Highlights An optimal strategy for vaccine administration in COVID-19 pandemic treatment is determined considering both mono and multi-objective optimization context. The present work proposes a methodology to solve an inverse problem aiming to determine the SIR model parameters to simulate the COVID-19 pandemic. The results indicate that optimal control approaches based on epidemiological models can provide information to assist in mitigating the spread of disease.

Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables, and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead, and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multiobjective optimization problem is formulated, considering the minimization of uncertainties associated with the estimation process and the maximization of the robustness parameter. To solve this problem, the Multiobjective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.

Recently, various countries from across the globe have been facing the second wave of COVID-19 infections. In order to understand the dynamics of the spread of the disease, much effort has been made in terms of mathematical modeling. In this scenario, compartmental models are widely used to simulate epidemics under various conditions. In general, there are uncertainties associated with the reported data, which must be considered when estimating the parameters of the model. In this work, we propose an effective methodology for estimating parameters of compartmental models in multiple wave scenarios by means of a dynamic data segmentation approach. This robust technique allows the description of the dynamics of the disease without arbitrary choices for the end of the first wave and the start of the second. Furthermore, we adopt a time-dependent function to describe the probability of transmission by contact for each wave. We also assess the uncertainties of the parameters and their influence on the simulations using a stochastic strategy. In order to obtain realistic results in terms of the basic reproduction number, a constraint is incorporated into the problem. We adopt data from Germany and Italy, two of the first countries to experience the second wave of infections. Using the proposed methodology, the end of the first wave (and also the start of the second wave) occurred on 166 and 187 days from the beginning of the epidemic, for Germany and Italy, respectively. The estimated effective reproduction number for the first wave is close to that obtained by other approaches, for both countries. The results demonstrate that the proposed methodology is able to find good estimates for all parameters. In relation to uncertainties, we show that slight variations in the design variables can give rise to significant changes in the value of the effective reproduction number. The results provide information on the characteristics of the epidemic for each country, as well as elements for decision-making in the economic and governmental spheres.

Reliable data are essential to obtain adequate simulations for forecasting the dynamics of epidemics. In this context, several political, economic, and social factors may cause inconsistencies in the reported data, which reflect the capacity for realistic simulations and predictions. In the case of COVID-19, for example, such uncertainties are mainly motivated by large-scale underreporting of cases due to reduced testing capacity in some locations. In order to mitigate the effects of noise in the data used to estimate parameters of models, we propose strategies capable of improving the ability to predict the spread of the diseases. Using a compartmental model in a COVID-19 study case, we show that the regularization of data by means of Gaussian process regression can reduce the variability of successive forecasts, improving predictive ability. We also present the advantages of adopting parameters of compartmental models that vary over time, in detriment to the usual approach with constant values.

Different types of mathematical models have been used to predict the dynamic behavior of the novel coronavirus (COVID-19). Many of them involve the formulation and solution of inverse problems. This kind of problem is generally carried out by considering the model, the vector of design variables, and system parameters as deterministic values. In this contribution, a methodology based on a double loop iteration process and devoted to evaluate the influence of uncertainties on inverse problem is evaluated. The inner optimization loop is used to find the solution associated with the highest probability value, and the outer loop is the regular optimization loop used to determine the vector of design variables. For this task, we use an inverse reliability approach and Differential Evolution algorithm. For illustration purposes, the proposed methodology is applied to estimate the parameters of SIRD (Susceptible-Infectious-Recovery-Dead) model associated with dynamic behavior of COVID-19 pandemic considering real data from China's epidemic and uncertainties in the basic reproduction number (R0). The obtained results demonstrate, as expected, that the increase of reliability implies the increase of the objective function value.

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Double retrograde vaporization is a phase behavior phenomenon that occurs close to the critical point of binary mixtures and characterized by wide relative difference of volatility between its components. In general, the phenomenon occurs in a very narrow composition range, making the prediction of the molar fraction and pressure of the phase equilibrium problem a challenging problem. Here we employ sophisticated modern numerical methodology to untangle the geometry of this complex phenomenon, based on the robust methodology of inversion of functions. The objective of this work is to evaluate the system that describes the phenomenon close to the singularity points of the problem, especially with respect to the degeneration of solutions. The method used offers an effective framework for the qualitative analysis of systems of nonlinear equations. We study an application of this methodology in the binary system formed by ethane + limonene, at three different configurations (four dew points, three dew points and only one dew point). The results indicate a very complex structure of the function in the neighborhood of the phenomenon.