On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative

This note is concerned with the convergence of a finite difference scheme to the solution of a second order ordinary differential equation with the right-hand-side nonlinearly dependent on the first derivative. By defining stability as the linear growth of the elements of the inverse of a certain matrix and combining this with consistency, convergence is demonstrated. This stability concept is then interpreted in terms of a root condition

Surface tension implementation for Gensmac 2D

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension

Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil

São Paulo is the most populous state in Brazil, home to around 22% of the country’s population. The total number of Covid-19-infected people in São Paulo has reached more than 1 million, while its total death toll stands at 25% of all the country’s fatalities. Joining the Brazilian academia efforts in the fight against Covid-19, in this paper we describe a unified framework for monitoring and forecasting the Covid-19 progress in the state of São Paulo. More specifically, a freely available, online platform to collect and exploit Covid-19 time-series data is presented, supporting decision-makers while still allowing the general public to interact with data from different regions of the state. Moreover, a novel forecasting data-driven method has also been proposed, by combining the so-called Susceptible-Infectious-Recovered-Deceased model with machine learning strategies to better fit the mathematical model’s coefficients for predicting Infections, Recoveries, Deaths, and Viral Reproduction Numbers. We show that the obtained predictor is capable of dealing with badly conditioned data samples while still delivering accurate 10-day predictions. Our integrated computational system can be used for guiding government actions mainly in two basic aspects: real-time data assessment and dynamic predictions of Covid-19 curves for different regions of the state. We extend our analysis and investigation to inspect the virus spreading in Brazil in its regions. Finally, experiments involving the Covid-19 advance in other countries are also given

Towards Providing Effective Data-Driven Responses to Predict the Covid-19 in São Paulo and Brazil

São Paulo is the most populous state in Brazil, home to around 22% of the country’s population. The total number of Covid-19-infected people in São Paulo has reached more than 1 million, while its total death toll stands at 25% of all the country’s fatalities. Joining the Brazilian academia efforts in the fight against Covid-19, in this paper we describe a unified framework for monitoring and forecasting the Covid-19 progress in the state of São Paulo. More specifically, a freely available, online platform to collect and exploit Covid-19 time-series data is presented, supporting decision-makers while still allowing the general public to interact with data from different regions of the state. Moreover, a novel forecasting data-driven method has also been proposed, by combining the so-called Susceptible-Infectious-Recovered-Deceased model with machine learning strategies to better fit the mathematical model’s coefficients for predicting Infections, Recoveries, Deaths, and Viral Reproduction Numbers. We show that the obtained predictor is capable of dealing with badly conditioned data samples while still delivering accurate 10-day predictions. Our integrated computational system can be used for guiding government actions mainly in two basic aspects: real-time data assessment and dynamic predictions of Covid-19 curves for different regions of the state. We extend our analysis and investigation to inspect the virus spreading in Brazil in its regions. Finally, experiments involving the Covid-19 advance in other countries are also given

Risk Factors Associated with Mortality in Hospitalized Patients with COVID-19 during the Omicron Wave in Brazil

Considering the imminence of new SARS-CoV-2 variants and COVID-19 vaccine availability, it is essential to understand the impact of the disease on the most vulnerable groups and those at risk of death from the disease. To this end, the odds ratio (OR) for mortality and hospitalization was calculated for different groups of patients by applying an adjusted logistic regression model based on the following variables of interest: gender, booster vaccination, age group, and comorbidity occurrence. A massive number of data were extracted and compiled from official Brazilian government resources, which include all reported cases of hospitalizations and deaths associated with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Brazil during the “wave” of the Omicron variant (BA.1 substrain). Males (1.242; 95% CI 1.196–1.290) aged 60–79 (3.348; 95% CI 3.050–3.674) and 80 years or older (5.453; 95% CI 4.966–5.989), and hospitalized patients with comorbidities (1.418; 95% CI 1.355–1.483), were more likely to die. There was a reduction in the risk of death (0.907; 95% CI 0.866–0.951) among patients who had received the third dose of the anti-SARS-CoV-2 vaccine (booster). Additionally, this big data investigation has found statistical evidence that vaccination can support mitigation plans concerning the current scenario of COVID-19 in Brazil since the Omicron variant and its substrains are now prevalent across the entire country

On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Eneström–Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K,L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)

Three-dimensional fluid–structure interaction simulation of the Wheatley aortic valve

Valvular heart diseases (such as stenosis and regurgitation) are recognized as a rapidly growing cause of global deaths and major contributors to disability. The most effective treatment for these pathologies is the replacement of the natural valve with a prosthetic one. Our work considers an innovative design for prosthetic aortic valves that combines the reliability and durability of artificial valves with the flexibility of tissue valves. It consists of a rigid support and three polymer leaflets which can be cut from an extruded flat sheet, and is referred to hereafter as the Wheatley aortic valve (WAV). As a first step towards the understanding of the mechanical behavior of the WAV, we report here on the implementation of a numerical model built with the ICFD multi-physics solver of the LS-DYNA software. The model is calibrated and validated using data from a basic pulsatile-flow experiment in a water-filled straight tube. Sensitivity to model parameters (contact parameters, mesh size, etc.) and to design parameters (height, material constants) is studied. The numerical data allow us to describe the leaflet motion and the liquid flow in great detail, and to investigate the possible failure modes in cases of unfavorable operational conditions (in particular, if the leaflet height is inadequate). In future work the numerical model developed here will be used to assess the thrombogenic properties of the valve under physiological conditions