Ecuaciones lineales en diferencias. Aplicaciones a la empresa y la economía

Este trabajo es una introducción desde el punto de vista matemático a las ecuaciones en diferencias, especialmente a las lineales, encaminado principalmente a resolver problemas económicos y empresariales cimentados en este tipo de ecuaciones. A pesar de ello, su contenido y exposición ha sido desarrollado para que pueda servir como apuntes de trabajo a cualquier persona que quiera introducirse en el mundo de las ecuaciones en diferencias. Las aplicaciones que aquí se plantean pueden ser comprendidas sin necesidad de grandes conocimientos empresariales o económicos. Algunos planteamientos económicos utilizan ecuaciones en diferencias muy simples, por lo que su resolución dentro del marco puramente práctico suele hacerse mediante una simple recurrencia. Para este tipo de problemas hemos intentado conjugar las técnicas recurrentes usadas en economía con un planteamiento desde el punto de vista de las ecuaciones en diferencias. Matemáticamente, este texto es autocontenido y para su total comprensión solo son necesarias algunas nociones básicas de álgebra lineal. Para ello se ha abordado el desarrollo teórico introduciendo demostraciones sencillas y la menor cantidad posible de notaciones. Las demostraciones están insertadas tras cada enunciado. Solo las pruebas de la proposición 2.3.3 y del teorema 2.3.4 las incluimos en el apéndice B por su tecnicismo. En el apéndice C damos una demostración alternativa del teorema 2.2.5 mediante el uso de las aplicaciones lineales. Los desarrollos que aquí se plantean se basan en textos matemáticos clásicos y en el desarrollo natural, para un matemático, de los distintos conceptos, estudiando primero las propiedades de los objetos y después sus técnicas de cálculo. Introducimos el uso del ordenador como una herramienta de resolución de problemas numéricos, así como un método para obtener las soluciones de una ecuación en diferencias con coeficientes no necesariamente numéricos. Una vez conocidas las técnicas que planteamos de resolución de las ecuaciones en diferencias, podemos emplear el ordenador, que aplicará dichas técnicas para ahorrarnos el tedioso trabajo manual. El software que empleamos en este libro es MapleV, un conocido programa de cálculo simbólico comercial

It is time to define an organizational model for the prevention and management of infections along the surgical pathway: a worldwide cross-sectional survey

Background The objectives of the study were to investigate the organizational characteristics of acute care facilities worldwide in preventing and managing infections in surgery; assess participants' perception regarding infection prevention and control (IPC) measures, antibiotic prescribing practices, and source control; describe awareness about the global burden of antimicrobial resistance (AMR) and IPC measures; and determine the role of the Coronavirus Disease 2019 pandemic on said awareness. Methods A cross-sectional web-based survey was conducted contacting 1432 health care workers (HCWs) belonging to a mailing list provided by the Global Alliance for Infections in Surgery. The self-administered questionnaire was developed by a multidisciplinary team. The survey was open from May 22, 2021, and June 22, 2021. Three reminders were sent, after 7, 14, and 21 days. Results Three hundred four respondents from 72 countries returned a questionnaire, with an overall response rate of 21.2%. Respectively, 90.4% and 68.8% of participants stated their hospital had a multidisciplinary IPC team or a multidisciplinary antimicrobial stewardship team. Local protocols for antimicrobial therapy of surgical infections and protocols for surgical antibiotic prophylaxis were present in 76.6% and 90.8% of hospitals, respectively. In 23.4% and 24.0% of hospitals no surveillance systems for surgical site infections and no monitoring systems of used antimicrobials were implemented. Patient and family involvement in IPC management was considered to be slightly or not important in their hospital by the majority of respondents (65.1%). Awareness of the global burden of AMR among HCWs was considered very important or important by 54.6% of participants. The COVID-19 pandemic was considered by 80.3% of respondents as a very important or important factor in raising HCWs awareness of the IPC programs in their hospital. Based on the survey results, the authors developed 15 statements for several questions regarding the prevention and management of infections in surgery. The statements may be the starting point for designing future evidence-based recommendations. Conclusion Adequacy of prevention and management of infections in acute care facilities depends on HCWs behaviours and on the organizational characteristics of acute health care facilities to support best practices and promote behavioural change. Patient involvement in the implementation of IPC is still little considered. A debate on how operationalising a fundamental change to IPC, from being solely the HCWs responsibility to one that involves a collaborative relationship between HCWs and patients, should be opened

Evolving trends in the management of acute appendicitis during COVID-19 waves. The ACIE appy II study

Background: In 2020, ACIE Appy study showed that COVID-19 pandemic heavily affected the management of patients with acute appendicitis (AA) worldwide, with an increased rate of non-operative management (NOM) strategies and a trend toward open surgery due to concern of virus transmission by laparoscopy and controversial recommendations on this issue. The aim of this study was to survey again the same group of surgeons to assess if any difference in management attitudes of AA had occurred in the later stages of the outbreak. Methods: From August 15 to September 30, 2021, an online questionnaire was sent to all 709 participants of the ACIE Appy study. The questionnaire included questions on personal protective equipment (PPE), local policies and screening for SARS-CoV-2 infection, NOM, surgical approach and disease presentations in 2021. The results were compared with the results from the previous study. Results: A total of 476 answers were collected (response rate 67.1%). Screening policies were significatively improved with most patients screened regardless of symptoms (89.5% vs. 37.4%) with PCR and antigenic test as the preferred test (74.1% vs. 26.3%). More patients tested positive before surgery and commercial systems were the preferred ones to filter smoke plumes during laparoscopy. Laparoscopic appendicectomy was the first option in the treatment of AA, with a declined use of NOM. Conclusion: Management of AA has improved in the last waves of pandemic. Increased evidence regarding SARS-COV-2 infection along with a timely healthcare systems response has been translated into tailored attitudes and a better care for patients with AA worldwide

Correction to: Two years later: Is the SARS-CoV-2 pandemic still having an impact on emergency surgery? An international cross-sectional survey among WSES members

Background: The SARS-CoV-2 pandemic is still ongoing and a major challenge for health care services worldwide. In the first WSES COVID-19 emergency surgery survey, a strong negative impact on emergency surgery (ES) had been described already early in the pandemic situation. However, the knowledge is limited about current effects of the pandemic on patient flow through emergency rooms, daily routine and decision making in ES as well as their changes over time during the last two pandemic years. This second WSES COVID-19 emergency surgery survey investigates the impact of the SARS-CoV-2 pandemic on ES during the course of the pandemic. Methods: A web survey had been distributed to medical specialists in ES during a four-week period from January 2022, investigating the impact of the pandemic on patients and septic diseases both requiring ES, structural problems due to the pandemic and time-to-intervention in ES routine. Results: 367 collaborators from 59 countries responded to the survey. The majority indicated that the pandemic still significantly impacts on treatment and outcome of surgical emergency patients (83.1% and 78.5%, respectively). As reasons, the collaborators reported decreased case load in ES (44.7%), but patients presenting with more prolonged and severe diseases, especially concerning perforated appendicitis (62.1%) and diverticulitis (57.5%). Otherwise, approximately 50% of the participants still observe a delay in time-to-intervention in ES compared with the situation before the pandemic. Relevant causes leading to enlarged time-to-intervention in ES during the pandemic are persistent problems with in-hospital logistics, lacks in medical staff as well as operating room and intensive care capacities during the pandemic. This leads not only to the need for triage or transferring of ES patients to other hospitals, reported by 64.0% and 48.8% of the collaborators, respectively, but also to paradigm shifts in treatment modalities to non-operative approaches reported by 67.3% of the participants, especially in uncomplicated appendicitis, cholecystitis and multiple-recurrent diverticulitis. Conclusions: The SARS-CoV-2 pandemic still significantly impacts on care and outcome of patients in ES. Well-known problems with in-hospital logistics are not sufficiently resolved by now; however, medical staff shortages and reduced capacities have been dramatically aggravated over last two pandemic years

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Evolving trends in the management of acute appendicitis during COVID-19 waves. The ACIE appy II study (vol 46, pg 2021, 2022)

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Two years later: Is the SARS-CoV-2 pandemic still having an impact on emergency surgery? An international cross-sectional survey among WSES members

Background The SARS-CoV-2 pandemic is still ongoing and a major challenge for health care services worldwide. In the first WSES COVID-19 emergency surgery survey , a strong negative impact on emergency surgery (ES) had been described already early in the pandemic situation. However, the knowledge is limited about current effects of the pandemic on patient flow through emergency rooms, daily routine and decision making in ES as well as their changes over time during the last two pandemic years. This second WSES COVID-19 emergency surgery survey investigates the impact of the SARS-CoV-2 pandemic on ES during the course of the pandemic. Methods A web survey had been distributed to medical specialists in ES during a four-week period from January 2022, investigating the impact of the pandemic on patients and septic diseases both requiring ES, structural problems due to the pandemic and time-to-intervention in ES routine. Results 367 collaborators from 59 countries responded to the survey. The majority indicated that the pandemic still significantly impacts on treatment and outcome of surgical emergency patients (83.1% and 78.5%, respectively). As reasons, the collaborators reported decreased case load in ES (44.7%), but patients presenting with more prolonged and severe diseases, especially concerning perforated appendicitis (62.1%) and diverticulitis (57.5%). Otherwise, approximately 50% of the participants still observe a delay in time-to-intervention in ES compared with the situation before the pandemic. Relevant causes leading to enlarged time-to-intervention in ES during the pandemic are persistent problems with in-hospital logistics, lacks in medical staff as well as operating room and intensive care capacities during the pandemic. This leads not only to the need for triage or transferring of ES patients to other hospitals, reported by 64.0% and 48.8% of the collaborators, respectively, but also to paradigm shifts in treatment modalities to non-operative approaches reported by 67.3% of the participants, especially in uncomplicated appendicitis, cholecystitis and multiple-recurrent diverticulitis. Conclusions The SARS-CoV-2 pandemic still significantly impacts on care and outcome of patients in ES. Well-known problems with in-hospital logistics are not sufficiently resolved by now; however, medical staff shortages and reduced capacities have been dramatically aggravated over last two pandemic years

Global attitudes in the management of acute appendicitis during COVID-19 pandemic: ACIE Appy Study

Background: Surgical strategies are being adapted to face the COVID-19 pandemic. Recommendations on the management of acute appendicitis have been based on expert opinion, but very little evidence is available. This study addressed that dearth with a snapshot of worldwide approaches to appendicitis. Methods: The Association of Italian Surgeons in Europe designed an online survey to assess the current attitude of surgeons globally regarding the management of patients with acute appendicitis during the pandemic. Questions were divided into baseline information, hospital organization and screening, personal protective equipment, management and surgical approach, and patient presentation before versus during the pandemic. Results: Of 744 answers, 709 (from 66 countries) were complete and were included in the analysis. Most hospitals were treating both patients with and those without COVID. There was variation in screening indications and modality used, with chest X-ray plus molecular testing (PCR) being the commonest (19\ub78 per cent). Conservative management of complicated and uncomplicated appendicitis was used by 6\ub76 and 2\ub74 per cent respectively before, but 23\ub77 and 5\ub73 per cent, during the pandemic (both P < 0\ub7001). One-third changed their approach from laparoscopic to open surgery owing to the popular (but evidence-lacking) advice from expert groups during the initial phase of the pandemic. No agreement on how to filter surgical smoke plume during laparoscopy was identified. There was an overall reduction in the number of patients admitted with appendicitis and one-third felt that patients who did present had more severe appendicitis than they usually observe. Conclusion: Conservative management of mild appendicitis has been possible during the pandemic. The fact that some surgeons switched to open appendicectomy may reflect the poor guidelines that emanated in the early phase of SARS-CoV-2

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

AimThe SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery.MethodsThis was an international prospective cohort study of consecutive colorectal cancer patients with a decision for curative surgery (January-April 2020). Surgical delay was defined as an operation taking place more than 4 weeks after treatment decision, in a patient who did not receive neoadjuvant therapy. A subgroup analysis explored the effects of delay in elective patients only. The impact of longer delays was explored in a sensitivity analysis. The primary outcome was complete resection, defined as curative resection with an R0 margin.ResultsOverall, 5453 patients from 304 hospitals in 47 countries were included, of whom 6.6% (358/5453) did not receive their planned operation. Of the 4304 operated patients without neoadjuvant therapy, 40.5% (1744/4304) were delayed beyond 4 weeks. Delayed patients were more likely to be older, men, more comorbid, have higher body mass index and have rectal cancer and early stage disease. Delayed patients had higher unadjusted rates of complete resection (93.7% vs. 91.9%, P = 0.032) and lower rates of emergency surgery (4.5% vs. 22.5%, P ConclusionOne in 15 colorectal cancer patients did not receive their planned operation during the first wave of COVID-19. Surgical delay did not appear to compromise resectability, raising the hypothesis that any reduction in long-term survival attributable to delays is likely to be due to micro-metastatic disease