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Background: Whether the COVID-19 pandemic has had a disproportionate impact on mortality among persons with diagnosed HIV (PWDH) in the United States is unclear. Through our macroscale analysis, we seek to better understand how the COVID-19 pandemic affected mortality among PWDH. Methods: We obtained mortality and population data for the years 2018-2020 from the National HIV Surveillance System for the US PWDH population and from publicly available data for the general population. We computed mortality rates and excess mortality for both the general and PWDH populations. Stratifications by age, race/ethnicity, and sex were considered. For each group, we determined whether the 2020 mortality rates and mortality risk ratio showed a statistically significant change from 2018 to 2019. Results: Approximately 1550 excess deaths occurred among PWDH in 2020, with Black, Hispanic/Latino, and PWDH aged 55 years and older comprising the majority of excess deaths. Mortality rates increased in 2020 from 2018-2019 across the general population in all groups. Among PWDH, mortality rates either increased or showed no statistically significant change. These increases were similar to, or smaller than, those observed in the general population, resulting in a 7.7% decrease in the mortality risk ratio between PWDH and the general population. Conclusions: While mortality rates among PWDH increased in 2020 relative to 2018-2019, the increases were smaller, or of similar magnitude, to those observed in the general population. We thus do not find evidence of elevated mortality risk from the COVID-19 pandemic among PWDH. These findings held across subpopulations stratified by age, sex, and racial/ethnic group. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic is still ongoing, even if the emergency is over, and we now have enough data to analyze the outbreak over a long timeline. There is evidence that the outbreak alternates periods of high and low infections. Retrospectively, this can help in understanding the nature of an appropriate mathematical model for this dramatic infection. The periodic behavior may be the consequence of time-dependent coefficients related to seasonal effects and specific political actions, or an intrinsic feature of the model. The present paper relies on the assumption that the periodic spikes are an intrinsic feature of the disease, and, as such, it should be properly reflected in the mathematical model. Based on the concept of waning immunity proposed for other pathologies, we introduce a new model with (i) a compartment for weakly immune people subject to immunity booster, represented by a non-linear term; (ii) discrimination between individuals infected/vaccinated for the first time, and individuals already infected/vaccinated, undergoing to new infections/doses. We analyze some preliminary properties of our model, called SIRW2, and provide a proof-of-concept that it is capable of reproducing qualitatively the long-term oscillatory behavior of COVID-19 infection. [ABSTRACT FROM AUTHOR]

Supplemental Digital Content is Available in the Text. 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. [ABSTRACT FROM AUTHOR]

Additive manufacturing techniques have grown significantly in recent years due to their ability to produce designs almost impossible to obtain with standard production technologies. This growth has in turn led to increased demand for numerical simulation of additive processes. Unfortunately, such simulations are difficult from the computational point of view, since additive problems are characterized by the presence of highly local nonlinearities requiring fine mesh resolutions on small portions of the domain. These difficulties are compounded by the fact that such regions of local high nonlinearities move in the domain with time, and further, by the fact that the physical domain itself evolves with time. Accordingly, the present article addresses these complex computational issues by employing a two‐level technique. The two‐level method provides a natural framework for the resolution of localized nonlinearities while avoiding the need for complex meshing operations, such as refinement‐and‐derefinement algorithms. The proposed approach is validated on a series of one‐ and two‐dimensional problems to establish the viability of the introduced two‐level method for additive manufacturing problems. [ABSTRACT FROM AUTHOR]

In the wake of the 2020 COVID‐19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic and of disease models generally. Most works follow the susceptible‐infected‐removed (SIR) compartmental framework, modeling the epidemic with a system of ordinary differential equations. Alternative formulations using a partial differential equation (PDE) to incorporate both spatial and temporal resolution have also been introduced, with their numerical results showing potentially powerful descriptive and predictive capacity. In the present work, we introduce a new variation to such models by using delay differential equations (DDEs). The dynamics of many infectious diseases, including COVID‐19, exhibit delays due to incubation periods and related phenomena. Accordingly, DDE models allow for a natural representation of the problem dynamics, in addition to offering advantages in terms of computational time and modeling, as they eliminate the need for additional, difficult‐to‐estimate, compartments (such as exposed individuals) to incorporate time delays. In the present work, we introduce a DDE epidemic model in both an ordinary and partial differential equation framework. We present a series of mathematical results assessing the stability of the formulation. We then perform several numerical experiments, validating both the mathematical results and establishing model's ability to reproduce measured data on realistic problems. [ABSTRACT FROM AUTHOR]

Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and preconditioning. These difficulties are increased if the region of localized dynamics changes in time. Overlapping domain decomposition methods, which split the problem at the continuous level, show promise due to their ease of implementation and computational efficiency. Accordingly, the present work aims to further develop the mathematical theory of such methods at both the continuous and discrete levels. For the continuous formulation of the problem, we provide a full convergence analysis. For the discrete problem, we show how the described method may be interpreted as a Gauss-Seidel scheme or as a Neumann series approximation, establishing a convergence criterion in terms of the spectral radius of the system. We then provide a spectral scaling argument and provide numerical evidence for its justification. [ABSTRACT FROM AUTHOR]

We propose new, efficient, and simple nonlinear iteration methods for the incompressible Navier-Stokes equations. The methods are constructed by applying Yosida-type algebraic splitting to the linear systems that arise from grad-div stabilized finite element implementations of incremental Picard and Newton iterations. They are efficient because at each nonlinear iteration, the same symmetric positive definite Schur complement system needs to be solved, which allows for CG to be used for inner and outer solvers, simple preconditioning, and the reusing of preconditioners. For the proposed incremental Picard-Yosida and Newton-Yosida iterations, we prove under small data conditions that the methods converge to the solution of the discrete nonlinear problem. Numerical tests are performed which illustrate the effectiveness of the method on a variety of test problems. [ABSTRACT FROM AUTHOR]

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]

The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of the patient's affected organ. These patient-specific computational forecasts have been regarded as a promising approach to personalize the clinical management of cancer and derive optimal treatment plans for individual patients, which constitute timely and critical needs in clinical oncology. However, the computer simulation of the underlying spatiotemporal models can entail a prohibitive computational cost, which constitutes a barrier to the successful development of clinically-actionable computational technologies for personalized tumor forecasting. To address this issue, here we propose to utilize dynamic-mode decomposition (DMD) to construct a low-dimensional representation of cancer models and accelerate their simulation. DMD is an unsupervised machine learning method based on the singular value decomposition that has proven useful in many applications as both a predictive and a diagnostic tool. We show that DMD may be applied to Fisher--Kolmogorov models, which constitute an established formulation to represent untreated solid tumor growth that can further accommodate other relevant cancer phenomena (e.g., therapeutic effects, mechanical deformation). Our results show that a DMD implementation of this model over a clinically relevant parameter space can yield promising predictions, with short to medium-term errors remaining under 1% and long-term errors remaining under 20%, despite very short training periods. In particular, we have found that, for moderate to high tumor cell diffusivity and low to moderate tumor cell proliferation rate, DMD reconstructions provide accurate, bounded-error reconstructions for all tested training periods. Additionally, we also show that the three-dimensional DMD reconstruction of the tumor field can be leveraged to accurately reconstruct the displacement fields of the tumor-induced deformation of the host tissue. Thus, we posit the proposed data-driven approach has the potential to greatly reduce the computational overhead of personalized simulations of cancer models, thereby facilitating tumor forecasting, parameter identification, uncertainty quantification, and treatment optimization. [ABSTRACT FROM AUTHOR]

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.)