCap survey was developed using relevant Theoretical Framework of Acceptability domains and validated with health-care professionals. Descriptive analyses and multivariate Poisson regression were conducted to assess factors associated with increased acceptability. Free-text responses were analyzed using a rapid qualitative approach, and findings were presented using a joint display., Results: Among 385 responses, 74.2% of health-care professionals were female and 48.6% were nurses. On average, respondents had been in their position for 60 months, and one-third (33.2%) were based at level-4 facilities. The majority (75.84%) thought that giving a single-dose of the HPV vaccine to adolescent girls and young women was either acceptable or very acceptable. Qualitative findings highlighted that lack of information was the underlying reason for health-care professionals who were resistant, and most clinicians thought that a singled-dose schedule was less burdensome to clinicians and patients. Hospital directors had a non-statistically significantly lower acceptability likelihood than nurses (incident rate ratio = 0.93, 95% confidence interval = 0.45 to 1.71) and health-care professionals at urban facilities had a non-statistically significantly lower acceptability likelihood than clinicians in rural facilities (incident rate ratio = 0.97, 95% confidence interval = 0.83 to 1.13)., Conclusion: Although not statistically significant, predictors of increased acceptability provide information to tailor strategies to increase HPV vaccination coverage and accelerate progress toward cervical cancer elimination., (© The Author(s) 2024. Published by Oxford University Press.)

Non-neutralizing functions of antibodies, including phagocytosis, may play a role in Chlamydia trachomatis (CT) infection, but these functions have not been studied and assays are lacking. We utilized a flow-cytometry-based assay to determine whether serum samples from a well-characterized cohort of CT-infected and naïve control individuals enhanced phagocytosis via Fc-receptor-expressing THP-1 cells, and whether this activity correlated with antibody titers. Fc-receptor-mediated phagocytosis was detected only in CT+ donors. Phagocytosis generally did not correlate well with antibody titer. In addition, we found that complement from both CT+ and negative individuals enhanced phagocytosis of CT into primary neutrophils. These results suggest that anti-CT antibodies can have functions that are not reflected by titer. This method could be used to quantitively measure Fc-receptor-mediated function of anti-CT antibodies or complement activity and could reveal new immune correlates of protection., Competing Interests: N.R.M. and K.N. report receiving research funding under the Merck Investigator Sponsored Program. The other authors report no conflict of interest.

Objective: To determine bacterial vaginosis (BV) status at multiple time points among adolescent girls and young women (AGYW) and assess the impact of pregnancy on their BV status., Design: Longitudinal cohort study., Setting: Thika, Kenya., Participants: AGYW aged 16-20 years enrolled prior to first sex or reporting only a single lifetime partner., Main Outcome Measures: The primary outcome was relative risk (RR) of BV during pregnancy compared with before pregnancy by analysing longitudinal trends in BV over time. BV risk was estimated using Poisson regression models., Results: A total of 121 AGYW became pregnant in the parent cohort and had BV results before, during or after pregnancy. Point prevalence of BV was 11.0% at visits >12 months pre-pregnancy, 13.0% at 3-12 months pre-pregnancy, 22.1% at <3 months pre-pregnancy and 13.4% during pregnancy. Compared with visits during pregnancy, RR of BV was 1.65 (95% CI: 1.00 to 2.71; p=0.05) at visits <3 months pre-pregnancy, 0.97 (95% CI: 0.62 to 1.52; p=0.90) at visits 3-12 months pre-pregnancy and 0.82 (95% CI: 0.44 to 1.53; p=0.53) at visits 12 months pre-pregnancy. An adjusted analysis including age, income, residence, date of first sex, recent sexual activity and positive sexually transmitted infection test resulted in small changes in risk estimates, with adjusted RR of BV of 1.66 (95% CI: 1.04 to 2.67; p=0.04) at visits <3 months pre-pregnancy compared with visits during pregnancy., Conclusions: BV risk during pregnancy was lower than during the immediate pre-pregnancy period. Hormonal changes in pregnancy may reduce BV., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2023. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

Purpose: The risk of human immunodeficiency virus (HIV) among adolescent girls (AGs) may be reduced if they know the HIV status of their male partners. We assessed the ability of AGs in Siaya County, Kenya, to offer HIV self-tests to their partners to promote partner and couples testing., Methods: Eligible AGs were 15-19 years old, self-tested HIV-negative, and had a male partner not tested in the past 6 months. Participants were randomly assigned to receive two oral fluid-based self-tests (intervention arm) or a referral coupon for facility-based testing (comparison arm). The intervention included counseling on ways to safely introduce self-tests to partners. Follow-up surveys were conducted within 3 months., Results: Among 349 AGs enrolled, median age was 17 years (interquartile range 16-18), 88.3% of primary partners were noncohabiting boyfriends, and 37.5% were unaware if their partner had ever tested. At 3 months, 93.9% of the intervention arm and 73.9% of the comparison arm reported that partner testing occurred. Compared to the comparison arm, partner testing was more likely in the intervention arm (risk ratio = 1.27; 95% confidence interval 1.15-1.40; p < .001). Among participants whose partners got tested, 94.1% and 81.5% in the intervention and comparison arms, respectively, reported that couples testing occurred; couples testing was more likely in the intervention than comparison arm (risk ratio = 1.15; 95% confidence interval 1.15-1.27; p = .003). Five participants reported partner violence, one study-related., Discussion: Provision of multiple self-tests to AGs for the purpose of promoting partner and couples testing should be considered in Kenya and other settings where AGs face a high risk of HIV acquisition., (Copyright © 2023 Society for Adolescent Health and Medicine. All rights reserved.)

Background: Cervical cancer is the leading cause of cancer-related deaths among Kenyan women. Persistent infection with high-risk oncogenic Human papillomavirus (HPV) genotypes is a necessary cause of cervical cancer. HPV vaccines are safe, durable, and efficacious in preventing incident HPV infections. In Kenya, despite efforts to increase HPV vaccination, coverage remains low. We sought to assess: (1) barriers and facilitators of HPV vaccination from the perspective of adolescent girls and young women (AGYW), their guardians as well as stakeholders involved in HPV vaccine delivery, and (2) the acceptability of the single dose of the HPV vaccination among healthcare providers (HCPs)., Methods: Our study is nested within the KENya Single-dose HPV-vaccine Efficacy study (KEN SHE) that sought to test the efficacy of single-dose bivalent (HPV 16/18) and single-dose nonavalent (HPV 16/18/31/33/45/52/58/6/11) vaccination. We are conducting this study in Kiambu, Nairobi, and Kisumu counties. In these counties, we are interviewing stakeholders ( n  = ∼25), selected based on their role in HPV vaccination at the county and national levels. Interviews are audio recorded and conducted in English or Swahili. The semi-structured interview guides were designed based on: (1) the Theoretical Domains Framework (TDF) for AGYW and guardians and (2) the Consolidated Framework for Implementation Research (CFIR) for other stakeholders. The Theoretical Framework of Acceptability (TFA) was leveraged to design the survey administered to HCPs ( n  = ∼309) involved in HPV vaccination. We will develop a codebook based on emerging codes from the transcripts and constructs from the TDF and CFIR. Emerging themes will be summarized highlighting similarities and differences between and within the different stakeholder groups and counties. Descriptive statistics and a χ 2 test will be used to assess the distribution of responses between the different sites and regression analysis will be used to assess factors associated with high acceptability of the single-dose strategy while controlling for confounding variables., Discussion: Our study will describe key barriers and facilitators that affect HPV vaccination from the perspective of multiple stakeholders as well as insights on the perspective of HCPs towards the single-dose strategy to inform the designing of strategies to increase HPV vaccination uptake in Kenya and comparable settings., Competing Interests: RVB reports Regeneron Pharmaceuticals provided abstract and manuscript writing support outside this study. KN and NRM report research funding from the Merck Investigator Studies Program, outside this study. All reported funders were not involved in the study design, data collection, analysis, interpretation, the writing of this article, or the decision to submit it for publication. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (© 2023 Umutesi, Oluoch, Weiner, Bukusi, Onono, Njoroge, Mecca, Ngure, Mugo and Barnabas.)

Background: Adolescent girls and young women (AGYW) have a high incidence of unplanned pregnancies, especially in low-resource settings. AGYW assess the overlapping risks of pregnancy, contraception, and STIs as they navigate relationships. Few studies have examined how AGYW consider the comparative risks of their decisions around sexual and reproductive health in this context or how risk perception influences contraceptive use., Methods: Twenty in-depth interviews (IDIs) and 5 focus group discussions (FGDs) were conducted with a subset of sexually active AGYW enrolled in the Girls Health Study (GHS), a longitudinal cohort study in Thika, Kenya, assessing HSV-2 incidence in a cohort of AGYW aged 16-20. Interview questions were focused on perspectives and decision-making around sexual and reproductive health. Interviews were conducted in both English and Kiswahili, transcribed, and coded using inductive and deductive approaches to identify emerging themes., Results: Misconceptions about long-acting reversible contraceptives (LARCs), injectables, and daily oral contraceptive pills strongly disincentivized their use among AGYW. Participants described pregnancy as undesirable, and AGYW reported prioritizing contraceptive methods that were effective and reliable in pregnancy prevention, even if not effective in preventing STI/HIV infection. Participants reported that AGYW relied heavily on emergency contraceptive (EC) pills for pregnancy prevention., Conclusions: Though the goal of avoiding unintended pregnancy was common, this did not suffice to motivate the uptake of long-term contraceptives among AGYWs. Given the convenience, cost-effectiveness, and lower perceived risk of side effects, EC pills were more likely to be accepted as a form of contraception. Understanding the reasons for AGYW's acceptance of certain contraceptive methods over others can help future interventions better target communication and counseling about contraception and influence key drivers of AGYW behavior and decision-making around sexual and reproductive health., (© 2023. The Author(s).)

Background: Adolescent girls and young women (AGYW) are at high risk of sexually transmitted infections (STIs). It is unknown whether beginning to have sexual intercourse results in changes to immune mediators in the cervicovaginal tract that contribute to this risk., Methods: We collected cervicovaginal lavages from Kenyan AGYW in the months before and after first penile-vaginal sexual intercourse and measured the concentrations of 20 immune mediators. We compared concentrations pre- and post-first sex using mixed effect models. We additionally performed a systematic review to identify similar studies and combined them with our results by meta-analysis of individual participant data., Results: We included 180 samples from 95 AGYW, with 44% providing only pre-first sex samples, 35% matched pre and post, and 21% only post. We consistently detected 19/20 immune mediators, all of which increased post-first sex (p<0.05 for 13/19; Holm-Bonferroni-adjusted p<0.05 for IL-1β, IL-2, and CXCL8). Effects remained similar after excluding samples with STIs and high Nugent scores. Concentrations increased cumulatively over time after date of first sex, with an estimated doubling time of about 5 months.Our systematic review identified two eligible studies, one of 93 Belgian participants, and the other of 18 American participants. Nine immune mediators were measured in at least two-thirds of studies. Meta-analysis confirmed higher levels post-first sex for 8/9 immune mediators (p<0.05 for six mediators, most prominently IL-1α, IL-1β, and CXCL8)., Conclusions: Cervicovaginal immune mediator concentrations were higher in women who reported that they started sexual activity. Results were consistent across three studies conducted on three different continents., Funding: This research was funded by R01 HD091996-01 (ACR), by P01 AI 030731-25 (Project 1) (AW), R01 AI116292 (FH), R03 AI154366 (FH) and by the Center for AIDS Research (CFAR) of the University of Washington/Fred Hutchinson Cancer Research Center AI027757., Competing Interests: SH, CL, FC, KM, SS, KT, BC, LO, CK, AW, MG, LH, FH, AR No competing interests declared, KN Kenneth Ngure was supported by the International AIDS Society to attend AIDS 2022. The author has no other competing interests to declare, NM Nelly R Mugo received honoraria from MERCK Ltd in support of a presentation on HPV vaccination uptake in LMIC. The author has no other competing interests to declare, (© 2022, Hughes et al.)

BACKGROUND: Single-dose human papillomavirus (HPV) vaccination, if efficacious, would be tremendously advantageous, simplifying implementation and decreasing costs. METHODS: We performed a randomized, multicenter, double-blind, controlled trial of single-dose nonavalent (HPV 16/18/31/33/45/52/58/6/11 infection) or bivalent (HPV 16/18 infection) HPV vaccination compared with meningococcal vaccination among Kenyan women 15 to 20 years of age. Enrollment and 6-monthly cervical swabs and a month 3 vaginal swab were tested for HPV deoxyribonucleic acid (DNA). Enrollment sera were tested for HPV antibodies. The modified intent-to-treat (mITT) cohort comprised participants who had an HPV antibody-negative result at enrollment and an HPV DNA-negative result at enrollment and month 3. The primary outcome was incident persistent vaccine-type HPV infection by month 18. RESULTS: Between December 2018 and June 2021, 2275 women were randomly assigned and followed. A total of 758 participants received the nonavalent HPV vaccine, 760 received the bivalent HPV vaccine, and 757 received the meningococcal vaccine; retention was 98%. Thirty-eight incident persistent infections were detected in the HPV 16/18 mITT cohort: one each among participants assigned to the bivalent and nonavalent groups and 36 among those assigned to the meningococcal group. Nonavalent vaccine efficacy (VE) was 97.5% (95% confidence interval [CI], 81.7 to 99.7%; P≤0.0001), and bivalent VE was 97.5% (95% CI, 81.6 to 99.7%; P≤0.0001). Thirty-three incident persistent infections were detected in the HPV 16/18/31/33/45/52/58 mITT cohort: four in the nonavalent group and 29 in the meningococcal group. Nonavalent VE for HPV 16/18/31/33/45/52/58 was 88.9% (95% CI, 68.5 to 96.1; P<0.0001). The rate of serious adverse events was 4.5% to 5.2% by group. CONCLUSIONS: Over the 18-month timeframe we studied, single-dose bivalent and nonavalent HPV vaccines were each highly effective in preventing incident persistent oncogenic HPV infection, similar to multidose regimens. (Funded by the National Institutes of Health, the Bill and Melinda Gates Foundation, and the University of Washington; ClinicalTrials.gov number, NCT03675256.), (Copyright: © 2022 Author(s), Massachusetts Medical Society. All rights reserved.)

Background: For couples affected by HIV, and serodifferent couples in particular, pregnancy desire is often juxtaposed against the risk of HIV transmission between the couple and the potential neonate leading to thinking about measures to minimize risk of HIV transmission. We assess the use of fertility awareness methods [FAM] and evaluate the drivers of alignment between indicators of fertility and sexual behavior among HIV-serodifferent couples desiring pregnancy., Methods: HIV-serodifferent couples from Thika, Kenya were enrolled into an open-label pilot evaluation of safer conception strategies. Women responded to daily 7-item short message service [SMS] surveys on FAM and sexual activity. Menstrual cycles were categorized as having condomless sex aligned, not aligned, or partially aligned to the predicted peak fertility. We used binomial logit models with generalized estimating equations to assess alignment between condomless sex during peak fertility days and FAM results. We used Cox proportional hazards to compare pregnancy incidence among months with sex and peak fertility aligned and mis-aligned., Results: A total of 6929 SMS surveys across 252 menstrual cycles of 65 women were included. Reporting "sticky" cervical mucus (adjusted odds ratio [aOR]: 2.25, 95% confidence interval [95% CI]: 1.30, 3.90) and positive ovulation prediction kit [OPK] result (aOR: 2.07, 95% CI: 1.11, 3.86) were associated with increased likelihood of alignment of condomless sex during peak fertility. Pregnancy incidence was statistically similar among periods with sex aligned and not aligned with peak fertility., Conclusions: Among women engaged in a comprehensive safer conception program, a moderate percentage of women aligned condomless sex and predicted peak fertility days at least once. While FAM, particularly cervical mucus and OPK, are an inexpensive option for couples to consider using as a component of their safer conception strategies, antiretroviral-based strategies remain important to minimize risk.

Adolescent girls and young women (AGYW) are at high risk of HIV and other sexually transmitted infections (STIs), including at first sexual intercourse. The literature is scarce on factors influencing use of protective strategies at this critical time. We conducted 20 in-depth interviews and five focus group discussions with purposively sampled AGYW aged 16-20 years who reported first sex while enrolled in a larger cohort study and willing to participate. All AGYW were counseled on HIV prevention and had access to reproductive health information and services. Data collected were transcribed, translated and analyzed thematically. We identified two approaches to first sex. In one approach, the AGYW facilitated protection use, and those AGYW reported intention and preparation to initiate sexual activity and ability to request condom use, as well as their male partner's willingness to use and provide condoms. In another approach, AGYW experienced first sexual intercourse without agency (the feeling of control over actions and their consequences [Moore, 2016]) and described lack of prior intentions and planning, discomfort with discussions about sex and condom use, and desire to experience sexual pleasure as reported by peers. No AGYW mentioned parents/adults as playing any role as facilitators of protection use at first sex, highlighting the need for further research on the missing gap. The AGYW were trusting of verbal reports by male partners describing themselves as having never engaged in sex, HIV negative, and free of STIs. We found that some AGYW were empowered to plan, discuss, and request protection at first sex, and others did not take agency. First sex is a time of vulnerability where innovative strategies are needed to strengthen AGYW's agency and promote condom use and other HIV/STI prevention methods.

Objectives: Globally, the highest rates of sexually transmitted infections (STIs) are among the 15-24 age group. Studying adolescent girls and young women (AGYW) pre-sexual debut could identify risk factors for STI acquisition. Methods: We recruited a prospective cohort of low-risk AGYW aged 16-20 in Kenya. Participants were HIV and HSV-2 seronegative and reported no history of sexual intercourse or reported sex with one partner. Participants underwent genital exams, nucleic acid testing of vaginal swabs for Neisseria gonorrhea (NG), Chlamydia trachomatis (CT), Trichomonas vaginalis (TV), and vaginal gram stains for vaginal dysbiosis by Nugent score. STI correlates were described using χ 2 test and t -test. Results: We enrolled 400 AGYW, of which 322 (80.5%) reported never having had sex, while 78 (19.5%) reported prior sex with 1 partner. Among the 78 participants reporting prior sex, 20 (25.6%) reported contraception use in the last 3 months, with 60% using only emergency contraceptive pills. Despite self-reported history, of 373 subjects who underwent STI testing, 49 subjects (13.1%) tested positive for STIs, with 41 CT, 5 GC, and 3 TV cases. Of these 49 subjects, 33 (67.3%) reported no prior sexual intercourse. Bacterial vaginosis was rare and 90% of subjects had a normal Nugent score (0-3). Conclusions: Upon baseline evaluation of a cohort of low risk AGYW, we found high numbers of STIs, especially CT, which is not routinely screened for in Kenyan settings. Interventions to address STIs and unintended pregnancy should target girls pre-sexual debut, including those who do not self-identify as at risk., (Copyright © 2020 Yuh, Micheni, Selke, Oluoch, Kiptinness, Magaret, Chohan, Ngure, Wald, Mugo and Roxby.)

We establish a compartmental model to study the transmission of Zika virus disease including spread through sexual contacts and the role of asymptomatic carriers. To incorporate the impact of the seasonality of weather on the spread of Zika, we apply a nonautonomous model with time-dependent mosquito birth rate and biting rate, which allows us to explain the differing outcome of the epidemic in different countries of South America: using Latin Hypercube Sampling for fitting, we were able to reproduce the different outcomes of the disease in various countries. Sensitivity analysis shows that, although the most important factors in Zika transmission are the birth rate of mosquitoes and the transmission rate from mosquitoes to humans, spread through sexual contacts also highly contributes to the transmission of Zika virus: our study suggests that the practice of safe sex among those who have possibly contracted the disease, can significantly reduce the number of Zika cases.

Promoting awareness of serostatus and frequent HIV testing is especially important among high risk populations such as female sex workers (FSW) and their sexual partners. HIV self-testing is an approach that is gaining ground in sub-Saharan Africa as a strategy to increase knowledge of HIV status and promote safer sexual decisions. However, little is known about self-test distribution strategies that are optimal for increasing testing access among hard-to-reach and high risk individuals. We conducted a qualitative study with 18 FSW who participated in a larger study that provided them with five oral fluid-based self-tests, training on how to use the tests, and encouragement to offer the self-tests to their sexual partners using their discretion. Women demonstrated agency in the strategies they used to introduce self-tests to their partners and to avoid conflict with partners. They carefully considered with whom to share self-tests, often assessing the possibility for negative reactions from partners as part of their decision making process. When women faced negative reactions from partners, they drew on strategies they had used before to avoid conflict and physical harm from partners, such as not responding to angry partners and forgoing payment to leave angry partners quickly. Some women also used self-tests to make more informed sexual decisions with their partners.

Introduction: The customs of widow cleansing and widow inheritance are practiced in several communities throughout sub-Saharan Africa. In the Nyanza Province of Kenya, according to tradition, Luo widows are expected to engage in sexual intercourse with a "cleanser," without the use of a condom, in order to remove the impurity ascribed to her after her husband's death. Luo couples, including widows, are also expected to engage in sex preceding specific agricultural activities, building homes, funerals, weddings, and other significant cultural and social events. Widows who are inherited for the purpose of fulfilling cultural obligation have a higher prevalence of HIV than those who remain un-inherited or are inherited for the purpose of companionship., Methods: As part of a larger descriptive qualitative study to inform study procedures for FEM-PrEP, an HIV prevention pre-exposure prophylaxis clinical trial, we conducted 15 semi-structured interviews (SSIs) with widows, 15 SSIs with inheritors, and four focus group discussions with widows in the Bondo and Rarieda districts in Nyanza Province to explore the HIV risk context within widow cleansing and inheritance practices. Thematic qualitative analysis was used to analyze the data., Results: The majority of widows reported in the demographic questionnaire being inherited, and most widows in the SSIs described participating in the cleansing ritual. We identified two main themes related to HIV prevention within the context of widow cleansing and inheritance: 1) widows must balance limiting their risk for HIV infection with meeting cultural expectations and ensuring that their livelihood needs are met, and 2) sexual abstinence undermines cultural expectations in widowhood while the use of condoms is deemed inappropriate in fulfilling culturally prescribed sexual rituals, and is often beyond the widow's ability to negotiate., Conclusions: Women-controlled HIV prevention methods such as antiretroviral-based oral pre-exposure prophylaxis, vaginal gels, and vaginal rings are needed for HIV-negative widows who engage in sexual rituals related to widowhood.