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.

The impact of the COVID-19 pandemic on people living with HIV in Zimbabwe

The COVID-19 pandemic was reported from March 2020 in Zimbabwe. COVID-19 containment measures which included repeated lockdowns have disrupted community interactions, reduced working hours, restricted travel and restricted HIV services for people living with HIV (PLHIV), among others. The study adopted a cross-sectional design. Both qualitative and quantitative data were collected in all the 10 provinces and analysed. A sample size of 480 was calculated for the cross-sectional survey. Secondary data on HIV early warning indicators from 2018 to 2021 were extracted from 20 randomly selected health facilities and used for modelling. Mathematical modelling was conducted to assess the impact of COVID-19 on PLHIV. AIDS-related deaths increased from 20 100 in 2019 to 22 200 in 2020. In addition, there were significant years of life lost (yLLs) from premature mortality and years of life lost due to disability (yLDs) from COVID-19. Prevalence of COVID-19 among PLHIV was 4%. COVID-19 vaccination coverage was 64%, which is higher than the national average of 42%. Stress and breach of confidentiality as ARV medicines were given out in open spaces and fear of contracting COVID-19 were the perceived psychological issues. COVID-19 disrupted HIV service provision, increased AIDS-related deaths and caused psychological challenges

Modeling transmission dynamics of severe acute respiratory syndrome coronavirus 2 in São Paulo, Brazil

Abstract INTRODUCTION Severe acute respiratory syndrome coronavirus 2 has been transmitted to more than 200 countries, with 92.5 million cases and 1,981,678 deaths. METHODS This study applied a mathematical model to estimate the increase in the number of cases in São Paulo state, Brazil during four epidemic periods and the subsequent 300 days. We used different types of dynamic transmission models to measure the effects of social distancing interventions, based on local contact patterns. Specifically, we used a model that incorporated multiple transmission pathways and an environmental class that represented the pathogen concentration in the environmental reservoir and also considered the time that an individual may sustain a latent infection before becoming actively infectious. Thus, this model allowed us to show how the individual quarantine and active monitoring of contacts can influence the model parameters and change the rate of exposure of susceptible individuals to those who are infected. RESULTS The estimated basic reproductive number, R o , was 3.59 (95% confidence interval [CI]: 3.48 - 3.72). The mathematical model data prediction coincided with the real data mainly when the social distancing measures were respected. However, a lack of social distancing measures caused a significant increase in the number of infected individuals. Thus, if social distancing measures are not respected, we estimated a difference of at least 100,000 cases over the next 300 days. CONCLUSIONS: Although the predictive capacity of this model was limited by the accuracy of the available data, our results showed that social distancing is currently the best non-pharmacological measure.

Comparison between Thin-Layer Models and Non-Traditional Methods in the Modelling of Drying Kinetics of Crustacean Wastes

Abstract This research aims to compare the classical thin-layer models, stepwise fit regression method (SRG) and artificial neural networks (ANN) in the modelling of drying kinetics of shrimp shell and crab exoskeleton. Thus, drying curves were obtained using a convective dryer (3.0 m/s) at temperatures of 30.45 and 60oC. The results showed a decreasing tendency for the drying time as the temperature increased for both materials. Drying curves modelling of both materials showed fitted results with R 2 adj >0.998 and MRE<13.128% for some thin-layer models. On the other hand, by SRG a simple model could be obtained as a function of time and temperature, with the greatest accuracy being found in the modelling of experimental data of crab exoskeleton, with MRE<10.149%. Finally, the ANNs were employed successfully in the modelling of drying kinetics, showing high prediction quality with the trained recurrent ANN models.

Fractalidad en un patrón de cristalización de moco cervical humano obtenido en período periovulatorio / Fractality in a pattern of crystallization of human cervical mucus obtained at periovulatory period

Introducción: La secreción cervical cumple una función importante en el proceso reproductivo humano y algunas sus características (e.g., el cristalizar) cambian dependiendo de las variaciones en los niveles de hormonas esteroidales sexuales. Objetivo: Reportar la fractalidad observada en un patrón de cristalización de moco cervical humano. Métodos: El moco fue obtenido de una paciente en período periovulatorio. La imagen de un patrón cristalino de moco cervical fue transformada a blanco y negro y analizada mediante Fractalyse v. 2.4, el cual determina la dimensión fractal (DF) para cada imagen estudiada. Se analizaron tres zonas para la imagen seleccionada. Resultados: Se encontró, para la Zona 1, DF (± desviación estándar) = 1,36 ± 0,02 (r² = 0,9985); para la Zona 2, DF = 1,35 ± 0,02 (r² = 0,9979); y para la Zona 3, DF = 1,36 ± 0,03 (r² = 0,9958). Las DF encontradas para las zonas estudiadas fueron estadísticamente iguales entre sí. Conclusiones: El moco cervical humano en período periovulatorio puede seguir un patrón de cristalización tipo fractal, especialmente en lo referente a la semejanza de sus componentes estructurales (criterio de autosimilitud) (AU)

Introduction: Cervical secretion plays an important role in the human reproductive process and its characteristics (e.g., crystallization) change depending on variations in the levels of sex steroid hormones. Objective: The purpose of this brief communication is to report the fractality observed in a crystallization pattern of human cervical mucus. Methods: Mucus samples were obtained from a patient in the periovulatory period and an image of the crystalline pattern of cervical mucus was transformed to black and white and analysed by Fractalyse v. 2.4, which determines the fractal dimension (FD) for each studied image. Three zones were analysed for the selected image. Results: It was found that, for Zone 1, FD (± standard deviation) = 1.36 ± 0.02 (r² = 0.9985); for Zone 2, FD = 1.35 ± 0.02 (r² = 0.9979); and for Zone 3, FD = 1.36 ± 0.03 (r² = 0.9958). Zones studied were statistically equal to each other regarding their FD. Conclusions: Human cervical mucus obtained at periovulatory period can follow a fractal-like pattern of crystallization, especially in relation to the similarity of its structural components (criterion of self-similarity) (AU)

Evolutionary dynamics models in biometrical genetics supports QTL × environment interactions

The process of development of quantitative trait locus (QTL) involves interactions between many factors, both environmental and genetic, in which many genes interact often in no additive pathways together and with environment. Integration of the mathematical, statistical and biological aspects of these subjects has made important and interesting results. In this review, mathematical methods offered to study the QTL × environment interactions. The topic is circumscribed, going from basic selection equations to models of evolution of QTLs. Discrete and continuous time mathematical models and subsequently, QTL modelling were introduced with and without environmental interactions. The mathematical models derived here showed that the gradients of mean fitness which have revealed in studies by many researchers had a basic role in mathematical genetics, evolutionary aspects of biometrical genetics and QTL analysis. QTL × environment interactions were studied mathematically including fitness components too. It was revealed that QTL × environment interactions in fitness could generate a balancing selection. Also, QTL analysis could be used to calculate the geometry of the phenotype landscape. In this paper, models applied in biometrical genetics corresponds to QTL analysis and matched with results from other researchers. The originality of this synthesis is the evolutionary modelling of QTL × environment interactions which can be used to investigate the extinction or stability of a population. Also to emphasize that although some scientific subjects like Brownian motion, quantum mechanics, general relativity, differential geometry, and evolutionarybiometrical genetics were apparently different subjects, but the mathematical models were the backbone of these branches of science. This implies that such matters in nature have probably common and elegant basis. The perspective of the subject of this paper in future will be a new and interesting branch of interdisciplinary science.

Plumas em escoamento uniforme com estratificação de duas camadas / Plumes in uniform flow with two-layer stratification

RESUMO Plumas ocorrem quando um fluido é descarregado em outro fluido com densidade diferente, como poluentes na atmosfera. Neste trabalho, desenvolveu-se um estudo experimental em um tanque de água e modelagem matemática usando a abordagem integral com o intuito de investigar o escoamento gerado por plumas salinas em escoamento uniforme e com estratificação de duas camadas. Os resultados indicaram que a altura da camada superior (menos densa) aumentou com a vazão de retirada da camada inferior e diminuiu com o fluxo de empuxo da pluma, corroborando os resultados disponíveis na literatura para sistemas alimentados por fontes pontuais (não uniformes). Após ajuste de parâmetros presentes na teoria clássica para plumas turbulentas, foi possível prever a altura da interface com desvios máximos de ±8% e coeficiente de Nash-Sutcliffe de 0,98. Isso indica que o escoamento uniforme não afetou significativamente a hidrodinâmica das plumas em comparação a estudos anteriores. Por outro lado, diferentemente dos sistemas alimentados por fontes pontuais, as linhas de fluxo obtidas por meio da injeção de corante no escoamento uniforme seguiram padrão de escoamento potencial, com toda a vazão sendo direcionada para a pluma e não havendo, portanto, mistura na interface entre as duas camadas. Dessa forma, partindo do princípio de conservação de massa, foram propostas equações para gerar as linhas de fluxo ao redor das plumas, as quais foram confirmadas com os dados experimentais. Finalmente, foram apresentadas aplicações práticas do modelo proposto em sistemas de ventilação natural em edifícios e descarga de poluentes na atmosfera sob condição de inversão térmica.

ABSTRACT Plumes occur when a fluid is discharged into another fluid with different density, such as pollutants in the atmosphere. In this work, an experimental study was carried out in a water tank and a mathematical modelling using the integral approach was performed to investigate the flow generated by saline plumes in uniform flow with two-layer stratification. The results indicated that the upper layer's height (less dense) increased with the outflow from the lower layer, and decreased with the buoyancy flux of the plume, confirming the results available in the literature for systems supplied by point sources (non-uniform sources). After fitting the parameters of the classical theory for turbulent plumes, it was possible to predict the interface's height with a maximum deviation of ±8%, and a Nash-Sutcliffe coefficient of 0.98. This indicates that the uniform flow did not affect significantly the plumes' hydrodynamics compared to previous studies. On the other hand, unlike the systems supplied by point sources, the streamlines obtained through the injection of dye into the uniform flow followed a potential flow pattern, with all the flow being directed to the plume, therefore not mixing at the interface between the two layers. Thus, based on the principle of mass conservation, equations were proposed to generate the streamlines around the plumes, which were validated with the experimental data. Finally, practical applications of the proposed model in natural ventilation in buildings and pollutant discharges in the atmosphere were presented.

Desestratificação de reservatórios por meio de aeração artificial / Reservoir destratification via artificial aeration

RESUMO No presente trabalho, avaliou-se em escala de laboratório e por meio de modelagem matemática o processo de desestratificação da coluna d'água usando aeração por ar difuso. Foram identificados dois padrões de escoamento: um regime de pluma, no qual o escoamento induzido pelas bolhas penetra na interface entre as duas camadas de diferentes densidades e ascende à superfície da água; e um regime de fonte, no qual o escoamento penetra parcialmente na interface e colapsa para formar uma camada de densidade intermediária. Os resultados experimentais mostraram que o regime de pluma promove mistura mais rápida da camada superior (epilímnio) do que o regime de fonte. Os tempos de mistura da camada inferior (hipolímnio), entretanto, foram praticamente os mesmos para os dois regimes. Após o ajuste de parâmetros do modelo que descreve a incorporação do fluido ambiente na pluma e na fonte, pôde-se simular o processo de desestratificação da coluna d'água com boa aderência aos dados experimentais obtidos nesta pesquisa e em trabalhos anteriores. Por fim, o modelo validado foi aplicado para a simulação do impacto de diferentes vazões de ar na evolução temporal do processo de desestratificação de reservatórios (escala real), sendo discutidos os custos com energia elétrica para bombeamento e as possíveis implicações na qualidade da água desses corpos hídricos.

ABSTRACT In the present work, the destratification process of water column using diffused-aeration was evaluated at laboratorial scale by mathematical modelling. Two flow patterns were identified, a plume regime, in which the bubble-induced flow penetrates the interface (density gradient) and rises to the water surface, and a fountain regime, in which the flow partially penetrates the interface and collapses to form an intermediate-density layer. The experimental results showed that the plume regime promotes a faster mixing of the upper layer (epilimnion) than the fountain regime. However, the mixing times of the lower layer (hypolimnion) were practically the same for both regimes. After adjusting the parameters that describe the entrainment of the ambient fluid into the plume and fountain, it was possible to simulate the process of water column destratification with good adherence to the experimental data obtained in this research and previous studies. Finally, the validated model was applied to simulate the impact of different airflow rates on the reservoir destratification process' (real scale) time evolution, and the possible implications for the water quality of these water bodies were discussed.

Dynamic Analysis of the Temperature and the Concentration Profiles of an Industrial Rotary Kiln Used in Clinker Production

ABSTRACT Cement is one of the most used building materials in the world. The process of cement production involves numerous and complex reactions that occur under different temperatures. Thus, there is great interest in the optimization of cement manufacturing. Clinker production is one of the main steps of cement production and it occurs inside the kiln. In this paper, the dry process of clinker production is analysed in a rotary kiln that operates in counter flow. The main phenomena involved in clinker production is as follows: free residual water evaporation of raw material, decomposition of magnesium carbonate, decarbonation, formation of C3A and C4AF, formation of dicalcium silicate, and formation of tricalcium silicate. The main objective of this study was to propose a mathematical model that realistically describes the temperature profile and the concentration of clinker components in a real rotary kiln. In addition, the influence of different speeds of inlet gas and solids in the system was analysed. The mathematical model is composed of partial differential equations. The model was implemented in Mathcad (available at CCA/UFES) and solved using industrial input data. The proposal model is satisfactory to describe the temperature and concentration profiles of a real rotary kiln.

Modelos matemáticos en memoria de reconocimiento de palabras: un análisis roc multinivel / Mathematical Models in Word Recognition Memory: A Multilevel Analysis Roc

En esta investigación se muestran los modelos más eficientes desde el punto de vista experimental y formal para la evaluación de la memoria de reconocimiento de ítemspalabras: En primer lugar se muestra un modelo matemático general que subyace a las diferentes formas de registro de datos. En segundo lugar se controla experimentalmente la elección, organización y tiempos de presentación del estímulo (ítems-palabras en castellano). En tercer lugar se aplica un análisis multinivel para modelar todos los niveles de respuesta de los participantes en las pruebas de memoria de reconocimiento. En cuarto lugar, se evalúa mediante escalas de estimación (EE) y mediante las características operativas del receptor (ROC) propias de la teoría de la detección de señales (TDS) y de los modelos de umbral. Los resultados concuerdan principalmente con un modelo de detección de señales, cuando los estímulos son palabras de frecuencia alta, y con un modelo de umbral (o de diferente varianza) cuando los estímulos son palabras de clase abierta; mientras que las palabras de frecuencia baja ocupan un lugar intermedio, situado entre la TDS y los modelos de umbral.

In this research we show the best efficient models in the evaluation of the recognition memory: First, a general mathematical model which underlies different data records ways. Second the election, organization and the presentation time of the stimulus is controlled experimentally. Third, we show the multilevel analysis for the rating scales, and a ROC and z-ROC distribution for the discrimination between TDS models and the threshold models. The results agree mainly with a TDS model when the stimuli are high frequency words, a model of threshold (or unequalvariance) when the stimuli are open class words, whereas the low frequency words occupy an intermediate place located between the TDS model and the threshold model.

In vivo NMR study of yeast fermentative metabolism in the presence of ferric irons.

Mathematical modelling analysis of experimental data, obtained with in vivo NMR spectroscopy and 13C-labelled substrates, allowed us to describe how the fermentative metabolism in Saccharomyces cerevisiae, taken as eukaryotic cell model, is influenced by stress factors. Experiments on cellular cultures subject to increasing concentrations of ferric ions were conducted in order to study the effect of oxidative stress on the dynamics of the fermentative process. The developed mathematical model was able to simulate the cellular activity, the metabolic yield and the main metabolic fluxes occurring during fermentation and to describe how these are modulated by the presence of ferric ions.

Correlación entre modelos in vitro, in situ e in vivo en estudios de absorción: [revisión] / In vitro, in situ and in vivo correlations in drug absorption: [review]

Predecir la magnitud y la velocidad de absorción de una sustancia es crucial en el diseño de medicamentos. En este campo se han empleado distintas metodologías, como modelos in vitro o ensayos in situ o in vivo en animales. Este trabajo analiza modelos matemáticos empleados para estudiar la absorción intestinal y analizar la influencia de tensioactivos en la permeabilidad intestinal; predecir la fracción de dosis absorbida; caracterizar parámetros de absorción pasiva y activa; y establecer correlaciones entre parámetros obtenidos in vitro e in situ. Cuanto más complejo es el modelo tanto mejor se correlaciona con los valores en humanos, pero resultan más difíciles de implementar. Los modelos in vitro resultan bastante adecuados para predecir la absorción cuando se produce por difusión pasiva, pero deficitarios cuando se produce por transporte activo. Se pone de manifiesto la necesidad de continuar desarrollando modelos que permitan el escalado a humanos...

Predicting drug rate and extent from the gastrointestinal tract is a key step in the process of new drug design and development. To predict oral absorption different approaches, like in vitro methods or in situ or in vivo animal experiments, have been used. We will analyse some of the mathematical models that have been applied: (a) to study intestinal drug absorption and the influence of surfactants on intestinal permeability, (b) to predict oral fraction absorbed, (c) to characterize active and passive transport parameters, and (d) correlations between in vitro and in situ results. More complex models lead to better correlations with human values, but these systems have a lower throughput, so there is a need to develop models that allow scaling up from the in vitro data. In vitro systems perform well for estimating passive diffusion absorption but more research is necessary with regard to carrier-mediated absorption processes...