Modeling and analysis of systems with nonlinear functional dependence on random quantities

Many real-world systems exhibit noisy evolution; interpreting their finite-time behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis in a variety of fields. Here we argue that a class of differential equations where evolution depends nonlinearly on a random or effectively-random quantity may exhibit finite-time stochastic behavior in line with an equivalent It\^o process, which is of great utility for their numerical simulation and theoretical analysis. We put forward a method for this conversion, develop an equilibrium-moment relation for It\^o attractors, and show that this relation holds for our example system. This work enables the theoretical and numerical examination of a wide class of mathematical models which might otherwise be oversimplified due to a lack of appropriate tools.Comment: 13 pages, 6 figure

Use of antibiotics and risk of type 2 diabetes, overweight and obesity : the Cardiovascular Risk in Young Finns Study and the national FINRISK study

Purpose To investigate whether exposure to systemic antibiotics influences the risk of developing type 2 diabetes and overweight/obesity. Methods The study sample comprised 2209 (110 with incident diabetes) participants from the population-based Cardiovascular Risk in Young Finns Study (YFS) aged 24-39 years in 2001. The exposure was national linked register data on purchased antibiotic courses between 1993 and 2001. Clinical examinations including BMI were conducted in 2001, 2007 and 2011. Participants with prevalent diabetes in 2001 were excluded. Data on type 2 diabetes was also obtained from two national registers until 2017. Data from four population-based National FINRISK studies were used for replication (N = 24,674, 1866 with incident diabetes). Results Prior antibiotic exposure (> 5 versus 0-1 antibiotic courses) was associated with subsequent type 2 diabetes in both YFS (OR 2.29; 95%CI 1.33-3.96) and FINRISK (HR 1.73; 95%CI 1.51-1.99). An increased risk for type 2 diabetes was observed in YFS (OR 1.043; 95%CI 1.013-1.074) and FINRISK (HR 1.022; 95%CI 1.016-1.029) per course. Exposure to antibiotics increased the risk of overweight/obesity (BMI > 25 kg/m(2)) after a 10-year follow-up in YFS (OR 1.043; 95%CI 1.019-1.068) and in FINRISK (OR 1.023; 95%CI 1.018-1.029) at baseline per antibiotic course. Adjustments for confounders from early life in YFS and at baseline in FINRISK, including BMI, socioeconomic status, smoking, insulin, blood pressure, and physical activity, did not appreciably alter the findings. Conclusion Our results show that exposure to antibiotics was associated with increased risk for future type 2 diabetes and overweight/obesity and support judicious antibiotic prescribing.Peer reviewe

Recommendations for defining preventable HIV-related mortality for public health monitoring in the era of Getting to Zero: an expert consensus

Getting to Zero is a commonly cited strategic aim to reduce mortality due to both HIV and avoidable deaths among people with HIV. However, no clear definitions are attached to these aims with regard to what constitutes HIV-related or preventable mortality, and their ambition is limited. This Position Paper presents consensus recommendations to define preventable HIV-related mortality for a pragmatic approach to public health monitoring by use of national HIV surveillance data. These recommendations were informed by a comprehensive literature review and agreed by 42 international experts, including clinicians, public health professionals, researchers, commissioners, and community representatives. By applying the recommendations to 2019 national HIV surveillance data from the UK, we show that 30% of deaths among people with HIV were HIV-related or possibly HIV-related, and at least 63% of these deaths were preventable or potentially preventable. The application of these recommendations by health authorities will ensure consistent monitoring of HIV elimination targets and allow for the identification of inequalities and areas for intervention

Does HAART Efficacy Translate to Effectiveness? Evidence for a Trial Effect

Background: Patients who participate in clinical trials may experience better clinical outcomes than patients who initiate similar therapy within clinical care (trial effect), but no published studies have evaluated a trial effect in HIV clinical trials. Methods: To examine a trial effect we compared virologic suppression (VS) among patients who initiated HAART in a clinical trial versus in routine clinical care. VS was defined as a plasma HIV RNA #400 copies/ml at six months after HAART initiation and was assessed within strata of early (1996–99) or current (2000–06) HAART periods. Risk ratios (RR) were estimated using binomial models. Results: Of 738 persons initiating HAART, 30.6 % were women, 61.7 % were black, 30 % initiated therapy in a clinical trial and 67 % (n = 496) had an evaluable six month HIV RNA result. HAART regimens differed between the early and current periods (p,0.001); unboosted PI regimens (55.6%) were more common in the early and NNRTI regimens (46.4%) were more common in the current period. Overall, 78 % (95%CI 74, 82%) of patients achieved VS and trial participants were 16 % more likely to achieve VS (unadjusted RR 1.16, 95%CI 1.06, 1.27). Comparing trial to non-trial participants, VS differed by study period. In the early period, trial participants initiating HAART were significantly more likely to achieve VS than non-trial participants (adjusted RR 1.33; 95%CI 1.15, 1.54), but not in the current period (adjusted RR 0.98; 95%CI 0.87, 1.11). Conclusions: A clear clinical trial effect on suppression of HIV replication was observed in the early HAART period but not i

Crystal Structure and Size-Dependent Neutralization Properties of HK20, a Human Monoclonal Antibody Binding to the Highly Conserved Heptad Repeat 1 of gp41

The human monoclonal antibody (mAb) HK20 neutralizes a broad spectrum of primary HIV-1 isolates by targeting the highly conserved heptad repeat 1 (HR1) of gp41, which is transiently exposed during HIV-1 entry. Here we present the crystal structure of the HK20 Fab in complex with a gp41 mimetic 5-Helix at 2.3 Å resolution. HK20 employs its heavy chain CDR H2 and H3 loops to bind into a conserved hydrophobic HR1 pocket that is occupied by HR2 residues in the gp41 post fusion conformation. Compared to the previously described HR1-specific mAb D5, HK20 approaches its epitope with a different angle which might favor epitope access and thus contribute to its higher neutralization breadth and potency. Comparison of the neutralization activities of HK20 IgG, Fab and scFv employing both single cycle and multiple cycle neutralization assays revealed much higher potencies for the smaller Fab and scFv over IgG, implying that the target site is difficult to access for complete antibodies. Nevertheless, two thirds of sera from HIV-1 infected individuals contain significant titers of HK20-inhibiting antibodies. The breadth of neutralization of primary isolates across all clades, the higher potencies for C-clade viruses and the targeting of a distinct site as compared to the fusion inhibitor T-20 demonstrate the potential of HK20 scFv as a therapeutic tool

Isolation of a Human Anti-HIV gp41 Membrane Proximal Region Neutralizing Antibody by Antigen-Specific Single B Cell Sorting

Broadly neutralizing antibodies are not commonly produced in HIV-1 infected individuals nor by experimental HIV-1 vaccines. When these antibodies do occur, it is important to be able to isolate and characterize them to provide clues for vaccine design. CAP206 is a South African subtype C HIV-1-infected individual previously shown to have broadly neutralizing plasma antibodies targeting the envelope gp41 distal membrane proximal external region (MPER). We have now used a fluoresceinated peptide tetramer antigen with specific cell sorting to isolate a human neutralizing monoclonal antibody (mAb) against the HIV-1 envelope gp41 MPER. The isolated recombinant mAb, CAP206-CH12, utilized a portion of the distal MPER (HXB2 amino acid residues, 673–680) and neutralized a subset of HIV-1 pseudoviruses sensitive to CAP206 plasma antibodies. Interestingly, this mAb was polyreactive and used the same germ-line variable heavy (VH1-69) and variable kappa light chain (VK3-20) gene families as the prototype broadly neutralizing anti-MPER mAb, 4E10 (residues 672–680). These data indicate that there are multiple immunogenic targets in the C-terminus of the MPER of HIV-1 gp41 envelope and suggests that gp41 neutralizing epitopes may interact with a restricted set of naive B cells during HIV-1 infection

Virological failure and development of new resistance mutations according to CD4 count at combination antiretroviral therapy initiation

Objectives: No randomized controlled trials have yet reported an individual patient benefit of initiating combination antiretroviral therapy (cART) at CD4 counts > 350 cells/μL. It is hypothesized that earlier initiation of cART in asymptomatic and otherwise healthy individuals may lead to poorer adherence and subsequently higher rates of resistance development. Methods: In a large cohort of HIV-positive individuals, we investigated the emergence of new resistance mutations upon virological treatment failure according to the CD4 count at the initiation of cART. Results: Of 7918 included individuals, 6514 (82.3%), 996 (12.6%) and 408 (5.2%) started cART with a CD4 count ≤ 350, 351-499 and ≥ 500 cells/μL, respectively. Virological rebound occurred while on cART in 488 (7.5%), 46 (4.6%) and 30 (7.4%) with a baseline CD4 count ≤ 350, 351-499 and ≥ 500 cells/μL, respectively. Only four (13.0%) individuals with a baseline CD4 count > 350 cells/μL in receipt of a resistance test at viral load rebound were found to have developed new resistance mutations. This compared to 107 (41.2%) of those with virological failure who had initiated cART with a CD4 count < 350 cells/μL. Conclusions: We found no evidence of increased rates of resistance development when cART was initiated at CD4 counts above 350 cells/μL. HIV Medicin

Global, regional, and national incidence and mortality for HIV, tuberculosis, and malaria during 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

BACKGROUND: The Millennium Declaration in 2000 brought special global attention to HIV, tuberculosis, and malaria through the formulation of Millennium Development Goal (MDG) 6. The Global Burden of Disease 2013 study provides a consistent and comprehensive approach to disease estimation for between 1990 and 2013, and an opportunity to assess whether accelerated progress has occured since the Millennium Declaration. METHODS: To estimate incidence and mortality for HIV, we used the UNAIDS Spectrum model appropriately modified based on a systematic review of available studies of mortality with and without antiretroviral therapy (ART). For concentrated epidemics, we calibrated Spectrum models to fit vital registration data corrected for misclassification of HIV deaths. In generalised epidemics, we minimised a loss function to select epidemic curves most consistent with prevalence data and demographic data for all-cause mortality. We analysed counterfactual scenarios for HIV to assess years of life saved through prevention of mother-to-child transmission (PMTCT) and ART. For tuberculosis, we analysed vital registration and verbal autopsy data to estimate mortality using cause of death ensemble modelling. We analysed data for corrected case-notifications, expert opinions on the case-detection rate, prevalence surveys, and estimated cause-specific mortality using Bayesian meta-regression to generate consistent trends in all parameters. We analysed malaria mortality and incidence using an updated cause of death database, a systematic analysis of verbal autopsy validation studies for malaria, and recent studies (2010-13) of incidence, drug resistance, and coverage of insecticide-treated bednets. FINDINGS: Globally in 2013, there were 1·8 million new HIV infections (95% uncertainty interval 1·7 million to 2·1 million), 29·2 million prevalent HIV cases (28·1 to 31·7), and 1·3 million HIV deaths (1·3 to 1·5). At the peak of the epidemic in 2005, HIV caused 1·7 million deaths (1·6 million to 1·9 million). Concentrated epidemics in Latin America and eastern Europe are substantially smaller than previously estimated. Through interventions including PMTCT and ART, 19·1 million life-years (16·6 million to 21·5 million) have been saved, 70·3% (65·4 to 76·1) in developing countries. From 2000 to 2011, the ratio of development assistance for health for HIV to years of life saved through intervention was US$4498 in developing countries. Including in HIV-positive individuals, all-form tuberculosis incidence was 7·5 million (7·4 million to 7·7 million), prevalence was 11·9 million (11·6 million to 12·2 million), and number of deaths was 1·4 million (1·3 million to 1·5 million) in 2013. In the same year and in only individuals who were HIV-negative, all-form tuberculosis incidence was 7·1 million (6·9 million to 7·3 million), prevalence was 11·2 million (10·8 million to 11·6 million), and number of deaths was 1·3 million (1·2 million to 1·4 million). Annualised rates of change (ARC) for incidence, prevalence, and death became negative after 2000. Tuberculosis in HIV-negative individuals disproportionately occurs in men and boys (versus women and girls); 64·0% of cases (63·6 to 64·3) and 64·7% of deaths (60·8 to 70·3). Globally, malaria cases and deaths grew rapidly from 1990 reaching a peak of 232 million cases (143 million to 387 million) in 2003 and 1·2 million deaths (1·1 million to 1·4 million) in 2004. Since 2004, child deaths from malaria in sub-Saharan Africa have decreased by 31·5% (15·7 to 44·1). Outside of Africa, malaria mortality has been steadily decreasing since 1990. INTERPRETATION: Our estimates of the number of people living with HIV are 18·7% smaller than UNAIDS's estimates in 2012. The number of people living with malaria is larger than estimated by WHO. The number of people living with HIV, tuberculosis, or malaria have all decreased since 2000. At the global level, upward trends for malaria and HIV deaths have been reversed and declines in tuberculosis deaths have accelerated. 101 countries (74 of which are developing) still have increasing HIV incidence. Substantial progress since the Millennium Declaration is an encouraging sign of the effect of global action. FUNDING: Bill & Melinda Gates Foundation