Behaviour of the extended Toda lattice

We consider the first member of an extended Toda lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptotic analysis to consider the long wavelength limits of the system. By considering various magnitudes for the parameters involved, we derive reduced equations related to the Korteweg-de Vries and potential Boussinesq equations

B\"acklund transformations for fourth Painlev\'e hierarchies

B\"acklund transformations (BTs) for ordinary differential equations (ODEs), and in particular for hierarchies of ODEs, are a topic of great current interest. Here we give an improved method of constructing BTs for hierarchies of ODEs. This approach is then applied to fourth Painlev\'e ($P_{IV}$) hierarchies recently found by the same authors [{\em Publ. Res. Inst. Math. Sci. (Kyoto)} {\bf 37} 327--347 (2001)]. We show how the known pattern of BTs for $P_{IV}$ can be extended to our $P_{IV}$ hierarchies. Remarkably, the BTs required to do this are precisely the Miura maps of the dispersive water wave hierarchy. We also obtain the important result that the fourth Painlev\'e equation has only one nontrivial fundamental BT, and not two such as is frequently stated.Comment: 23 pages, 2 figures, to appear Journal of Differential Equation

Aproximación al impacto sobre el reclutamiento del atún rojo (Thunnus thynnus) de las capturas de cerco en Baleares con el actual periodo de veda.

4 páginas, 1 figura.[EN]This study estimates the impact which the purse seine catch in the Balearic Islands has on bluefin tuna recruitment with the current closed period. The estimate is carried out using available information on: fecundity in female spawners, the ratio of females, time pattern of spawning in the Balearic Islands and potential larval survival. This information has been applied to the catch extracted in the Balearic Islands in 2010, from the Balfegó and Fuentes groups combined, to assess failed recruitment and to propose periods and practices that minimize the impact of the quota extracted.[ES]En este estudio se realiza una aproximación al impacto sobre el reclutamiento del atún rojo que produce la captura de cerco en Baleares con el actual periodo de veda. La aproximación se realiza utilizando la información existente en: fecundidad de hembras reproductoras, proporción de hembras, patrón temporal de reproducción en Baleares y supervivencia larvaria potencial. Esta información se ha aplicado sobre la captura extraída en Baleares en 2010, de los grupos Balfegó y Fuentes conjuntamente, para valorar el reclutamiento fracasado y proponer periodos y prácticas que minimicen el impacto de la cuota extraída.[FR]Ce document étudie l'incidence de la capture des senneurs dans les Baléares sur le recrutement du thon rouge compte tenu de la période de fermeture actuelle. Ce rapprochement est réalisé au moyen de l'information existante relative aux éléments suivants : fécondité des femelles reproductrices, proportion de femelles, schéma temporel de reproduction dans les Baléares et survie larvaire potentielle. Ces informations ont été appliquées à la capture réalisée dans les Baléares en 2010 par les groupes Balfegó et Fuentes conjointement afin d’estimer l’échec du recrutement et de proposer des périodes et des pratiques qui réduisent l’incidence de la ponction réalisée.Peer reviewe

Economic evaluation of the breast cancer screening programme in the Basque Country: retrospective cost-effectiveness and budget impact analysis

Background Breast cancer screening in the Basque Country has shown 20 % reduction of the number of BC deaths and an acceptable overdiagnosis level (4 % of screen detected BC). The aim of this study was to evaluate the breast cancer early detection programme in the Basque Country in terms of retrospective cost-effectiveness and budget impact from 1996 to 2011. Methods A discrete event simulation model was built to reproduce the natural history of breast cancer (BC). We estimated for lifetime follow-up the total cost of BC (screening, diagnosis and treatment), as well as quality-adjusted life years (QALY), for women invited to participate in the evaluated programme during the 15-year period in the actual screening scenario and in a hypothetical unscreened scenario. An incremental cost-effectiveness ratio was calculated with the use of aggregated costs. Besides, annual costs were considered for budget impact analysis. Both population level and single-cohort analysis were performed. A probabilistic sensitivity analysis was applied to assess the impact of parameters uncertainty. Results The actual screening programme involved a cost of 1,127 million euros and provided 6.7 million QALYs over the lifetime of the target population, resulting in a gain of 8,666 QALYs for an additional cost of 36.4 million euros, compared with the unscreened scenario. Thus, the incremental cost-effectiveness ratio was 4,214€/QALY. All the model runs in the probabilistic sensitivity analysis resulted in an incremental cost-effectiveness ratio lower than 10,000€/QALY. The screening programme involved an increase of the annual budget of the Basque Health Service by 5.2 million euros from year 2000 onwards. Conclusions The BC screening programme in the Basque Country proved to be cost-effective during the evaluated period and determined an affordable budget impact. These results confirm the epidemiological benefits related to the centralised screening system and support the continuation of the programme

New contiguity relation of the sixth Painlev\'e equation from a truncation

For the master Painlev\'e equation P6(u), we define a consistent method, adapted from the Weiss truncation for partial differential equations, which allows us to obtain the first degree birational transformation of Okamoto. Two new features are implemented to achieve this result. The first one is the homography between the derivative of the solution $u$ and a Riccati pseudopotential. The second one is an improvement of a conjecture by Fokas and Ablowitz on the structure of this birational transformation. We then build the contiguity relation of P6, which yields one new second order nonautonomous discrete equation.Comment: LaTex 2e. To appear, Physica

Budget impact analysis of the use of Souvenaid in patients with prodromal Alzheimer’s Disease in Spain

Introduction The effectiveness, safety, and cost-effectiveness of the use of Souvenaid for Alzheimer’s disease (AD) have been previously evidenced. To complete the economic analysis, there is a need to assess whether society can afford it. The objective of this study was to carry out a budget impact analysis of the use of Souvenaid in Spain under the conditions of the LipiDidiet clinical trial from a societal perspective. Methods We built a population model that took into account all the cohorts of individuals with AD, their individual progression, and the potential impact of Souvenaid treatment on their trajectories. Patient progression data were obtained from mixed models. The target population was estimated based on the population forecast for 2020–2035 and the incidence of dementia. Individual progression to dementia measured by the Clinical Dementia Rating-Sum of Boxes was reproduced using mixed models. Besides the costs of treatment and diagnosis, direct costs of medical and non-medical care and indirect costs were included. Results The epidemiological indicators and the distribution of life expectancy by stages validated the model. From the third year (2022), the differences in the cost of dementia offset the incremental cost of diagnosis and treatment. The costs of dependency reached €500 million/year while those of the intervention were limited to €40 million. Conclusions Souvenaid, with modest effectiveness in delaying dementia associated with AD, achieved a positive economic balance between costs and savings. Its use in the treatment of prodromal AD would imply an initial cost that would be ongoing, but this would be offset by savings in the care system for dependency associated with dementia from the third year. These results were based on adopting a societal perspective taking into account the effect of treatment on the use of health, social, and family resources

Diagnóstico participativo: un instrumento para el planeamiento estratégico en el desarrollo comunitario

Las teorías sobre el desarrollo que fundamentan las estrategias de cooperación internacional han evolucionado notablemente durante los últimos años. La literatura sobre el desarrollo ha dado un giro extraordinario desde conceptos unidimensionales, como el ingreso y el consumo, hacia otros más amplios y más comprensivos. Se les ha otorgado a los actores locales cada vez más control y responsabilidad durante todo el ciclo de la intervención. Gobiernos, donantes, organizaciones de la sociedad civil y agencias multilaterales como el Banco Mundial y el Fondo Monetario Internacional han llegado al consenso de que el desarrollo no puede ser sostenible ni duradero si no se incluye la participación de la gente en el proceso.

Economic evaluation of supplementing the diet with 1 Souvenaid in patients with prodromal Alzheimer's disease

Background: The LipiDiDiet trial showed that Souvenaid, a medical food, might delay progression to dementia in prodromal Alzheimer’s disease (AD). The objective of this study was to assess the cost-utility of Souvenaid compared to placebo in patients with prodromal AD under the conditions applied in that trial. Methods: A discrete event simulation model was developed based on the LipiDiDiet trial and a literature review to assess the cost-utility of Souvenaid from a societal perspective considering direct and indirect costs. For both intervention and control groups, patient trajectories in terms of functional decline on the Clinical Dementia Rating Sum of Boxes (CDR-SB) scale in LipiDiDiet were reproduced statistically with mixed models by assigning time until events to simulated patients. From the societal perspective, four scenarios were analysed by combining different options for treatment duration and diagnostic test cost. Univariate sensitivity analysis assessed parameter uncertainties. Results: Validation results at year 2 of disease progression fit with CDR-SB progression in LipiDiDiet. The incremental cost-utility ratio (ICUR) in the baseline case was €22,743/quality-adjusted life year (QALY). All scenarios rendered an ICUR lower than €25,000/QALY (the societal threshold). Moreover, the treatment option was costsaving and increased health benefits when diagnostic costs were not considered and treatment was only administered during the prodromal stage. Conclusions: Treating prodromal AD with Souvenaid is a cost-effective intervention in all scenarios analysed. The LipiDiDiet trial showed a modest improvement in disease course but as the social costs of AD are very high, the intervention was efficient. Assessing small benefits at specific stages of AD is relevant because it is reasonable to expect that no effective, safe and affordable disease-modifying therapies will become available in the short to medium term