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Evolution equations with convolution-type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, including delayed and fractional differential equations. We demonstrate, starting from the logistic model structure, that classical, delayed, and fractional models are special cases of a framework using a gamma Mittag-Leffler memory kernel. We discuss and classify different types of this general kernel, analyze the asymptotic behavior of the general model, and provide numerical simulations. A detailed classification of the memory kernels is presented through parameter analysis. The fractional models we constructed possess distinctive features as they maintain dimensional balance and explicitly relate fractional orders to past data points. Additionally, we illustrate how our models can reproduce the dynamics of COVID-19 infections in Australia, Brazil, and Peru. Our research expands mathematical modeling by presenting a unified framework that facilitates the incorporation of historical data through the utilization of integro-differential equations, fractional or delayed differential equations, as well as classical systems of ordinary differential equations.

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This paper aims to introduce a novel family of probability distributions by the well-known method of the T-X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan-Quinn information criterion (HQINC), the Cramer-von-Misses (CRMI), and the ANDA (Anderson-Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study.

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ABSTRACT Introduction: Since the coronavirus disease 2019 (COVID-19) pandemic, cardiac surgeries in patients with previous infection by COVID-19 were suspended or postponed, which led to surgeries performed in patients with an advanced stage of their disease and an increase in the waiting list. There is a heterogeneous attitude in Latin America on the optimal timing to cardiac surgery in patients with previous COVID-19 infection due to scarce data on its outcome. Two Latin American associations joined to establish common suggestions on the optimal timing of surgery in patients with previous COVID-19 infection. Methods: Data collection was performed using a pre-established form, which included year of publication, objective, type of study (prospective/retrospective, descriptive/analytical), number of patients, year of study, waiting time between infection and surgery, type of surgery, morbidity, mortality, and conclusions regarding the association between mortality and morbidity. Final recommendations were approved by the board of directors of Latin American Association of Cardiac and Endovascular Surgery (LACES) and Latin American Confederation of Anesthesia Societies (CLASA). Results: Of the initial 1,016 articles, 11 comprised the final selection. Only six of them included patients who underwent cardiac surgery. According to the analyzed literature, optimal timing for cardiac surgery needs to consider the following aspects: deferable surgery, symptomatic COVID-19 infection, completeness of COVID-19 vaccination. Conclusion: These recommendations derive from the analysis of the scarce literature published at present on outcomes after cardiac surgery in patients with previous COVID-19 infection. These are to be taken as a dynamic recommendation in which Latin American reality was taken into consideration.

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INTRODUCTION: Since the coronavirus disease 2019 (COVID-19) pandemic, cardiac surgeries in patients with previous infection by COVID-19 were suspended or postponed, which led to surgeries performed in patients with an advanced stage of their disease and an increase in the waiting list. There is a heterogeneous attitude in Latin America on the optimal timing to cardiac surgery in patients with previous COVID-19 infection due to scarce data on its outcome. Two Latin American associations joined to establish common suggestions on the optimal timing of surgery in patients with previous COVID-19 infection. METHODS: Data collection was performed using a pre-established form, which included year of publication, objective, type of study (prospective/retrospective, descriptive/analytical), number of patients, year of study, waiting time between infection and surgery, type of surgery, morbidity, mortality, and conclusions regarding the association between mortality and morbidity. Final recommendations were approved by the board of directors of Latin American Association of Cardiac and Endovascular Surgery (LACES) and Latin American Confederation of Anesthesia Societies (CLASA). RESULTS: Of the initial 1,016 articles, 11 comprised the final selection. Only six of them included patients who underwent cardiac surgery. According to the analyzed literature, optimal timing for cardiac surgery needs to consider the following aspects: deferable surgery, symptomatic COVID-19 infection, completeness of COVID-19 vaccination. CONCLUSION: These recommendations derive from the analysis of the scarce literature published at present on outcomes after cardiac surgery in patients with previous COVID-19 infection. These are to be taken as a dynamic recommendation in which Latin American reality was taken into consideration.

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