A model of behavioural response to risk accurately predicts the statistical distribution of COVID-19 infection and reproduction numbers.

One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This homeostatic response is active until approximate herd immunity is reached: in this domain the model predicts that the reproduction rate R will be centred around a median of 1, that proportional change in infection numbers will follow the standard Cauchy distribution with location and scale parameters 0 and 1, and that high infection numbers will follow a power-law frequency distribution with exponent 2. To test these predictions we used worldwide COVID-19 data from 1st February 2020 to 30th June 2022 to calculate [Formula: see text] confidence interval estimates across countries for these R, location, scale and exponent parameters. The resulting median R estimate was [Formula: see text] (predicted value 1) the proportional change location estimate was [Formula: see text] (predicted value 0), the proportional change scale estimate was [Formula: see text] (predicted value 1), and the frequency distribution exponent estimate was [Formula: see text] (predicted value 2); in each case the observed estimate agreed with model predictions.

General two-parameter distribution: Statistical properties, estimation, and application on COVID-19.

In this paper, we introduced a novel general two-parameter statistical distribution which can be presented as a mix of both exponential and gamma distributions. Some statistical properties of the general model were derived mathematically. Many estimation methods studied the estimation of the proposed model parameters. A new statistical model was presented as a particular case of the general two-parameter model, which is used to study the performance of the different estimation methods with the randomly generated data sets. Finally, the COVID-19 data set was used to show the superiority of the particular case for fitting real-world data sets over other compared well-known models.

Beta distribution misspecification tests with application to Covid-19 mortality rates in the United States.

The beta distribution is routinely used to model variables that assume values in the standard unit interval, (0, 1). Several alternative laws have, nonetheless, been proposed in the literature, such as the Kumaraswamy and simplex distributions. A natural and empirically motivated question is: does the beta law provide an adequate representation for a given dataset? We test the null hypothesis that the beta model is correctly specified against the alternative hypothesis that it does not provide an adequate data fit. Our tests are based on the information matrix equality, which only holds when the model is correctly specified. They are thus sensitive to model misspecification. Simulation evidence shows that the tests perform well, especially when coupled with bootstrap resampling. We model state and county Covid-19 mortality rates in the United States. The misspecification tests indicate that the beta law successfully represents Covid-19 death rates when they are computed using either data from prior to the start of the vaccination campaign or data collected when such a campaign was under way. In the latter case, the beta law is only accepted when the negative impact of vaccination reach on death rates is moderate. The beta model is rejected under data heterogeneity, i.e., when mortality rates are computed using information gathered during both time periods.

Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data.

In this work, we presented the type I half logistic Burr-Weibull distribution, which is a unique continuous distribution. It offers several superior benefits in fitting various sorts of data. Estimates of the model parameters based on classical and nonclassical approaches are offered. Also, the Bayesian estimates of the model parameters were examined. The Bayesian estimate method employs the Monte Carlo Markov chain approach for the posterior function since the posterior function came from an uncertain distribution. The use of Monte Carlo simulation is to assess the parameters. We established the superiority of the proposed distribution by utilising real COVID-19 data from varied countries such as Saudi Arabia and Italy to highlight the relevance and flexibility of the provided technique. We proved our superiority using both real data.

A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family.

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions.

Exponentiated Odd Lomax Exponential distribution with application to COVID-19 death cases of Nepal.

This study suggested a new four-parameter Exponentiated Odd Lomax Exponential (EOLE) distribution by compounding an exponentiated odd function with Lomax distribution as a generator. The proposed model is unimodal and positively skewed whereas the hazard rate function is monotonically increasing and inverted bathtubs. Some important properties of the new distribution are derived such as quintile function and median; asymptotic properties and mode; moments; mean residual life, mean path time; mean deviation; order statistics; and Bonferroni & Lorenz curve. The value of the parameters is obtained from the maximum likelihood estimation, least-square estimation, and Cramér-Von-Mises methods. Here, a simulation study and two real data sets, "the number of deaths per day due to COVID-19 of the first wave in Nepal" and ''failure stresses (In Gpa) of single carbon fibers of lengths 50 mm", have been applied to validate the different theoretical findings. The finding of an order of COVID-19 deaths in 153 days in Nepal obey the proposed distribution, it has a significantly positive relationship between the predictive test positive rate and the predictive number of deaths per day. Therefore, the intended model is an alternative model for survival data and lifetime data analysis.

Inspection plan for COVID-19 patients for Weibull distribution using repetitive sampling under indeterminacy.

BACKGROUND: This research work is elaborated investigation of COVID-19 data for Weibull distribution under indeterminacy using time truncated repetitive sampling plan. The proposed design parameters like sample size, acceptance sample number and rejection sample number are obtained for known indeterminacy parameter. METHODS: The plan parameters and corresponding tables are developed for specified indeterminacy parametric values. The conclusion from the outcome of the proposed design is that when indeterminacy values increase the average sample number (ASN) reduces. RESULTS: The proposed repetitive sampling plan methodology application is given using COVID-19 data belong to Italy. The efficiency of the proposed sampling plan is compared with the existing sampling plans. CONCLUSIONS: Using the tables and COVID-19 data illustration, it is concluded that the proposed plan required a smaller sample size as examined with the available sampling plans in the literature.

Interim estimates in null models of COVID-19 vaccine effectiveness.

Recently released interim numbers from advanced vaccine candidate clinical trials suggest that a COVID-19 vaccine effectiveness (VE) of >90% is achievable. However, SARS-CoV-2 transmission dynamics are highly heterogeneous and exhibit localized bursts of transmission, which may lead to sharp localized peaks in the number of new cases, often followed by longer periods of low incidence. Here we show that, for interim estimates of VE, these characteristic bursts in SARS-CoV-2 infection may introduce a strong positive bias in VE. Specifically, we generate null models of vaccine effectiveness, i.e., random models with bursts that over longer periods converge to zero VE but that for interim periods frequently produce apparent VE near 100%. As an example, by following the relevant clinical trial protocol, we can reproduce recently reported interim outcomes from an ongoing phase 3 clinical trial of an RNA-based vaccine candidate. Thus, to avoid potential random biases in VE, it is suggested that interim estimates on COVID-19 VE should control for the intrinsic inhomogeneity in both SARS-CoV-2 infection dynamics and reported cases.

Benchmarking of public health surveillance of COVID-19 in Colombia: First semester / [Evaluación comparativa de la vigilancia en salud pública de COVID-19 en Colombia: primer semestre].

Introduction: Public health surveillance together with good sanitary decisions is essential for the proper management of the SARS-CoV-2 pandemic. Objective: To compare the performance of Colombian departments based on the quality of the data and to build the national ranking. Materials and methods: We analyzed the accumulated cases published between March 6 and September 1, 2020, by the Instituto Nacional de Salud. To achieve comparability, the analyses considered the day the first case was diagnosed as the first analysis date for each department. The fulfillment of Benford's law was assessed with p-values in the log-likelihood ratio or chi-square tests. The analysis was completed with the lethality observed in each department and then the performance ranking was established. Results: Bogotá and Valle del Cauca had optimal public health surveillance performance all along. The data suggest that Antioquia, Nariño, and Tolima had good containment and adequate public health surveillance after the economic opening beginning on June 1, 2020. Conclusion: We obtained the ranking of the departments regarding the quality of public health surveillance data. The best five departments can be case studies to identify the elements associated with good performance.

Introducción. La vigilancia en salud pública y las decisiones sanitarias recomendadas son fundamentales para el manejo adecuado de la pandemia de SARS-CoV-2. Objetivo. Hacer una evaluación comparativa del desempeño de los departamentos colombianos de este atributo del sistema de vigilancia con base en la calidad de los datos y construir la clasificación nacional según el desempeño. Materiales y métodos. Se analizaron los casos acumulados publicados por el Instituto Nacional de Salud entre el 6 de marzo y el 1° de septiembre de 2020. Para la comparación, los análisis consideraron el día en que se diagnosticó el primer caso como la primera fecha de análisis de cada departamento. El cumplimiento de la ley de Benford se evaluó con los valores de p en las pruebas de razón del logaritmo de la verosimilitud o ji al cuadrado. Se completó el análisis del atributo de calidad del dato con la letalidad observada en cada departamento, y se estableció la clasificación según el desempeño. Resultados. La ciudad de Bogotá y el departamento del Valle del Cauca tuvieron un desempeño óptimo en la vigilancia en salud pública durante todo el periodo observado. Los datos sugieren que los departamentos de Antioquia, Nariño y Tolima tuvieron una buena contención y una adecuada vigilancia en salud pública después de la apertura económica iniciada el 1° de junio de 2020. Conclusión. Se obtuvo una clasificación de los departamentos y de Bogotá según la calidad de los datos de vigilancia en salud pública. Los mejores cinco entes territoriales pueden ser casos de estudio para determinar los elementos asociados con el buen desempeño.