Mean square solution of Bessel differential equation with uncertainties

[EN] This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. Using the so-called Lp-random calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized power series solution is constructed. As a result of this convergence, the sequences of the mean and standard deviation obtained from the truncated power series solution are convergent as well. The results obtained in the random framework extend their deterministic counterpart. The theory is illustrated in two examples in which several distributions on the random inputs are assumed. Finally, we show through examples that the proposed method is computationally faster than Monte Carlo method.This work has been partially supported by the Spanish Ministerio de Economía y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement No. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and Mexican Conacyt.Cortés, J.; Jódar Sánchez, LA.; Villafuerte, L. (2017). Mean square solution of Bessel differential equation with uncertainties. Journal of Computational and Applied Mathematics. 309:383-395. https://doi.org/10.1016/j.cam.2016.01.034S38339530

Solving linear and quadratic random matrix differential equations: A mean square approach

[EN] In this paper linear and Riccati random matrix differential equations are solved taking advantage of the so called L-p-random calculus. Uncertainty is assumed in coefficients and initial conditions. Existence of the solution in the L-p-random sense as well as its construction are addressed. Numerical examples illustrate the computation of the expectation and variance functions of the solution stochastic process. (C) 2016 Elsevier Inc. All rights reserved.This work has been partially supported by the Spanish Ministerio de Economia y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance).Casabán Bartual, MC.; Cortés López, JC.; Jódar Sánchez, LA. (2016). Solving linear and quadratic random matrix differential equations: A mean square approach. Applied Mathematical Modelling. 40(21-22):9362-9377. https://doi.org/10.1016/j.apm.2016.06.017S936293774021-2

Modeling the epidemiological impact of the UNAIDS 2025 targets to end AIDS as a public health threat by 2030

Background: UNAIDS has established new program targets for 2025 to achieve the goal of eliminating AIDS as a public health threat by 2030. This study reports on efforts to use mathematical models to estimate the impact of achieving those targets. // Methods and findings: We simulated the impact of achieving the targets at country level using the Goals model, a mathematical simulation model of HIV epidemic dynamics that includes the impact of prevention and treatment interventions. For 77 high-burden countries, we fit the model to surveillance and survey data for 1970 to 2020 and then projected the impact of achieving the targets for the period 2019 to 2030. Results from these 77 countries were extrapolated to produce estimates for 96 others. Goals model results were checked by comparing against projections done with the Optima HIV model and the AIDS Epidemic Model (AEM) for selected countries. We included estimates of the impact of societal enablers (access to justice and law reform, stigma and discrimination elimination, and gender equality) and the impact of Coronavirus Disease 2019 (COVID-19). Results show that achieving the 2025 targets would reduce new annual infections by 83% (71% to 86% across regions) and AIDS-related deaths by 78% (67% to 81% across regions) by 2025 compared to 2010. Lack of progress on societal enablers could endanger these achievements and result in as many as 2.6 million (44%) cumulative additional new HIV infections and 440,000 (54%) more AIDS-related deaths between 2020 and 2030 compared to full achievement of all targets. COVID-19–related disruptions could increase new HIV infections and AIDS-related deaths by 10% in the next 2 years, but targets could still be achieved by 2025. Study limitations include the reliance on self-reports for most data on behaviors, the use of intervention effect sizes from published studies that may overstate intervention impacts outside of controlled study settings, and the use of proxy countries to estimate the impact in countries with fewer than 4,000 annual HIV infections. // Conclusions: The new targets for 2025 build on the progress made since 2010 and represent ambitious short-term goals. Achieving these targets would bring us close to the goals of reducing new HIV infections and AIDS-related deaths by 90% between 2010 and 2030. By 2025, global new infections and AIDS deaths would drop to 4.4 and 3.9 per 100,000 population, and the number of people living with HIV (PLHIV) would be declining. There would be 32 million people on treatment, and they would need continuing support for their lifetime. Incidence for the total global population would be below 0.15% everywhere. The number of PLHIV would start declining by 2023

Solving the random diffusion model in an infinite medium: A mean square approach

[EN] This paper deals with the construction of an analytic-numerical mean square solution of the random diffusion model in an infinite medium. The well-known Fourier transform method, which is used to solve this problem in the deterministic case, is extended to the random framework. Mean square operational rules to the Fourier transform of a stochastic process are developed and stated. The main statistical moments of the stochastic process solution are also computed. Finally, some illustrative numerical examples are included.This work has been partially supported by the Ministerio de Economia y Competitividad grant: DPI2010-20891-c0-01, and Universitat Politecnica de Valencia grant: PAID06-11-2070.Casabán, M.; Company Rossi, R.; Cortés, J.; Jódar Sánchez, LA. (2014). Solving the random diffusion model in an infinite medium: A mean square approach. Applied Mathematical Modelling. 38(24):5922-5933. https://doi.org/10.1016/j.apm.2014.04.063S59225933382

Removing the societal and legal impediments to the HIV response: An evidence-based framework for 2025 and beyond.

Societal and legal impediments inhibit quality HIV prevention, care, treatment and support services and need to be removed. The political declaration adopted by UN member countries at the high-level meeting on HIV and AIDS in June 2021, included new societal enabler global targets for achievement by 2025 that will address this gap. Our paper describes how and why UNAIDS arrived at the societal enabler targets adopted. We conducted a scoping review and led a participatory process between January 2019 and June 2020 to develop an evidence-based framework for action, propose global societal enabler targets, and identify indicators for monitoring progress. A re-envisioned framework called the '3 S's of the HIV response: Society, Systems and Services' was defined. In the framework, societal enablers enhance the effectiveness of HIV programmes by removing impediments to service availability, access and uptake at the societal level, while service and system enablers improve efficiencies in and expand the reach of HIV services and systems. Investments in societal enabling approaches that remove legal barriers, shift harmful social and gender norms, reduce inequalities and improve institutional and community structures are needed to progressively realize four overarching societal enablers, the first three of which fall within the purview of the HIV sector: (i) societies with supportive legal environments and access to justice, (ii) gender equal societies, (iii) societies free from stigma and discrimination, and (iv) co-action across development sectors to reduce exclusion and poverty. Three top-line and 15 detailed targets were recommended for monitoring progress towards their achievement. The clear articulation of societal enablers in the re-envisioned framework should have a substantial impact on improving the effectiveness of core HIV programmes if implemented. Together with the new global targets, the framework will also galvanize advocacy to scale up societal enabling approaches with proven impact on HIV outcomes

Long-Term Costs and Health Impact of Continued Global Fund Support for Antiretroviral Therapy

Background: By the end of 2011 Global Fund investments will be supporting 3.5 million people on antiretroviral therapy (ART) in 104 low- and middle-income countries. We estimated the cost and health impact of continuing treatment for these patients through 2020. Methods and Findings: Survival on first-line and second-line ART regimens is estimated based on annual retention rates reported by national AIDS programs. Costs per patient-year were calculated from country-reported ARV procurement prices, and expenditures on laboratory tests, health care utilization and end-of-life care from in-depth costing studies. Of the 3.5 million ART patients in 2011, 2.3 million will still need treatment in 2020. The annual cost of maintaining ART falls from $1.9 billion in 2011 to$1.7 billion in 2020, as a result of a declining number of surviving patients partially offset by increasing costs as more patients migrate to second-line therapy. The Global Fund is expected to continue being a major contributor to meeting this financial need, alongside other international funders and domestic resources. Costs would be $150 million less in 2020 with an annual 5$150-370 million less with a 5%-12% annual decline in second-line prices, but $200 million higher in 2020 with phase out of stavudine (d4T), or$200 million higher with increased migration to second-line regimens expected if all countries routinely adopted viral load monitoring. Deaths postponed by ART correspond to 830,000 life-years saved in 2011, increasing to around 2.3 million life-years every year between 2015 and 2020. Conclusions: Annual patient-level direct costs of supporting a patient cohort remain fairly stable over 2011-2020, if current antiretroviral prices and delivery costs are maintained. Second-line antiretroviral prices are a major cost driver, underscoring the importance of investing in treatment quality to improve retention on first-line regimens

Resource flows and levels of spending for the response to HIV and AIDS in Belarus

<p>Abstract</p> <p>Background</p> <p>Belarus has a focused HIV epidemic concentrated among injecting drug users, female sex workers and men who have sex with men. However, until 2008, Belarus had no way of evaluating HIV spending priorities. In 2008, Belarus committed to undertaking a comprehensive National AIDS Spending Assessment (NASA) in order to analyze HIV spending priorities. NASA was used to 'follow the money' from the funding sources to agents and providers, and eventually to beneficiary populations.</p> <p>Findings</p> <p>Belarus spent the majority of its funding on prevention, diagnosis and treatment of sexually transmitted infections and on securing the blood supply. International donors and NGOs working within Belarus spent the majority of their funding on preventative activities for high risk groups while Global Fund to Fight AIDS, Tuberculosis, and Malaria (GFATM) solely funded antiretroviral treatment.</p> <p>Conclusions</p> <p>The data and experience obtained through conducting NASA will help build capacity for future resource tracking activities for HIV and other health priorities. This experience established the foundation for enhanced and future consistent quality-reporting of National Health Accounts. Monitoring the flow of resources for Belarus' HIV response provides valuable strategic information that can improve operations and planning as well as mobilize greater resources. NASA offers Belarusian policy makers an overview of HIV activities that merit their priority attention. In addition, the findings from Belarus are particularly relevant for the rest of the Commonwealth of Independent States due to their similar epidemiological profiles and centrally planned systems. The Belarusian government faces future challenges, especially in increasing public investments in HIV prevention for female sex workers and their clients, men who have sex with men, and among intravenous drug users.</p

Variational formulas and cocycle solutions for directed polymer and percolation models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder