Discrete Erlang-2 distribution and its application to leukemia and COVID-19

Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution. © 2023 the Author(s), licensee AIMS Press.

TTRISK: Tensor train decomposition algorithm for risk averse optimization

This article develops a new algorithm named TTRISK to solve high‐dimensional risk‐averse optimization problems governed by differential equations (ODEs and/or partial differential equations [PDEs]) under uncertainty. As an example, we focus on the so‐called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid nonsmoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the Karush–Kuhn–Tucker (KKT) system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large‐scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID‐19. The results indicate that the risk‐averse framework is feasible with the tensor approximations under tens of random variables.

A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries.

The aim of this paper is to introduce a discrete mixture model from the point of view of reliability and ordered statistics theoretically and practically for modeling extreme and outliers' observations. The base distribution can be expressed as a mixture of gamma and Lindley models. A wide range of the reported model structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, reversed hazard rate function, min-max models, mean residual life, mean past life, moments, order statistics and L-moment statistics. These properties can be formulated as closed forms. It is found that the proposed model can be used effectively to evaluate over- and under-dispersed phenomena. Moreover, it can be applied to analyze asymmetric data under extreme and outliers' notes. To get the competent estimators for modeling observations, the maximum likelihood approach is utilized under conditions of the Newton-Raphson numerical technique. A simulation study is carried out to examine the bias and mean squared error of the estimators. Finally, the flexibility of the discrete mixture model is explained by discussing three COVID-19 data sets.

Optimal control of COVID-19

Coronavirus disease of 2019 or COVID-19 (acronym for coronavirus disease 2019) is an emerging infectious disease caused by a strain of coronavirus called SARS-CoV-22, contagious with human-to-human transmission via respiratory droplets or by touching contaminated surfaces then touching them face. Faced with what the world lives, to define this problem, we have modeled it as an optimal control problem based on the models of William Ogilvy Kermack et Anderson Gray McKendrick, called SEIR model, modified by adding compart-ments suitable for our study. Our objective in this work is to maximize the number of recovered people while minimizing the number of infected. We solved the problem theoretically using the Pontryagin maximum principle, nu-merically we used and compared results of two methods namely the indirect method (shooting method) and the Euler discretization method, implemented in MATLAB.

A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response.

The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021.

Artificial intelligence and big data processing for the development of predictive models to support Covid-19 hospital patients

Coronavirus disease 2019 (COVID-19) has caused more than 6 million deaths. Higher values of the FIB-4 index have been shown to be associated with disease severity. Although vaccination has helped to improve clinical outcomes and overall mortality, it remains important to identify clinical parameters that can predict a likely worse prognosis. Artificial intelligence and big data processing were used to retrieve data from patients with Covid-19 admitted during the period March 2020-January 2022 at the Fondazione Policlinico Gemelli IRCCS. Patients and clinical characteristics of patients with available FIB 4 data derived from the Gemelli Generator Real World Data (G2 RWD) were used to develop predictive models of mortality during the 4 waves of the Covid-19 pandemic. A logistic regression model was applied to the training and test set. The performance of the model was assessed by means of the ROC curve. After the pre-processing steps, 1143 patients and 35 variables were included in the final dataset. The FIB-4 discretization algorithm identified a cut-off of 2.54. After fitting the model for multiple mortality regression analysis: FIB-4>= 2.53 (OR=4.53, [CI: 2.83 - 7.25]), wave 3 (OR=0.34, [CI: 0.15 - 0.75], wave 4 (OR=0.40 [CI: 0.24 - 0.66]) and LDH (OR=1.001, [CI: 1.000 - 1.002]) were considered. The machine learning approach identified a cut-off of 2.53 for FIB-4 above which the risk of death increases significantly. These data may be useful in the clinical management of patients with Covid-19, as they can be calculated from the blood test after hospital admission.

An Overview of Discrete Distributions in Modelling COVID-19 Data Sets.

The mathematical modeling of the coronavirus disease-19 (COVID-19) pandemic has been attempted by a large number of researchers from the very beginning of cases worldwide. The purpose of this research work is to find and classify the modelling of COVID-19 data by determining the optimal statistical modelling to evaluate the regular count of new COVID-19 fatalities, thus requiring discrete distributions. Some discrete models are checked and reviewed, such as Binomial, Poisson, Hypergeometric, discrete negative binomial, beta-binomial, Skellam, beta negative binomial, Burr, discrete Lindley, discrete alpha power inverse Lomax, discrete generalized exponential, discrete Marshall-Olkin Generalized exponential, discrete Gompertz-G-exponential, discrete Weibull, discrete inverse Weibull, exponentiated discrete Weibull, discrete Rayleigh, and new discrete Lindley. The probability mass function and the hazard rate function are addressed. Discrete models are discussed based on the maximum likelihood estimates for the parameters. A numerical analysis uses the regular count of new casualties in the countries of Angola,Ethiopia, French Guiana, El Salvador, Estonia, and Greece. The empirical findings are interpreted in-depth.

An evolutionary approach to the discretization of gene expression profiles to predict the severity of COVID-19

In this work, we propose to use a state-of-the-art evolutionary algorithm to set the discretization thresholds for gene expression profiles, using feedback from a classifier in order to maximize the accuracy of the predictions based on the discretized gene expression levels, while at the same time minimizing the number of different profiles obtained, to ease the understanding of the expert. The methodology is applied to a dataset containing COVID-19 patients that developed either mild or severe symptoms. The results show that the evolutionary approach performs better than a traditional discretization based on statistical analysis, and that it does preserve the sense-making necessary for practitioners to trust the results. © 2022 Owner/Author.

A new one-parameter discrete exponential distribution: Properties, inference, and applications to COVID-19 data

A new one-parameter discrete length-biased exponential distribution called the discrete moment exponential (DMEx) distribution is introduced using the survival discretizing approach. We derive the reliability measures including survival function, hazard function, residual reliability function, and the second rate of failure function. Further, the mathematical properties of the DMEx distribution are derived. The parameters of the DMEx distribution are estimated using seven estimation methods. A simulation study is carried out to explore the behavior of the proposed estimators. It is observed that the maximum likelihood approach provides efficient estimates. Finally, the DMEx is adopted for fitting the number of COVID-19 deaths in China and Europe countries. It is shown that the DMEx distribution fits the data better than other competing discrete distributions.

Discretization Fractional-Order Biological Model with Optimal Harvesting

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined;also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications

In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

The new discrete distribution with application to COVID-19 Data.

This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall-Olkin family and the inverse Toppe-Leone distribution, both of them were used to introduce a new discrete distribution called Marshall-Olkin inverse Toppe-Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall-Olkin Inverse Toppe-Leone (DMOITL). This new model possesses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte-Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).