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International audience; In March 2020, the World Health Organization (WHO) defined the outbreak of COVID-19 disease, caused by the SARS-CoV-2 virus, like a pandemic. In the meantime, the first cases of COVID-19 in Brazil were identified. Despite the start of the vaccination campaign in Brazil in January 2021 and in several other countries, the demand for immunizers is still much higher than the supply of doses. Thus, the pandemic should still be a reality for a long time, requiring actions of surveillance, mitigation, or even suppression of the cycle of transmission of the disease. Mathematical-computational models are important tools for the analysis and diagnosis of the pandemic, which can indicate how to prevent new outbreaks or how to control current ones. Such models can also help to understand qualitative and quantitative characteristics of the propagation process of COVID-19, establishing cause and effect relationships that are vital to guide decision making. Epidemiological data record the history of the pandemic's evolution since its beginnings, encapsulating, among many characteristics, the effects of accelerating or reducing the spread of contagion due to the change in the social behavior of the population of interest. Although these data are subject to the effects of underreporting and delay, there is already a significant amount of spatio-temporal information accumulated in them (12 months of evolution, in all Brazilian cities). Thus, such data emerge as an important source of information about the dynamics of COVID-19, which can be explored (without ad hoc considerations) via machine / artificial intelligence learning techniques, with a view to extracting coherent structures/patterns that reveal relevant characteristics about the spread of the disease in Brazilian soil. This work proposes to develop a study of the spatial-temporal dynamics of COVID-19 in Brazilian states, using models based purely on data, ie, without any ad hoc hypothesis, constructed with the aid of two state-of-the-art techniques in statistical learning, they are: (i) Dynamic Mode Decomposition (DMD), which in some sense combines dimension reduction (principal component analysis) and spectral content analysis (Fourier transform) to extract coherent patterns in spatiotemporal data; (ii) Sparse Identification of Nonlinear Dynamics (SINDy), which seeks to reconstruct in a non-parametric way the law of evolution associated with data, imposing a sparse representation (which facilitates interpretation) to the function dictionary that generates the identified equations. COVID-19 data from Brazilian states and capitals are used to test the proposed framework.

International audience; In 2019, the first cases of COVID-19 were reported in China. In January 2020, recognizing that the disease was spread to 20 other countries, the World Health Organization declared that the outbreak constitutes a Public Health Emergency of International Concern. Nowadays, (April 2021) the novel coronavirus already taken 3.1M lives worldwide. Under this catastrophic situation, mathematical models are extremity necessary to help understand the spread of the disease and guide control measures to contain COVID-19. Under the Brazilian scenario, a good model must be capable of covering the asymmetric 2-wave behavior where the second moment of the pandemic is being more aggressive than the first one. For that, this work applies a generalized logistic model of 5 parameters to the data of new deaths in Brazil. To create the multi-wave behavior, the parameters are considered time variable under the form a sigmoid function between a minimum e maximum value to each one, controlled by two shape parameters. A calibration process was executed and the fitted parameters were used as mean to a global sensitivity analysis through the Sobol index method with use of Polynomial Chaos Surrogate. After the identification of the most important parameters, an uncertainty quantification study was conducted considering the important inputs as random variables described by beta distributions. Confidence intervals of 50, 75 and 95% to the number of new deaths and the cumulative number of deaths were obtained to analyze the model robustness under the presence of uncertainties. Combined with other complementary statistics, the model shows itself efficiently to describe the data and to be used to previous goals.

International audience; Many mechanical systems can operate with strong nonlinear behavior, making the negligence of such effects a source of errors in the prediction of the system response. A methodology, that has been successfully used, to predict the behavior of such systems is based on the identification of Volterra kernels. However, this technique is subject to uncertainties that are induced by the measurements noise. This work presents a study that assesses the influence of these uncertainties in the Volterra kernels, expanded with Kautz functions, and their propagation through the nonlinear dynamic system. The proposed method is applied to a nonlinear beam. Monte-Carlo simulations are used to compute the propagation of uncertainties in Volterra kernels. The results have been shown that the kernels are greatly influenced by the presence of uncertainties and confidence limits for the system responses can be established.