The Extended Exponential-Weibull Accelerated Failure Time Model with Application to Sudan COVID-19 Data

A fully parametric accelerated failure time (AFT) model with a flexible, novel modified exponential Weibull baseline distribution called the extended exponential Weibull accelerated failure time (ExEW-AFT) model is proposed. The model is presented using the multi-parameter survival regression model, where more than one distributional parameter is linked to the covariates. The model formulation, probabilistic functions, and some of its sub-models were derived. The parameters of the introduced model are estimated using the maximum likelihood approach. An extensive simulation study is used to assess the estimates' performance using different scenarios based on the baseline hazard shape. The proposed model is applied to a real-life right-censored COVID-19 data set from Sudan to illustrate the practical applicability of the proposed AFT model.

New Lifetime Distribution for Modeling Data on the Unit Interval: Properties, Applications and Quantile Regression

Probability distributions are very useful in modeling lifetime datasets. However, no specific distribution is suitable for all kinds of datasets. In this study, the bounded truncated Cauchy power exponential distribution is proposed for modeling datasets on the unit interval. The probability density function exhibits desirable shapes, such as left-skewed, right-skewed, reversed J, and bathtub shapes, whereas the hazard rate function displays J and bathtub shapes. For the purpose of modeling dependence between measures in a dataset, a bivariate extension of the proposed distribution is developed. The bivariate probability density function displays monotonic and non-monotonic shapes, making it suitable for modeling complex bivariate relations. Subsequently, the applications of the distribution are illustrated using COVID-19 data. The results revealed that the new distribution provides a better fit to the datasets compared to other existing distributions. Finally, a new quantile regression model is developed and its application demonstrated. The generated quantile regression model offers a decent fit to the data, according to the residual analysis.

A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic

The importance of Lagrangian distributions and their applicability in real-world events have been highlighted in several studies. In light of this, we create a new zero-truncated Lagrangian distribution. It is presented as a generalization of the zero-truncated binomial distribution (ZTBD) and hence named the Lagrangian zero-truncated binomial distribution (LZTBD). The moments, probability generating function, factorial moments, as well as skewness and kurtosis measures of the LZTBD are discussed. We also show that the new model's finite mixture is identifiable. The unknown parameters of the LZTBD are estimated using the maximum likelihood method. A broad simulation study is executed as an evaluation of the well-established performance of the maximum likelihood estimates. The likelihood ratio test is used to assess the effectiveness of the third parameter in the new model. Six COVID-19 datasets are used to demonstrate the LZTBD's applicability, and we conclude that the LZTBD is very competitive on the fitting objective.

On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19

In this paper, we study a type of disease that unknowingly spreads for a long time, but by default, spreads only to a minimal population. This disease is not usually fatal and often goes unnoticed. We propose and derive a novel epidemic mathematical model to describe such a disease, utilizing a fractional differential system under the Atangana–Baleanu–Caputo derivative. This model deals with the transmission between susceptible, exposed, infected, and recovered classes. After formulating the model, equilibrium points as well as stability and feasibility analyses are stated. Then, we present results concerning the existence of positivity in the solutions and a sensitivity analysis. Consequently, computational experiments are conducted and discussed via proper criteria. From our experimental results, we find that the loss and regain of immunity result in the gain and loss of infections. Epidemic models can be linked to symmetry and asymmetry from distinct points of view. By using our novel approach, much research may be expected in epidemiology and other areas, particularly concerning COVID-19, to state how immunity develops after being infected by this virus.

COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

The purpose of this research is the segmentation of lungs computed tomography (CT) scan for the diagnosis of COVID-19 by using machine learning methods. Our dataset contains data from patients who are prone to the epidemic. It contains three types of lungs CT images (Normal, Pneumonia, and COVID-19) collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur, Pakistan, and the second one is a publicly free available medical imaging database known as Radiopaedia. For the preprocessing, a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest (ROIs) and acquire 52 hybrid statistical features for each ROIs. Also, 12 optimized statistical features are selected via the chi-square feature reduction technique. For the classification, five machine learning classifiers named as deep learning J4, multilayer perceptron, support vector machine, random forest, and naive Bayes are deployed to optimize the hybrid statistical features dataset. It is observed that the deep learning J4 has promising results (sensitivity and specificity: 0.987;accuracy: 98.67%) among all the deployed classifiers. As a complementary study, a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

Topp-Leone Odd Frechet Generated Family of Distributions with Applications to COVID-19 Data Sets

Recent studies have pointed out the potential of the odd Frechet family (or class) of continuous distributions in fitting data of all kinds. In this article, we propose an extension of this family through the so-called "Topp-Leone strategy", aiming to improve its overall flexibility by adding a shape parameter. The main objective is to offer original distributions with modifiable properties, from which adaptive and pliant statistical models can be derived. For the new family, these aspects are illustrated by the means of comprehensive mathematical and numerical results. In particular, we emphasize a special distribution with three parameters based on the exponential distribution. The related model is shown to be skillful to the fitting of various lifetime data, more or less heterogeneous. Among all the possible applications, we consider two data sets of current interest, linked to the COVID-19 pandemic. They concern daily cases confirmed and recovered in Pakistan from March 24 to April 28, 2020. As a result of our analyzes, the proposed model has the best fitting results in comparison to serious challengers, including the former odd Frechet model.