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This paper continues some recent work on the numerical solution of the steady incompressible Navier–Stokes equations. We present a new method, similar to the one presented in Rebholz et al., but with superior convergence and numerical properties. The method is efficient as it allows one to solve the same symmetric positive‐definite system for the pressure at each iteration, allowing for the simple preconditioning and the reuse of preconditioners. We also demonstrate how one can replace the Schur complement system with a diagonal matrix inversion while maintaining accuracy and convergence, at a small fraction of the numerical cost. Convergence is analyzed for Newton and Picard‐type algorithms, as well as for the Schur complement approximation. [ABSTRACT FROM AUTHOR]

Background: The OraQuick In-Home HIV self-test represents a fast, inexpensive, and convenient method for users to assess their HIV status. If integrated thoughtfully into existing testing practices, accompanied by efficient pathways to formal diagnosis, self-testing could enhance both HIV awareness and reduce HIV incidence. However, currently available self-tests are less sensitive, particularly for recent infection, when compared to gold-standard laboratory tests. It is important to understand the impact if some portion of standard testing is replaced by self-tests. We used a compartmental model to evaluate the effects of self-testing in diverse scenarios among gay, bisexual and other men who have sex with men (MSM) in the United States for the period 2020-2030, and to understand which scenarios maximize the advantages of self-testing., Methods: We introduced a novel 4-compartment model for HIV self-testing. We employed the model under different screening rates, self-test proportions, and delays to diagnosis for those identified through self-tests to determine the potential effects of self-testing on HIV incidence and awareness of status when applied to the US MSM population. We studied scenarios in which self-tests supplement laboratory-based tests, with no replacement, and scenarios in which some replacement occurs. We also examined how future improvements in self-test sensitivity may affect our results., Results: When HIV self-tests are supplemental rather than substitutes for laboratory-based testing, self-testing can decrease HIV incidence among MSM in the US by up to 10 % and increase awareness of status among MSM from 85 % to 91 % over a 10-year period, provided linkage to care and formal diagnosis occur promptly following a positive self-test (90 days or less). As self-tests replace a higher percentage laboratory-based testing algorithms, increases in overall testing rates were necessary to ensure reductions in HIV incidence. However, such needed increases were relatively small (under 10 % for prompt engagement in care and moderate levels of replacement). Improvements in self-test sensitivity and/or decreases in the detection period may further reduce any necessary increases in overall testing by up to 40 %., Conclusions: If properly utilized, self-testing can provide significant long-term reductions to HIV incidence and improve awareness of HIV status. Ensuring that self-testing increases overall testing and that formal diagnosis and engagement in care occur promptly following a positive self-test are necessary to maximize the benefits of self-testing. Future improvements in self-test sensitivity and reductions in the detection period would further reduce HIV incidence and the potential risks associated with replacing laboratory tests with self-tests., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Published by Elsevier B.V.)

Background: Clusters of rapid HIV transmission in the United States are increasingly recognized through analysis of HIV molecular sequence data reported to the National HIV Surveillance System. Understanding the full extent of cluster networks is important to assess intervention opportunities. However, full cluster networks include undiagnosed and other infections that cannot be systematically observed in real life., Methods: We replicated HIV molecular cluster networks during 2015-2017 in the United States using a stochastic dynamic network simulation model of sexual transmission of HIV. Clusters were defined at the 0.5% genetic distance threshold. Ongoing priority clusters had growth of ≥3 diagnoses/year in multiple years; new priority clusters first had ≥3 diagnoses/year in 2017. We assessed the full extent, composition, and transmission rates of new and ongoing priority clusters., Results: Full clusters were 3-9 times larger than detected clusters, with median detected cluster sizes in new and ongoing priority clusters of 4 (range 3-9) and 11 (range 3-33), respectively, corresponding to full cluster sizes with a median of 14 (3-74) and 94 (7-318), respectively. A median of 36.3% (range 11.1%-72.6%) of infections in the full new priority clusters were undiagnosed. HIV transmission rates in these clusters were >4 times the overall rate observed in the entire simulation., Conclusions: Priority clusters reflect networks with rapid HIV transmission. The substantially larger full extent of these clusters, high proportion of undiagnosed infections, and high transmission rates indicate opportunities for public health intervention and impact., Competing Interests: The authors have no other funding or conflicts of interest to disclose., (Copyright © 2024 Wolters Kluwer Health, Inc. All rights reserved.)

Background: Diagnoses of HIV in the United States decreased by 17% in 2020 due to COVID-related disruptions. The extent to which this decrease is attributable to changes in HIV testing versus HIV transmission is unclear. We seek to better understand this issue by analyzing the discrepancy in expected versus observed HIV diagnoses in 2020 among persons who acquired HIV between 2010 and 2019 because changes in diagnosis patterns in this cohort cannot be attributed to changes in transmission., Methods: We developed 3 methods based on the CD4-depletion model to estimate excess missed diagnoses in 2020 among persons with HIV (PWH) infected from 2010 to 2019. We stratified the results by transmission group, sex assigned at birth, race/ethnicity, and region to examine differences by group and confirm the reliability of our estimates. We performed similar analyses projecting diagnoses in 2019 among PWH infected from 2010 to 2018 to evaluate the accuracy of our methods against surveillance data., Results: There were approximately 3100-3300 (approximately 18%) fewer diagnoses than expected in 2020 among PWH infected from 2010 to 2019. Females (at birth), heterosexuals, persons who inject drugs, and Hispanic/Latino PWH missed diagnoses at higher levels than the overall population. Validation and stratification analyses confirmed the accuracy and reliability of our estimates., Conclusions: The substantial drop in number of previously infected PWH diagnosed in 2020 suggests that changes in testing played a substantial role in the observed decrease. Levels of missed diagnoses differed substantially across population subgroups. Increasing testing efforts and innovative strategies to reach undiagnosed PWH are needed to offset this diagnosis gap. These analyses may be used to inform future estimates of HIV transmission during the COVID-19 pandemic., Competing Interests: The authors have no conflicts of interest to disclose., (Copyright © 2022 Wolters Kluwer Health, Inc. All rights reserved.)