ABSTRACT
In this article, we proposed a new extension of the Topp–Leone family of distributions. Some important properties of the model are developed, such as quantile function, stochastic ordering, model series representation, moments, stress–strength reliability parameter, Renyi entropy, order statistics, and moment of residual life. A particular member called new extended Topp–Leone exponential (NETLE) is discussed. Maximum likelihood estimation (MLE), least-square estimation (LSE), and percentile estimation (PE) are used for the model parameter estimation. Simulation studies were conducted using NETLE to assess the MLE, LSE, and PE performance by examining their bias and mean square error (MSE), and the result was satisfactory. Finally, the applications of the NETLE to two real data sets are provided to illustrate the importance of the NETLG families in practice;the data sets consist of daily new deaths due to COVID-19 in California and New Jersey, USA. The new model outperformed many other existing Topp–Leone's and exponential related distributions based on the real data illustrations.
ABSTRACT
This article presents a novel discrete distribution with a single parameter, called the discrete Teissier distribution. It is noted that this model, with one parameter, offers a high degree of fitting flexibility as it is capable of modelling equi-, over-, and under-dispersed, positive and negative skewed, and increasing failure rate datasets. In this article, we have explored its numerous essential distributional features such as recurrence relation, moments, generating function, index of dispersion, coefficient of variation, entropy, survival and hazard rate functions, mean residual life and mean past life functions, stress-strength reliability, order statistics, and infinite divisibility. The classical point estimators have been developed using the method of maximum likelihood, method of moment, and least-squares estimation, whilst an interval estimation based on Fisher’s information has also been presented. Finally, the applicability of the suggested discrete model has been demonstrated using two complete real datasets. © Reliability: Theory and Applications 2022.
ABSTRACT
The mathematical characteristics of the mixture of Lindley model with 2-component (2-CMLM) are discussed. In this paper, we investigate both the practical and theoretical aspects of the 2-CMLM. We investigate several statistical features of the mixed model like probability generating function, cumulants, characteristic function, factorial moment generating function, mean time to failure, Mills Ratio, mean residual life. The density, hazard rate functions, mean, coefficient of variation, skewness, and kurtosis are all shown graphically. Furthermore, we use appropriate approaches such as maximum likelihood, least square and weighted least square methods to estimate the pertinent parameters of the mixture model. We use a simulation study to assess the performance of suggested methods. Eventually, modelling COVID-19 patient data demonstrates the effectiveness and utility of the 2-CMLM. The proposed model outperformed the two component mixture of exponential model as well as two component mixture of Weibull model in practical applications, indicating that it is a good candidate distribution for modelling COVID-19 and other related data sets. © 2022 the Author(s), licensee AIMS Press.
ABSTRACT
As people around the world work to stop the COVID-19 pandemic, mutated COVID-19 (Delta strain) that are more contagious are emerging in many places. How to develop effective and reasonable plans to prevent the spread of mutated COVID-19 is an important issue. In order to simulate the transmission of mutated COVID-19 (Delta strain) in China with a certain proportion of vaccination, we selected the epidemic situation in Jiangsu Province as a case study. To solve this problem, we develop a novel epidemic model with a vaccinated population. The basic properties of the model is analyzed, and the expression of the basic reproduction number R 0 is obtained. We collect data on the Delta strain epidemic in Jiangsu Province, China from July 20, to August 5, 2021. The weighted nonlinear least square estimation method is used to fit the daily asymptomatic infected people, common infected people and severe infected people. The estimated parameter values are obtained, the approximate values of the basic reproduction number are calculated R 0 ≈ 1.378 . Through the global sensitivity analysis, we identify some parameters that have a greater impact on the prevalence of the disease. Finally, according to the evaluation results of parameter influence, we consider three control measures (vaccination, isolation and nucleic acid testing) to control the spread of the disease. The results of the study found that the optimal control measure is to dynamically adjust the three control measures to achieve the lowest number of infections at the lowest cost. The research in this paper can not only enrich theoretical research on the transmission of COVID-19, but also provide reliable control suggestions for countries and regions experiencing mutated COVID-19 epidemics.
ABSTRACT
As the first-wave COVID-19 has passed in 2020, people's awareness of self-protection began to decline gradually. How to prevent and control the second-wave COVID-19 has become an important issue in many countries and regions. By analyzing the transmission of the second-wave COVID-19 caused by an imported case in Tonghua City, Jilin Province, China, in January 2021, we establish a new mathematical COVID-19 model to simulate the transmission characteristics of the second-wave COVID-19. First, we analyze the basic properties of the model, prove the existence of the equilibrium point, and obtain the expression of the basic reproduction number with important biological significance. Secondly, we use the weighted nonlinear least square estimation method to fit the cases in Tonghua City of Jilin Province in January 2021, and get the estimated value of the parameters. The basic reproduction number of the second-wave COVID-19 in Tonghua City is R 0 = 1 . 0695 , which is much smaller than that of the first-wave COVID-19 in Wuhan in 2020. Finally, in the optimal control part, we consider two control methods (keeping social distance and nucleic acid detection of all people in the city) to simulate the control of the disease. The results show that the control intensity of the two control methods needs to be dynamically changed and adjusted, so that the cost can be minimized with the least infection. The results of this paper can not only provide suggestions for health management departments, but also provide a reference for the analysis of the second-wave COVID-19 in other countries or regions.