The value of mathematical modelling approaches in epidemiology for public health decisión making

It is discussed the relevance of quantitative approaches, specifically mathematical modelling in epidemiology, in the public health decision-making process. This topic is discussed here based on the experience of various experts in mathematical epidemiology and public health. First, the definition of mathematical modelling is presented, especially in the context of epidemiology. Second, the different uses and socio-political implications, including empirical examples of recent experiences that have taken place at the international level are addressed. Finally, some general considerations regarding the challenges encountered in the use and application of mathematical modelling in epidemiology in the decision-making process at the local and national levels.

Se trata sobre la importancia de los abordajes cuantitativos, específicamente la formulación de modelos matemáticos en epidemiología, dentro del proceso de toma de decisiones en salud pública. Esta importante temática se analiza basándose en la experiencia de algunos expertos en epidemiología matemática y salud pública. En primer lugar, se presenta la definición de modelación matemática, particularmente dentro del contexto de la epidemiología. En segundo lugar, se abordan los diferentes usos y las implicaciones socio-políticas, incluyendo ejemplos de experiencias recientes que han ocurrido a nivel internacional. Finalmente, se hace referencia a ciertas consideraciones generales respecto a los retos que representa el uso y la aplicación de modelos matemáticos en epidemiología para el proceso de toma de decisiones a nivel local y nacional.

Modelado matemático del efecto de las medidas de cuidado por COVID-19 sobre otras enfermedades respiratorias / Mathematical modelling of the impact of COVID-19 care measures on other respiratory diseases

RESUMEN INTRODUCCIÓN Los modelos matemáticos de la transmisión de enfermedades infecciosas permiten estudiar distintos mecanismos que afectan su comportamiento temporal. Este trabajo analizó el efecto sobre la dinámica de la influenza y el virus sincitial respiratorio (VSR) de la disminución de la transmisibilidad debida a las medidas de cuidado adoptadas para reducir la circulación de COVID-19. MÉTODOS Se empleó un modelo determinista tipo SIRS (susceptible-infectado-recuperado-susceptible) con modulación estacional para representar la influenza y el VSR, en ambos casos con inmunidad de corta duración y ciclo anual. Los cambios en la transmisibilidad de la enfermedad se modelaron reduciéndola durante dos años y planteando distintos escenarios. RESULTADOS En el modelo planteado, la reducción en la transmisibilidad genera cambios que se sostienen en los años siguientes: eventos epidémicos muy pronunciados con alargamiento del intervalo interbrote. Este efecto resulta dominante respecto del comportamiento estacional. El escenario de una reducción inicial de la transmisibilidad del 40% resulta compatible con el comportamiento de influenza y VSR reportados actualmente para Argentina. DISCUSIÓN El modelo general propuesto, en condiciones de disminución transitoria en la transmisibilidad, exhibe una epidemiología compatible con la observada recientemente en Argentina para ambas enfermedades e ilustra el modelado como herramienta útil en la comprensión de efectos no intuitivos.

ABSTRACT INTRODUCTION Mathematical models of infectious diseases transmission allow to study different mechanisms which affect their temporal behavior. This work analyzed the impact of the decrease in transmissibility, as a result of measures of personal care adopted to reduce circulation of COVID-19, on the dynamics of influenza and respiratory syncytial virus (RSV). METHODS A deterministic SIRS (susceptible-infected-recovered-susceptible) model with seasonal modulation was used to represent two diseases with short-term immunity and annual cycle: influenza and RSV. Changes in disease transmissibility were modeled by reducing it for two years and analyzing different scenarios. RESULTS In the proposed model, transmissibility reduction brings changes which sustain in the following years: very pronounced epidemic events with lengthening of the inter-outbreak interval. This effect prevails over the seasonal behavior. The scenario of 40% initial reduction in transmissibility is compatible with the behavior of influenza and RSV currently reported in Argentina. DISCUSSION The general model proposed here, under conditions of temporary reduced transmissibility, shows an epidemiology compatible with recently reported data of influenza and RSV in Argentina. This result illustrates modeling as a useful tool to understand non-intuitive effects.

Efetividade de intervenções para redução da ansiedade matemática / Effectiveness of interventions to reduce mathematical anxiety

O objetivo deste estudo foi investigar a efetividade de intervenções para redução da ansiedade matemática (AM) em crianças e/ou adolescentes, sistematizando sugestões para o atendimento psicopedagógico. Foi realizada uma revisão sistemática sobre AM, norteada pelo Protocolo PRISMA. A busca, conduzida nas bases de dados ERIC, LILACS, PePSIC, SciELO, Periódicos CAPES e Web of Science, abrangeu janeiro de 2010 a janeiro de 2021, artigos empíricos revisados por pares, em português, espanhol e inglês e as combinações dos descritores: mathematics anxiety OR math anxiety OR seus equivalentes em espanhol e português. Foram identificados 1.264 trabalhos e incluídos 24 por atenderem aos critérios de inclusão e exclusão. Esses estudos foram avaliados com relação à efetividade da intervenção, de acordo com os parâmetros: eficácia, eficiência, manutenção do efeito e generalização e as descobertas apresentadas por meio de síntese descritiva. Os resultados sugerem que intervenções que enfatizam aspectos pedagógicos e psicoterápicos são mais efetivas na redução da AM em crianças e adolescentes, enquanto as que utilizam apenas uma dessas estratégias apresentam menor efetividade. Quanto aos procedimentos de intervenção, destacam-se estratégias/programas educacionais que envolvem treinamento de habilidades matemáticas; jogos recreativos ativos; aprendizagem interativa na resolução de problemas; tutoria entre pares; e técnicas terapêuticas de redução de ansiedade, que abrangem a intervenção matemática integrada à aprendizagem autorregulada. Implicações para guiar a prática do psicopedagogo são discutidas à luz das evidências científicas e recomendações são apontadas para a sua atuação em caso de AM.

The aim of this study was to investigate the effectiveness of interventions to reduce mathematical anxiety (MA) in children and/or adolescents, systematizing suggestions for psycho-pedagogical care. A systematic review of MA was conducted, based on the PRISMA Protocol. The search, conducted in the ERIC, LILACS, PePSIC, SciELO, CAPES journals and Web of Science databases, covered January 2010 to January 2021, peer-reviewed empirical articles in Portuguese, Spanish and English and the combinations of descriptors: mathematics anxiety OR math anxiety, and their equivalents in Spanish and Portuguese. A total of 1,264 studies were identified and 24 were included because they met the inclusion and exclusion criteria. These studies were evaluated in relation to the effectiveness of the intervention, according to the parameters: efficacy, efficiency, effect maintenance and generalization and the findings presented through descriptive synthesis. The results suggest that interventions that emphasize pedagogical and psychotherapeutic aspects are more effective in reducing MA in children and adolescents, while those that use only one of these strategies have lower effectiveness. Regarding intervention procedures, educational strategies/programs involving mathematical skills training stand out; active recreational games; interactive learning in problem solving; peer-to-peer tutoring; and therapeutic anxiety reduction techniques, which cover mathematical intervention integrated into self-regulated learning. Implications to guide the practice of psycho-pedagogue are discussed in the light of scientific evidence and recommendations are pointed out for their action in case of MA.

Invitation to Mathematical Psychology: Models and Benefits of Formal Theorizing / Convite à Psicologia Matemática: Modelos e Benefícios da Teorização Formal

ABSTRACT In most areas, psychological phenomena tend to be explained only through textual constructions. Several authors, however, point to the need for theories that have a more formal nature, based on mathematical reasoning. In order to encourage broader access to its applications, we present the models and advantages of a mathematical psychology approach to the study of behavior. We review the limitations of verbal theorizing, then a common taxonomy in mathematical psychology follows, that classifies formal models as descriptive, process characterization, and explanatory. As well succeeded cases, we examine the mathematical psychology of decision making, of helping behavior, of memory, and of romantic relationships. Finally, we discuss the potential benefits and uses of this approach. Welcome to mathematical psychology.

RESUMO Na maior parte das áreas os fenômenos psicológicos tendem a ser explicados apenas por meio de construções textuais. Diversos autores, no entanto, apontam para a necessidade de teorias que tenham uma natureza mais formal, baseada em raciocínio matemático. A fim de incentivar acesso mais amplo às suas aplicações, apresentamos os modelos e vantagens da abordagem da psicologia matemática para o estudo do comportamento. Revisamos as limitações da teorização verbal, apresentando em seguida uma taxonomia, comum na psicologia matemática, que classifica os modelos de dados como descritivos, explicativos e de caracterização. Como casos bem sucedidos, examinamos a psicologia matemática da tomada de decisão, do comportamento de ajuda, da memória e dos relacionamentos românticos. Por fim, discutimos os benefícios e usos potenciais da abordagem. Bem-vindo(a) à psicologia matemática.

A study on the practice of online and offline hybrid teaching in the teaching of advanced mathematics in medical schools / 中华医学教育探索杂志

Objective:To solve the problems of medical advanced mathematics learning for medical school students, such as high difficulty, tight school hours, poor learning interest and low acceptance of students, and to actively carry out online and offline hybrid teaching mode.Methods:A total of 243 students majoring in clinical medicine, biomedical engineering and information management and information system from 6 classes in Batch 2022 were selected as the study subjects (experimental group). A hybrid online/offline teaching mode combining self-made online learning resources and MOOC teaching resources of China University was specifically adopted. Teaching objectives were set and teaching resources were uploaded according to the teaching content before the class. Super Star Learning Platform was employed to issue pre-class learning tasks to help students study before class. During the lesson, teachers taught face-to-face, and released classroom questions and quizzes on the learning platform to test the learning effect in class. It was convenient for teachers to grasp students' learning situation and took timely teaching adjustments to help students successfully complete their learning in class. After the class, we released the videos of class lectures and post-class exercises on Super Star Learning Platform to help students consolidate their learning from class. We also set up a QQ group for the course in each class to facilitate communication with students after class and to answer questions. SPSS 20.0 was used to conduct t-test. Results:The online and offline hybrid teaching effectively increased students' participation in class and greatly mobilized students' enthusiasm for learning, and the average teacher-student interaction in class increased from 6 to 10 times per session; the class attendance rate increased from 93.93% (232/247) to 97.94% (238/243); the homework submission rate increased from 92.71% (229/247) to 96.71% (235/243). After the course was finished, the final comprehensive scores of students increased from (81.27±4.56) to (89.52±3.42), with statistically significant differences ( t=8.25, P<0.001). Conclusion:The adoption of online and offline hybrid teaching not only has a benign effect on students' academic performance, but also stimulates students' enthusiasm to learn advanced mathematics to a greater extent, and subsequently expects students' ability to be further improved in applying mathematics to solve practical problems.

Research progress on three-dimensional evaluation methods for facial asymmetry / 口腔疾病防治

@#Facial symmetry evaluation has always been a hot topic of concern for doctors who engage in the study of facial beauty disciplines such as orthodontics, dentistry, and plastic surgery. Although scholars at home and abroad have carried out much research on the evaluation of facial symmetry with a variety of emerging technologies and methods, there is still a lack of unified standards for the evaluation of facial asymmetry due to the complexity of the content and methods and individual subjectivity. Facial asymmetry involves changes in the length, width and height of the face. It is a complex dental and maxillofacial malformation whose early identification and accurate evaluation are particularly important. Clinically, in addition to the necessary dental and maxillofacial examinations, it is also necessary to evaluate facial asymmetry with the help of corresponding auxiliary methods. This paper gives a summary of the commonly used three-dimensional evaluation methods. The evaluation methods of facial asymmetry can be divided into 5 categories: qualitative analysis, quantitative analysis, dynamic analysis, mathematical analysis, and artificial intelligence analysis. After the analysis and summarization of the characteristics, advantages and limitations of each method in clinical applications, it is found that although these methods vary in accuracy, evaluation scope, diagnosis nature and calculation method, etc., the three-dimensional evaluation methods are more objective, more accurate and more convenient and will become the mainstream evaluation method for facial asymmetry with further development of three-dimensional measurement technologies.

Research Progress on Disease Burden of Dengue in China / 中山大学学报(医学科学版)

The gradual relaxation of COVID-19 restrictions in China has increased the risk of imported dengue fever cases and may further prompt the outbreak. Systematic assessment of disease burden is crucial to improving prevention and control strategies， and resource allocation of dengue fever in China. After reviewing the definition， classification of disease burden， epidemiological evaluation methods such as potential years of life lost （PYLL） and disability adjusted of life years （DALY）， as well as economic evaluation methods such as step-by-step model method and human capital method， this article systematically summarizes the application of mixed models and catalytic models in quantifying the disease burden of latent dengue infected individuals， as well as the current research status and limitations of dengue disease burden in China， proposing suggestions for future assessment research on disease burden of dengue.

New bicompartmental model: an application for the production of gases using the in vitro technique / Novo modelo bicompartimental: uma aplicação para a produção de gases pela técnica in vitro

The purpose of this study was to propose a bicompartmental nonlinear model and to identify the best-performing model between the proposed model and the bicompartmental logistic (BL) mode regarding the quality of fit to the curve of cumulative gas production (CGP) using corn silage, sunflower, and their mixtures. Gas production was measured 2, 3, 4, 6, 8, 9, 10, 12, 15, 19, 24, 30, 36, 48, 72, and 96 h after beginning the in vitro fermentation process. The generated data were used to generate the parameters of each model tested using the stats package of the R computational tool version 4.0.4. The mathematical models were subjected to the following selection criteria: the adjusted coefficient of determination (Raj.), residual mean square (RMS), mean absolute deviation (MAD), and Akaike information criterion (AIC). It was demonstrated that the proposed model had better performance with a high Raj., and lower values of RMS, AIC, and MAD than the bicompartmental logistic model for the prediction of the parameters of cumulative gas production (CGP), per to present a superior fit in the set of criteria according to the methodology and conditions in which the present study was developed.(AU)

No presente trabalho, com silagem de milho, girassol e suas misturas, objetivou-se propor um modelo não linear bicompartimental e identificar entre o modelo proposto e Logístico Bicompartimental (LB), aquele que apresenta maior qualidade de ajuste à curva de cinética de produção cumulativa de gases (PCG). A leitura da produção de gás foi realizada nos tempos 2, 3, 4, 6, 8, 9, 10, 12, 15, 19, 24, 30, 36, 48, 72 e 96 horas, após o início do processo de fermentação in vitro. Os dados gerados foram utilizados para geração dos parâmetros de cada modelo testado com auxílio do pacote stats da ferramenta computacional R versão 4.0.4. Os modelos matemáticos foram submetidos aos seguintes critérios de seleção o coeficiente de determinação ajustado (Raj.), quadrado médio do resíduo (QMR), desvio médio absoluto (DMA) e o critério de informação de Akaike (AIC). Foi demonstrado que o modelo proposto teve melhor desempenho com altos Raj., e menores valores de QMR, AIC e DMA, por apresentar um ajustamento superior no conjunto dos critérios em comparação com o modelo logístico bicompartimental para a predição dos parâmetros de produção cumulativa de gases (PCG) de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.(AU)

Brecha en matemáticas según sexo Caso: universitarios de Colombia / Lacuna entre os sexos em matemática. Caso: estudantes universitários colombianos / Gap in math by gender. Case: university students from Colombia

Resumen Se analiza la brecha por sexo en matemáticas (razonamiento cuantitativo) en universitarios de Colombia, con base en los resultados de las pruebas estatales de salida de la educación superior Saber Pro, 2018; incluyendo el factor regional. A partir de una modelación cuantílica y una descomposición Juhn-Murphy-Pierce; se identifica la existencia y persistencia de una brecha por sexo en el área evaluada, y diferencias entre las regiones Andina y Caribe. Se destaca: favorabilidad hacia los hombres; importancia de las características educativas e institucionales; importancia de las matemáticas de secundaria (explican cerca del 25% del diferencial); ampliación de la brecha en los cuartiles más altos; v) heterogeneidad regional de la brecha, ampliada por la interacción sexo-región.

Resumo A diferença de gênero em matemática (raciocínio quantitativo) entre estudantes universitários na Colômbia é analisada, com base nos resultados dos exames de saída do ensino superior estadual Saber Pro 2018, incluindo o fator regional. Com base na modelização de quantis e numa decomposição Juhn-Murphy-Pierce, identificamos a existência e persistência de uma diferença de gênero na área avaliada, bem como diferenças entre as regiões andinas e das Caraíbas. Destacam-se: favorabilidade em relação aos homens; importância das características educacionais e institucionais; importância da matemática secundária (explicando cerca de 25% do diferencial); alargamento da lacuna nos quartis mais altos; e heterogeneidade regional da lacuna, amplificada pela interação gênero-região.

Abstract The paper analyzes the gender gap in mathematics (quantitative reasoning) among Colombian university students, based on the results of the State higher education exit tests Saber Pro, 2018; including the regional factor. Based on a quantile modeling and a Juhn-Murphy-Pierce decomposition, the study identifies the existence and persistence of a gender gap in the evaluated area and differences between the Andean and Caribbean regions. The most remarkable points include: favouring men; importance of educational and institutional characteristics; importance of secondary mathematics (accounting for about 25% of the differential); widening of the gap in the highest quartiles; and regional heterogeneity of the gap, widened by gender-region interaction.

Dificultad en Aritmética en niños con alta inteligencia: ¿efecto de la ansiedad matemática? / Dificuldade em aritmética em crianças com alta inteligência: efeito da ansiedade matemática? / Highly intelligent children with difficulty in arithmetic: an effect of math anxiety?

Ansiedade matemática (AM) é um conjunto de crenças, sintomas físicos e emocionais que algumas pessoas experimentam ao lidar com problemas matemáticos. O estudo objetivou investigar o efeito da AM no desempenho aritmético de crianças com alta inteligência. Participaram do estudo 52 crianças com desempenho inferior no subteste aritmética do TDE e classificação "acima da média" ou "intelectualmente superior" nas Matrizes de Raven. Os resultados demonstraram correlação forte entre inteligência e TDE aritmética (r = 0,82; p < 0,000); e correlações moderadas entre TDE aritmética e QAM-A (r = 0,32; p = 0,02) e QAM-B (r = 0,35; p = 0,01). A análise de regressão linear múltipla demonstrou uma predição de 8% da subescala QAM-A e de 11 % da QAM-B como preditores do desempenho aritmético. A ansiedade matemática interfere no desempenho em aritmética, mesmo em crianças com a inteligência fluída acima do esperado, sugerindo um importante efeito dos mecanismos emocionais.

Ansiedad matemática (AM) es un conjunto de creencias, síntomas físicos y emocionales que algunas personas experimentan al lidiar con problemas matemáticos. El estudio tuvo por objetivo investigar el efecto de la AM en el rendimiento aritmético de niños con alta inteligencia. Participaron del estudio 52 niños con rendimiento inferior en la subprueba aritmética del TDE y clasificación "superior de la media" o "intelectualmente superior" en las Matrices de Raven. Los resultados apuntan fuerte correlación entre inteligencia y TDE aritmética (r = 0,82; p < 0,000); y correlaciones moderadas entre TDE aritmética y QAM-A (r = 0,32; p = 0,02) y QAM-B (r = 0,35; p = 0,01). El análisis de regresión linear múltiple demostró una predicción del 8% de la subescala QAM-A y del 11 % de la QAM-B como predictores del rendimiento aritmético. La ansiedad matemática interfiere en el rendimiento en aritmética, incluso en niños con la inteligencia fluida superior al esperado, sugiriendo un importante efecto de los mecanismos emocionales.

Mathematical anxiety (MA) is a set of beliefs, physical and emotional symptoms that some people experience when dealing with mathematical problems. The study aimed to investigate the effect of MA on the arithmetic performance of children with high intelligence. Fifty-two children with lower performance on the STP arithmetic subtest and classification "above average" or "intellectually superior" in the Raven Matrices participated in the study. The results showed a strong correlation between intelligence and arithmetic EDT (r = 0.82; p < 0.000); and moderate correlations between arithmetic DET and MAQ (r = 0.32; p = 0.02) and MAQ-B (r = 0.35; p = 0.01). Multiple linear regression analysis showed an 8% prediction of the MAQ-A subscale and 11% of the MAQ-B as predictors of arithmetic performance. Mathematical anxiety interferes with arithmetic performance, even in children with higher than expected fluid intelligence, suggesting an important effect of emotional mechanisms.

School and language performance in children born with low birth weight

Abstract Objectives To identify the impact of birth weight on the development of metalinguistic skills and performance in reading, writing, and arithmetic in students aged 6 to 10 years, enrolled from the 1st to the 4th grade of Elementary School in public schools of the metropolitan region of São Paulo. Methods The concurrent cohort included 315 students. Birth weight was the exposure variable, and the outcomes were performance in receptive and expressive language, oral metalinguistic skills, and performance in writing, arithmetic, and reading. The tools employed were the Test of Language Competence (TLC) and the School Performance Test (SPT). Students were grouped into quartiles by birth weight for data analysis (P1: < 2170 g, P2: from 2171 g to 2450 g, P3: from 2451 g to 3150 g, and P4: > 3150 g). Results The authors observed a tendency for the lower performance of the two groups with lower birth weights in listening comprehension and oral expression. The lower-weight group tended to perform poorly compared to the other groups vis-à-vis reading. In the global result of the SPT, worse performance was observed in the students in the first quartile compared to the others (p= 0.019). The multivariate analysis revealed no association between birth weight and results in the tests applied after adjusting for maternal schooling. Conclusions Birth weight can interfere with oral and written language development. However, the determination of these processes occurs in the face of complex interaction that includes sociodemographic factors, especially family support and maternal schooling.

Programa talento matemático mexicano (tamme) - atividades de enriquecimento pa ra alunos de ensino fundamental e médio1 / Mexican mathematical talent program (tamme) - enrichment activities for elementary and high school students

RESUMO Este estudo teve como objetivos identificar estudantes com talento matemático no Ensino Fundamental e no Ensino Médio, no que se refere ao sistema numérico maia e babilônico para o Ensino Fundamental e ao pensamento computacional, com o uso do Scratch, para o Ensino Médio; projetar e implementar um programa de enriquecimento extraescolar com alunos do Ensino Fundamental e do Ensino Médio; estudar a evolução das ideias matemáticas, trabalhadas no programa de enriquecimento extracurricular. O aporte teórico foi baseado no Modelo de Enriquecimento para toda a Escola (School Wide Enrichment Model - SEM). Esse modelo teve origem no Modelo Triádico de Enriquecimento de Renzulli. Os resultados apresentados referem-se às atividades de enriquecimento extracurricular, com numeração babilônica e o sistema numérico maia, e as atividades em ambiente Scratch. Os resultados do estudo mostraram que ambos os grupos de idade foram capazes de abordar as atividades propostas e desenvolveram experiências de aprendizado que lhes deram habilidades para resolver problemas matemáticos, tanto no ambiente a lápis e papel quanto na linguagem de programação Scratch. O grupo de alunos do Ensino Fundamental representou números no sistema maia e babilônico e realizou operações aritméticas; dessa forma, este trabalho os ajudou a compreender o sistema posicional; e os estudantes do Ensino Médio aprenderam a fazer animações de dois personagens (sprites) e aprenderam a programar.

ABSTRACT The study aimed to identify students with mathematical talent in Elementary and High School, with regard to the Mayan and Babylonian numerical system for Elementary School and computational thinking, with the use of Scratch for High School; to design and implement an out-of-school enrichment program with Elementary and High School students; to study the evolution of mathematical ideas, worked on in the extracurricular enrichment program. Theoretical support was based on the School Wide Enrichment Model (SEM). This model is originated from Renzulli's Triadic Enrichment Model. The results presented refer to extracurricular enrichment activities, with Babylonian numerals and the Mayan numerical system, and activities in the Scratch environment. The results of the study showed that both age groups were able to approach the proposed activities and developed learning experiences that gave them skills to solve mathematical problems, both in the pencil and paper environment and in the Scratch programming language. The group of Elementary School students represented numbers in the Mayan and Babylonian system and performed arithmetic operations; in this way, this work helped them to understand the positional system; and the High School students learned to make animations of two characters (sprites) and learned how to program.

Mathematical modelling approach of the study of Ebola virus disease transmission dynamics in a developing country

Background: Ebola Virus causes disease both in human and non-human primatesespecially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date. Materials and Methods:We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus ina population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease-endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle's Invariant principle.Results: The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.Conclusions: Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.

Memoria de trabajo y planificación como predictores de las competencias matemáticas tempranas

Introducción: La relación entre funciones ejecutivas y habilidades matemáticas ha sido ampliamente estudiada. Sin embargo, no existe consenso respecto de la contribución específica de la memoria de trabajo y la planificación en el desarrollo de competencias matemáticas tempranas. El objetivo de este estudio fue determinar la capacidad predictiva de estos dos dominios ejecutivos sobre las competencias matemáticas de preescolares. Método: Se implementó un diseño no experimental ex post facto, con una muestra de 104 niños/as chilenos/as. La evaluación de sus funciones ejecutivas se realizó con la tarea "inversión de números" de la Batería IV Woodcock-Muñoz para evaluar la memoria de trabajo verbal, la subprueba "Torpo, el topo torpe" del Test de Evaluación Neuropsicológica Infantil (TENI) para evaluar la memoria de trabajo visoespacial y el Test de Laberintos de Porteus para evaluar la planificación. Con el fin de evaluar las habilidades matemáticas se utilizó el Test de Evaluación Matemática Temprana Utrecht (TEMT-U), versión chilena. Se realizaron análisis descriptivos, correlaciones y modelos de regresión múltiple. Resultados: La memoria de trabajo verbal seguida por la memoria de trabajo visoespacial y la planificación fueron los mejores predictores de las competencias matemáticas de los/as niños/as. Conclusiones: Estos resultados sugieren que estas funciones ejecutivas desempeñan un papel clave en el aprendizaje de las matemáticas y aportan información específica a las/os educadoras/es para que puedan planificar sus estrategias de enseñanza en función de las demandas cognitivas que requiere cada habilidad matemática, lo que puede ser una vía potencial para promover mejores logros de aprendizaje en esta importante disciplina.

Introduction: The relationship between executive functions and mathematical skills has been extensively studied. However, there is no consensus regarding the specific contribution of working memory and planning in the development of early mathematical skills. The aim of this study was to determine the predictive capacity of these two executive domains on preschoolers' mathematical skills. Method: A non-experimental ex post facto design was implemented with a sample of 104 Chilean children. The evaluation of their executive functions was performed with the "number inversion" task of the Woodcock-Muñoz IV Battery to assess verbal working memory, the "Clumsy Mole the Clumsy Mole" subtest of the TENI Child Neuropsychological Evaluation Test to assess visuospatial working memory, and the Porteus Maze Test to assess planning. To assess mathematical skills, the Test de Evaluación Matemática Temprana Utretch TEMT-U, Chilean version, was used. Descriptive analyses, correlations and multiple regression models were performed. Results: Verbal working memory followed by visuospatial working memory and planning were the best predictors of children's mathematical skills. Conclusions: These results suggest that these executive functions play a key role in mathematics learning and provide specific information to educators so that they can plan their teaching strategies according to the cognitive demands required by each mathematical skill, which may be a potential way to promote better learning achievements in this important discipline.

Effect of Tobacco Taxation on Smoking Prevalence and Smoking-Attributable Deaths in India

Background: Higher taxes are the single most effective way to encourage tobacco users to quit tobacco use and prevent youth from initiation. Objectives: The present study aims to estimate the effect of raising the tax on smoked tobacco products on its consumption and smoking‑attributable deaths in India. Materials and Methods: A mathematical model was developed which used the projected population of India, taxation rates on smoked tobacco products, smoking prevalence, and price elasticity of demand of cigarette and bidi from 2017 to 2025. Four scenarios of tax increment (0%, 25%, 50%, and 100%) on smoked tobacco products were created which were modeled to calculate smoking prevalence and smoking‑attributable deaths due to respiratory diseases, heart diseases, stroke tuberculosis, and cancer in country till 2025. Results: A relative decrease of 6.2% in the prevalence of smoking was observed between the existing tax rates and its increment to 100% over the last increment of 6%. Similarly, smoking‑attributable deaths (SAD) decreased by 6.04% on increasing the tax rates to 100% of the existing taxation rates. There has been a steady increase in SAD in scenario 1 which decreases effectively in scenario 4, which in turn leads to the saving of around 33,000 lives due to tobacco‑related diseases by 2025. Conclusion: The consumption of cigarettes and bidis can be reduced by raising the price of these products. The model will help policymakers in deciding to fix the tax and ultimately the price of cigarettes and bidi to reduce its consumption and smoking‑attributable mortality.

Study on Effect of Cognitive Intervention on Mathematical Difficulties of Children in Telangana.

The focus of this article is intervention for primary school students with mathematics difficulties at third grade students. Government schools from Telangana. GLAD (Grade level assessment device) skills test were used to assess their mathematical difficulties in primary school students. Total 100 sample was selected from two different government schools. 6 months' cognitive intervention programmes were implemented to enhance the mathematical performance of primary school students. Paired t-test was used for analysis. The study results revealed that there was no significant difference between pre-test score of control and experimental group of primary school student. Intervention results showed that there was significant difference between post test scores of control and experimental group of primary school students

Necesidad de superación en modelos matemáticos de epidemiología / Need for improvement in mathematical models of epidemiology

RESUMEN Introducción: En Cuba, se formulan modelos matemáticos, pero no están contemplados para la superación de posgrado ni en pregrado. Aunque los modelos idealizan la realidad, permiten, de manera sencilla, hacer predicciones sobre el comportamiento futuro de una enfermedad y tomar las medidas necesarias. Objetivo: Identificar necesidad de superación en modelos matemáticos de epidemiología. Métodos: Se utilizó un modelo estocástico presente en el paquete EpiModel del programa R. Se simularon tres situaciones diferentes, la primera con violaciones del distanciamiento y la higiene general, la segunda con mejoras en estos dos aspectos, más la inmunidad lograda al 70 % de la población por vacunación y la tercera con mejoras notables en higiene y distanciamiento junto a la vacunación. Se calculó, además, el comportamiento del número reproductivo con el paquete earlyR a partir de la incidencia. Resultados: Se valoró como las trayectorias con los modelos estocásticos tienen más variabilidad y como la reducción de contactos aplana la curva. Se evaluó la dispersión de la epidemia en situaciones de violaciones de la prevención y en otras donde hay prevención y además vacunación. La línea roja de cada modelo varía según las circunstancias, claramente en los casos de violaciones de distanciamiento e higiene esta curva se amplia y se aplana en el caso contrario. Conclusiones: Se identificaron suficientes evidencias sobre el uso y la necesidad de modelos matemáticos para apoyar la toma de decisiones en la epidemiología, se identificó la necesidad de superación en posgrado sobre la teoría de epidemias, que puede extenderse a pregrado.

ABSTRACT Introduction: In Cuba mathematical models are formulated, but they are not contemplated for passing graduate or undergraduate degrees. Objective: To identify the need to work with mathematical simulations. Methods: A stochastic model present in the EpiModel package of the R program was used. Three different situations were simulated, the first with violations of distancing and general hygiene, the second with improvements in these two aspects, plus the immunity achieved to 70% of the population by vaccination and the third with notable improvements in hygiene and distancing together with vaccination. The behavior of the reproductive number with the early R package was also calculated from the incidence. Results: It is assessed how the trajectories with the stochastic models have more variability and how the reduction of contacts flattens the curve. The spread of the epidemic is valued in situations of prevention violations and in others where there is prevention and also vaccination. Conclusions: Sufficient evidence is presented on the use and need of mathematical models to support decision-making in epidemiology, the need to improve the theory of epidemics in graduate school is identified, which can be extended to undergraduate.

Optimization and Quest of HPMC loaded Stavudine Controlled Release Dosage Development by Central Composite Design utilizing Reduced Factorial Screening Technique

Abstract The current research focused on screening and finding the significant independent variables in stavudine loaded tablet, followed by optimizing the best formulation using central composite design. The objective of the study to develop stavudine loaded controlled release tablet utilizing reduced factorial design, followed by optimization technique as well as characterization of prepared tablets. Preliminary trial batches were prepared using different grades of hydroxypropyl methylcellulose. The resolution-IV reduced factorial design was selected to screen the significant independent variables in the dosage form design. A total number of eight runs were prepared and responses were recorded. The signified factors identified by half-normal and Pareto chart. The prepared tablets are evaluated for various physiochemical characterizations. Three dependent responses such as hardness, dissolution at 6 hour and 12 hours are considered in optimization process. Later on, drug-polymer interaction study was carried out. The principal of the study design based on finding the best formulation with prefixed set parameter values utilizing the concept of screening technique. It observed that HPMC K15M (57.18 %), HPMC K100 (66.32 %) and PVP K30 (7.97 %) as best composition in a formulation batch would fulfill the predetermined parameter with specific values.

Number sense: the mediating effect between nonverbal intelligence and children's mathematical performance

The study explored the mediating effect of number sense between nonverbal intelligence and children's mathematical performance. The sample consisted of 131 pupils in Shaoxing City of China from grades 1, 3, and 5. The students completed measures of nonverbal intelligence, number sense, basic arithmetic ability, mathematical performance, rapid automatized naming, and working memory. Results show that although all variables significantly relate with each other (all p < .01), only nonverbal intelligence, number sense, and basic arithmetic ability significantly affect children's mathematical performance (all p < .01). According to multiple-mediation model, nonverbal intelligence significantly predicts children's mathematical performance through number sense and basic arithmetic ability. These findings suggest that domain-specific mathematical skills play a prominent role in children's mathematical performance in primary school, rather than domain-general cognitive functions. Educators should pay attention to develop children's number sense in order to improve children's mathematical ability. (AU)

Caracterización de viajeros confirmados a la COVID-19, según número reproductivo básico, provincia Camagüey

Introducción: Las enfermedades importadas constituyen un problema de salud para el individuo y para la población general. Debido al peligro sanitario que conlleva los viajes internacionales y el riesgo de introducción de enfermedades en la provincia. Objetivo: Caracterizar los viajeros notificados a la COVID-19 con fuente de infección en el extranjero según número reproductivo básico en la provincia Camagüey. Métodos: Se realizó un estudio observacional, descriptivo, transversal. El universo de estudio estuvo constituido por todos los viajeros notificados con la COVID-19 en la provincia que cumplieron con los criterios de inclusión y exclusión. Resultados: El escenario de intervención del 70 % de los notificados fue los centros de aislamiento para viajeros, predominaron los procedentes de Venezuela y el mes de marzo fue el de mayor incidencia, el 100 % procedían de áreas de transmisión de la enfermedad, el 55 % se encontraban asintomáticos en el momento del diagnóstico y el número reproductivo básico fue menor que uno en los municipios de destino y a nivel provincial. Conclusiones: Los centros de aislamientos para viajeros disminuyó el riesgo de dispersión de la enfermedad en los municipios de destino, los viajeros notificados tenían alta probabilidad de enfermar por proceder de países con transmisión de la enfermedad y los asintomáticos complejizaron el escenario de actuación.

Introduction: The cared illnesses constitute an important problem of health for the individual and for the general population. Due to the sanitary danger that bears the international trips and the risk of introduction of illnesses cared in the county, an investigation was carried out. Objective: To characterize the travelers notified to the COVID-19 with infection source abroad according to basic reproductive number in Camagüey's province. Methods: A observational, descriptive, traverse study was carried out. The study universe was constituted by all the travelers notified with the COVID-19 in the county that fulfilled the inclusion approaches and exclusion. Results: The scenario of intervention of 70% of those notified was the isolation centers for travelers, prevailing those coming from Venezuela and the month of March was that of more incidence, 100% came from areas of transmission of the illness, 55% was asymptomatic in the moment of the diagnosis and the basic reproductive number was smaller than one in the destination municipalities and at provincial level. Conclusions: The centers of isolations for travelers diminished the risk of dispersion of the illness in the destination municipalities, the notified travelers had high probability of making sick to come from countries with transmission of the illness and the asymptomatic ones worsen the performance scenario.