Un modelo matemático para sistemas de jubilación del seguro social con sistemas dinámicos

In this paper it is proposed a mathematical approach based on dynamic systems to study the effect of the increase in the Social Security normal retirement age on the worker and on the dynamics of retiree populations. In order to simplify this initial effoEn este documento se propone un enfoque matemático basado en sistemas dinámicos para estudiar el efecto del aumento de la edad normal de jubilación del Seguro Social en el trabajador y en la dinámica de las poblaciones de jubilados. Para simplificar est

Positividad y acotamiento de soluciones de un modelo epidemiologico estacional estocástico para el virus respiratorio sincitial

In this paper we investigate the positivity and boundedness of the solution of a stochastic seasonal epidemic model for the respira tory syncytial virus (RSV). The stochasticity in the model is due to fluctuating physical and social environments and is introduced by perturbing the transmission parameter of the seasonal disease. We show the existence and uniqueness of the positive solution of the stochastic seasonal epidemic model which is required in the modeling of populations since all populations must be positive from a biological point of view. In addition, the positivity and boundedness of solutions is important to other nonlinear models that arise in sciences and engineering. Numerical simulations of the stochastic model are performed using the Milstein numerical scheme and are included to support our analytic results.En este trabajo se investiga la positividad y acotamineto de la solución de un modelo epidemiologico estacional estocástico para el virus respiratorio sincitial (RSV). La estocasticidad en el modelo se debe a entornos físicos y sociales fluctuantes y se introduce perturbando el parámetro de transmisión de la enfermedad. Se demuestra la existencia y unicidad de la solución positiva del modelo epidemiologico estacional estocástico, lo cual se requiere en el modelado de las poblaciones ya que todas las poblaciones deben ser positivos desde el punto de vista biológico. Adicionalmente, la positividad y la acotación de las soluciones es importante para otros modelos no lineales que se presentan en las ciencias y la ingeniería. Las simulaciones numéricas del modelo estocástico se realizan utilizando el esquema numérico de Milstein y se incluyen para apoyar los resultados analíticos

Solución numérico-analítica de una ecuación de difusión bajo condiciones de incertidumbre utilizando DTM y Monte Carlo

A numerical method to solve a general random linear parabolic equation where the diffusion coefficient, source term, boundary and initial conditions include uncertainty, is developed -- Diffusion equations arise in many fields of science and engineering, and, in many cases, there are uncertainties due to data that cannot be known, or due to errors in measurements and intrinsic variability -- In order to model these uncertainties the corresponding parameters, diffusion coefficient, source term, boundary and initial conditions, are assumed to be random variables with certain probability distributions functions -- The proposed method includes finite difference schemes on the space variable and the differential transformation method for the time -- In addition, Monte Carlo method is used to deal with the random variables -- The accuracy of the hybrid method is investigated numerically using the closed form solution of the deterministic associatedUn método numérico para resolver una ecuación parabólica general aleatoria lineal donde el coeficiente de difusión, el término fuente, las condiciones de contorno e iniciales incluyen la incertidumbre, se ha desarrollado -- Ecuaciones de difusión surgen en muchos campos de la ciencia y la ingeniería, y en muchos casos, existen la incertidumbres debido a los datos que no se pueden saber, o debido a errores en las mediciones y la variabilidad intrínseca -- Para modelar estas incertidumbres los parámetros correspondientes, coeficiente de difusión, término fuente, condiciones de contorno e iniciales, se suponen que son variables aleatorias con determinadas distribuciones de probabilidad -- Basándose en los resultados numéricos, se obtienen los intervalos de confianza y valores medios esperados para la solución -- Además, se obtienen con las soluciones numéricas-analíticas del método híbrido propuest

Un modelo matemático para sistemas de jubilación del seguro social con sistemas dinámicos

Este artículo propone una primera aproximación matemática basada en los sistemas dinámicos para estudiar el efecto del aumento de la edad de jubilación de la Seguridad Social de los trabajadores y la dinámica de las poblaciones de jubilados. El modelo propuesto no incluye diversas variables económicas como el crecimiento salarial, los ingresos y la productividad con el fin de obtener un primer enfoque poco complejo. Las simulaciones numéricas del modelo se utilizan para investigar la dinámica de la fuerza de trabajo utilizando diferentes escenarios demográficos. El análisis de este tipo de modelos con simulaciones numéricas puede ayudar a los planificadores económicos de los gobiernos a generar las estrategias óptimas para mantener el sistema de pensiones y obtener pronósticos sobre las poblaciones de pensionistas y trabajadores. MSC:  97M10, 97M40

Dynamics of a model of Toxoplasmosis disease in human and cat populations

AbstractA mathematical model for the transmission of Toxoplasmosis disease in human and cat populations is proposed and analyzed. We explore the dynamics of the Toxoplasmosis disease at the population level using an epidemiological type model. Discussion of the basic concepts of the Toxoplasmosis transmission dynamics on human and cat populations are presented. The cats in this model plays a role of infectious agents and host of the protozoan Toxoplasma Gondii parasite. Qualitative dynamics of the model is determined by the basic reproduction number, R0. If the threshold parameter R0<1, then the solution converges to the disease free equilibrium point. On the other hand if R0>1 the convergence is to the endemic equilibrium point. Numerical simulations of the model illustrates several different dynamics depending on the threshold parameter R0 and show the importance of this parameter

The physics of spreading processes in multilayer networks

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.Comment: 25 pages, 4 figure

Bacterial Toxicity of Potassium Tellurite: Unveiling an Ancient Enigma

Biochemical, genetic, enzymatic and molecular approaches were used to demonstrate, for the first time, that tellurite (TeO(3) (2−)) toxicity in E. coli involves superoxide formation. This radical is derived, at least in part, from enzymatic TeO(3) (2−) reduction. This conclusion is supported by the following observations made in K(2)TeO(3)-treated E. coli BW25113: i) induction of the ibpA gene encoding for the small heat shock protein IbpA, which has been associated with resistance to superoxide, ii) increase of cytoplasmic reactive oxygen species (ROS) as determined with ROS-specific probe 2′7′-dichlorodihydrofluorescein diacetate (H(2)DCFDA), iii) increase of carbonyl content in cellular proteins, iv) increase in the generation of thiobarbituric acid-reactive substances (TBARs), v) inactivation of oxidative stress-sensitive [Fe-S] enzymes such as aconitase, vi) increase of superoxide dismutase (SOD) activity, vii) increase of sodA, sodB and soxS mRNA transcription, and viii) generation of superoxide radical during in vitro enzymatic reduction of potassium tellurite

Late Presentation With HIV in Africa: Phenotypes, Risk, and Risk Stratification in the REALITY Trial.

This article has been accepted for publication in Clinical Infectious Diseases Published by Oxford University PressBackground: Severely immunocompromised human immunodeficiency virus (HIV)-infected individuals have high mortality shortly after starting antiretroviral therapy (ART). We investigated predictors of early mortality and "late presenter" phenotypes. Methods: The Reduction of EArly MortaLITY (REALITY) trial enrolled ART-naive adults and children ≥5 years of age with CD4 counts .1). Results: Among 1711 included participants, 203 (12%) died. Mortality was independently higher with older age; lower CD4 count, albumin, hemoglobin, and grip strength; presence of World Health Organization stage 3/4 weight loss, fever, or vomiting; and problems with mobility or self-care at baseline (all P < .04). Receiving enhanced antimicrobial prophylaxis independently reduced mortality (P = .02). Of five late-presenter phenotypes, Group 1 (n = 355) had highest mortality (25%; median CD4 count, 28 cells/µL), with high symptom burden, weight loss, poor mobility, and low albumin and hemoglobin. Group 2 (n = 394; 11% mortality; 43 cells/µL) also had weight loss, with high white cell, platelet, and neutrophil counts suggesting underlying inflammation/infection. Group 3 (n = 218; 10% mortality) had low CD4 counts (27 cells/µL), but low symptom burden and maintained fat mass. The remaining groups had 4%-6% mortality. Conclusions: Clinical and laboratory features identified groups with highest mortality following ART initiation. A screening tool could identify patients with low CD4 counts for prioritizing same-day ART initiation, enhanced prophylaxis, and intensive follow-up. Clinical Trials Registration: ISRCTN43622374.REALITY was funded by the Joint Global Health Trials Scheme (JGHTS) of the UK Department for International Development, the Wellcome Trust, and Medical Research Council (MRC) (grant number G1100693). Additional funding support was provided by the PENTA Foundation and core support to the MRC Clinical Trials Unit at University College London (grant numbers MC_UU_12023/23 and MC_UU_12023/26). Cipla Ltd, Gilead Sciences, ViiV Healthcare/GlaxoSmithKline, and Merck Sharp & Dohme donated drugs for REALITY, and ready-to-use supplementary food was purchased from Valid International. A. J. P. is funded by the Wellcome Trust (grant number 108065/Z/15/Z). J. A. B. is funded by the JGHTS (grant number MR/M007367/1). The Malawi-Liverpool–Wellcome Trust Clinical Research Programme, University of Malawi College of Medicine (grant number 101113/Z/13/Z) and the Kenya Medical Research Institute (KEMRI)/Wellcome Trust Research Programme, Kilifi (grant number 203077/Z/16/Z) are supported by strategic awards from the Wellcome Trust, United Kingdom. Permission to publish was granted by the Director of KEMRI. This supplement was supported by funds from the Bill & Melinda Gates Foundation

Mathematical Modeling of SARS-CoV-2 Omicron Wave under Vaccination Effects

Over the course of the COVID-19 pandemic millions of deaths and hospitalizations have been reported. Different SARS-CoV-2 variants of concern have been recognized during this pandemic and some of these variants of concern have caused uncertainty and changes in the dynamics. The Omicron variant has caused a large amount of infected cases in the US and worldwide. The average number of deaths during the Omicron wave toll increased in comparison with previous SARS-CoV-2 waves. We studied the Omicron wave by using a highly nonlinear mathematical model for the COVID-19 pandemic. The novel model includes individuals who are vaccinated and asymptomatic, which influences the dynamics of SARS-CoV-2. Moreover, the model considers the waning of the immunity and efficacy of the vaccine against the Omicron strain. This study uses the facts that the Omicron strain has a higher transmissibility than the previous circulating SARS-CoV-2 strain but is less deadly. Preliminary studies have found that Omicron has a lower case fatality rate compared to previous circulating SARS-CoV-2 strains. The simulation results show that even if the Omicron strain is less deadly it might cause more deaths, hospitalizations and infections. We provide a variety of scenarios that help to obtain insight about the Omicron wave and its consequences. The proposed mathematical model, in conjunction with the simulations, provides an explanation for a large Omicron wave under various conditions related to vaccines and transmissibility. These results provide an awareness that new SARS-CoV-2 variants can cause more deaths even if their fatality rate is lower