[Age-specific regional characteristics of COVID-19 mortality in 2021]. / A COVID­19-halandóság életkor-specifikus regionális jellemzoi 2021-ben.

INTRODUCTION: In most countries, COVID-19 mortality increases exponentially with age, but the growth rate varies considerably between countries. The different progression of mortality may reflect differences in population health, the quality of health care or coding practices. OBJECTIVE: In this study, we investigated differences in age-specific county characteristics of COVID-19 mortality in the second year of the pandemic. METHOD: Age-specific patterns of COVID-19 adult mortality were estimated according to county level and sex using a Gompertz function with multilevel models. RESULTS: The Gompertz function is suitable for describing age patterns of COVID-19 adult mortality at county level. We did not find significant differences in the age progression of mortality between counties, but there were significant spatial differences in the level of mortality. The mortality level showed a relationship with socioeconomic and health care indicators with the expected sign, but with different strengths. DISCUSSION AND CONCLUSION: The COVID-19 pandemic in 2021 resulted in a decline in life expectancy in Hungary not seen since World War II. The study highlights the importance of healthcare in addition to social vulnerability. It also points out that understanding age patterns will help to mitigate the consequences of the epidemic. Orv Hetil. 2023; 164(17): 643-650.

A new copula-based bivariate Gompertz–Makeham model and its application to COVID-19 mortality data

One of the useful distributions in modeling mortality (or failure) data is the univariate Gompertz–Makeham distribution. To examine the relationship between the two variables, the extended bivariate Gompertz–Makeham distribution is introduced, and its properties are provided. Also, some reliability indices, including aging intensity and stress-strength reliability, are calculated for the proposed model. Here, a new copula function is constructed based on the extended bivariate Gompertz–Makeham distribution. Some of its features including dependency properties, such as dependence structure, some measures of dependence, and tail dependence, are studied. The estimation of the parameters of new copula is presented, and at the end, a simulation study and a performance analysis based on the real data are presented. So, by analyzing the mortality data due to COVID-19, the appropriateness of the proposed model is examined. [ FROM AUTHOR] Copyright of Iranian Journal of Fuzzy Systems is the property of University of Sistan & Baluchestan and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Asymptotic analysis of the SIR model and the Gompertz distribution

The SIR (Susceptible–Infected–Removed) is one of the simplest models for epidemic outbreaks. The present paper derives a novel, simple, analytical asymptotic solution for the I-variable, which is valid on the entire real line. Connections with the Gompertz and Gumbel distributions are also demonstrated. The approach is applied to the ongoing coronavirus disease 2019 (COVID-19) pandemic in four European countries — Belgium, Italy, Sweden, and Bulgaria. The reported raw incidence data from the outbreaks in 2020–2021 have been fitted using constrained least squares. It is demonstrated that the asymptotic solution can be used successfully for parametric estimation either in stand-alone mode or as a preliminary step in the parametric estimation using numerical inversion of the exact parametric solution. [ FROM AUTHOR]

THE PROLIFERATION OF COVID-19 IN SAUDI ARABIA ACCORDING TO GOMPERTZ MODEL

Mathematical modeling can be a powerful tool to predict disease spread in large populations as well as to understand different factors which can impact it such as social distancing and vaccinations. This study aimed to describe the spread the coronavirus disease 2019 (COVID-19) pandemic in Saudi Arabia using a simple discrete variant of the Gompertz model. Unlike time-continuous models which are based on differential equations, this model treats time as a discrete variable and is then represented by a first-order difference equation. Using this model, we performed a short-term prediction of the number of cumulative cases of COVID-19 in the country and we show that the results match the confirmed reports. © 2022 Fractals.

Efficient Function Integration and a Case Study with Gompertz Functions for Covid-19 Waves

Numerical algorithms are widely used in different applications, therefore, the execution time of the functions involved in numerical algorithms is important, and, in some cases, decisive, for example, in machine learning algorithms. Given a finite set of independent functions A(x), B(x), …, Z(x) with domains defined by disjoint, consecutive, and not necessarily adjacent intervals, the main goal is to integrate into a single function F(x) = k1×A(x) + k2×B(x) + … + kn×Z(x), where each activation coefficient k, is one if x is in the interval of the respective domain and zero otherwise. The novelty of this work is the presentation and formal demonstration of two general forms of integration of functions in a single function: The first is the mathematical version and the second is the computational version (with the AND function at the bit level), which is characterized by its efficiency. The result is applied in a case study (Peru), where two regression functions were obtained that integrate all the waves of Covid-19, that is, the epidemic curve of the variable global number of deaths/infected per day, the adjustment provided a highly statistically significant measure of correlation, a Pearson's product-moment correlation of 0.96 and 0.98 respectively. Finally, the size of the epidemic was projected for the next 30 days © 2022, International Journal of Advanced Computer Science and Applications.All Rights Reserved.

Forecasting the Future Excellence: 30 Years of Evaluating Service Organizations in Slovakia

The aim of this paper is to model and interpret the results obtained from the assessment of the Level of Excellence of Slovak service organizations using the criteria of the European Foundation for Quality Management (EFQM) excellence model. The Gompertz logistic function is effectively employed to fit the incremental improvement and predict the values of future Levels of Excellence. The EFQM model is usually used to improve organizational development and performance. The study focuses on the problem of the slow growth or even stagnation of Slovak service organizations towards Excellence. The questionnaire method was used to assess the Level of Excellence of the selected organizations, and the approach of measuring efficiency as a ratio of results and enablers was used to evaluate the organization’s ability to transform inputs into outputs. Data were collected from 30 service organizations over a period of 20 years. The first finding of the study is the demonstration of the applicability of the Gompertz function to model the evolution of the Level of Excellence. The accuracy of the model is very high, and this predisposes this function to be used to forecast the scores of organizations over time. Examining efficiency yielded a second finding, that organizations were failing to capitalize on the effort put into translating it into results. After the first few years of growth, efficiency stagnates and then even declines. This suggests that the application of the original EFQM excellence model has reached the end of its ability to improve the effectiveness of organizations as a whole. Individual firms may have been growing or declining, but the average service score across the country had no longer the capacity to improve anymore.

Wavelet-based Statistical and Mathematical Analysis of Spread of COVID-19

T he and spreadoutbreak mortality. of COVIDof Therefore, coronavirus-19−19 which the will researchers (NCoV-19)help in planninghas are developed using to control various a universalthe available diseasecrisis methods andduetotomanage to high study ratethe the ofhealth pattern infectioncare of resources. This study compares Autoregressive Integrated Moving Average (ARIMA) (statistical), Logistic, Gompertz (mathematical) and their hybrid using Wavelet−based Forecast (WBF) models to model and predict the number of confirmed cases of COVID−19. The study area includes the countries: Iran, Italy, Pakistan, Saudi Arabia, USA, UK and Canada. Moreover, root mean squares error (RMSE) is used to compare the performance of studied models. Empirical analysis shows that confirmed cases could be adequately modelled using ARIMA and ARIMA-WBF for all the countries under consideration. However, for future prediction significance of the models varies region to region. © 2021. Advancements in Life Sciences. All rights reserved.

Machine Learning Based Prediction of COVID-19 Infection in India

The novel coronavirus (COVID-19) infection had spread throughout the globe since the beginning of 2020 giving rise to a pandemic situation. In this paper, attempts have been made to model the COVID-19 infection in India using exponential, logistic and Gompertz-based mathematical machine learning regression models. These predictive methods show an excellent fit with the daily count of confirmed cases for the period between January 30, 2020, and February 3, 2021. The mean squared logarithmic error (MSLE) of the Gompertz model being lowest among the three machine learning regression methods considered in this paper making it ideal at least as a case study for future predictions in Indian scenario. Nevertheless, the epidemiologists, healthcare personnel, or other Government authorities may use this study as a reference for future planning in prevention of such pandemic situation in similar developing nations. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Modeling the Number of COVID-19 Total Cases in Iran Using Gompertz and Logistic Growth Curves

Introduction: The growth curve are time dependece regression models which commonly are useful in describing the rapid growth of total cases or deaths in a pandemic situation. Methods: The Gompertz and logistic functions are useful to describe the growth curve of a population or any time dependence variable such as metabolic rate, growth of tumors and total number of cases or deaths in a pervasive disease. The logistics family of growth curve including logistic, SSlogistic, generalized logistic and power logistic and Gompertz models were considered to describe the growth curve of total_cases_per_million (t_c_p_m) of COVID-19 in Iran during the 19-Feb-2020 to 28-May-2021. The models were fitted to data using nls function in R and the fitting accuracy was evaluated using the numerical and graphical approaches. Results: The logistic family and Gompertz growth curve were applied to fit the total_cases_per_million of COVID-19 in Iran as the response versus the time in days as predictor variable. The training and testing RMSE criterions were considered as the numerical criterions to assess the model accuracy. The growth curve of fitted models was compared with the growth curve of observed data. Results indicated that the logistic and Gompertz models provided a better description of target variable than the alternatives. Conclusion: As results shown, the logistic and Gompertz models provided a better description of response variable than the alternatives. Therefore, the logistic and Gompertz models are able to describe and forecast the COVID-19 variables (including total cases, death, recovered and so on) very well. © 2021 Tehran University of Medical Sciences. Published by Tehran University of Medical Sciences.

Hospital preparedness during epidemics using simulation: the case of COVID-19.

This paper presents a discrete event simulation model to support decision-making for the short-term planning of hospital resource needs, especially Intensive Care Unit (ICU) beds, to cope with outbreaks, such as the COVID-19 pandemic. Given its purpose as a short-term forecasting tool, the simulation model requires an accurate representation of the current system state and high fidelity in mimicking the system dynamics from that state. The two main components of the simulation model are the stochastic modeling of patient admission and patient flow processes. The patient arrival process is modelled using a Gompertz growth model, which enables the representation of the exponential growth caused by the initial spread of the virus, followed by a period of maximum arrival rate and then a decreasing phase until the wave subsides. We conducted an empirical study concluding that the Gompertz model provides a better fit to pandemic-related data (positive cases and hospitalization numbers) and has superior prediction capacity than other sigmoid models based on Richards, Logistic, and Stannard functions. Patient flow modelling considers different pathways and dynamic length of stay estimation in several healthcare stages using patient-level data. We report on the application of the simulation model in two Autonomous Regions of Spain (Navarre and La Rioja) during the two COVID-19 waves experienced in 2020. The simulation model was employed on a daily basis to inform the regional logistic health care planning team, who programmed the ward and ICU beds based on the resulting predictions.

Gompertz model in COVID-19 spreading simulation.

The paper reports on application of the Gompertz model to describe the growth dynamics of COVID-19 cases during the first wave of the pandemic in different countries. Modeling has been performed for 23 countries: Australia, Austria, Belgium, Brazil, Great Britain, Germany, Denmark, Ireland, Spain, Italy, Canada, China, the Netherlands, Norway, Serbia, Turkey, France, Czech Republic, Switzerland, South Korea, USA, Mexico, and Japan. The model parameters are determined by regression analysis based on official World Health Organization data available for these countries. The comparison of the predictions given by the Gompertz model and the simple logistic model (i.e., Verhulst model) is performed allowing to conclude on the higher accuracy of the Gompertz model.

A farewell to R: time-series models for tracking and forecasting epidemics.

The time-dependent reproduction number, Rt, is a key metric used by epidemiologists to assess the current state of an outbreak of an infectious disease. This quantity is usually estimated using time-series observations on new infections combined with assumptions about the distribution of the serial interval of transmissions. Bayesian methods are often used with the new cases data smoothed using a simple, but to some extent arbitrary, moving average. This paper describes a new class of time-series models, estimated by classical statistical methods, for tracking and forecasting the growth rate of new cases and deaths. Very few assumptions are needed and those that are made can be tested. Estimates of Rt, together with their standard deviations, are obtained as a by-product.

Predictive models for COVID-19 cases, deaths and recoveries in Algeria.

This study was conducted to predict the number of COVID-19 cases, deaths and recoveries using reported data by the Algerian Ministry of health from February 25, 2020 to January 10, 2021. Four models were compared including Gompertz model, logistic model, Bertalanffy model and inverse artificial neural network (ANNi). Results showed that all the models showed a good fit between the predicted and the real data (R2>0.97). In this study, we demonstrate that obtaining a good fit of real data is not directly related to a good prediction efficiency with future data. In predicting cases, the logistic model obtained the best precision with an error of 0.92% compared to the rest of the models studied. In deaths, the Gompertz model stood out with a minimum error of 1.14%. Finally, the ANNi model reached an error of 1.16% in the prediction of recovered cases in Algeria. .

Fuzzy rank-based fusion of CNN models using Gompertz function for screening COVID-19 CT-scans.

COVID-19 has crippled the world's healthcare systems, setting back the economy and taking the lives of several people. Although potential vaccines are being tested and supplied around the world, it will take a long time to reach every human being, more so with new variants of the virus emerging, enforcing a lockdown-like situation on parts of the world. Thus, there is a dire need for early and accurate detection of COVID-19 to prevent the spread of the disease, even more. The current gold-standard RT-PCR test is only 71% sensitive and is a laborious test to perform, leading to the incapability of conducting the population-wide screening. To this end, in this paper, we propose an automated COVID-19 detection system that uses CT-scan images of the lungs for classifying the same into COVID and Non-COVID cases. The proposed method applies an ensemble strategy that generates fuzzy ranks of the base classification models using the Gompertz function and fuses the decision scores of the base models adaptively to make the final predictions on the test cases. Three transfer learning-based convolutional neural network models are used, namely VGG-11, Wide ResNet-50-2, and Inception v3, to generate the decision scores to be fused by the proposed ensemble model. The framework has been evaluated on two publicly available chest CT scan datasets achieving state-of-the-art performance, justifying the reliability of the model. The relevant source codes related to the present work is available in: GitHub.

Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México.

The present work is focused on modeling and predicting the cumulative number of deaths from COVID-19 in México by comparing an artificial neural network (ANN) with a Gompertz model applying multiple optimization algorithms for the estimation of coefficients and parameters, respectively. For the modeling process, the data published by the daily technical report COVID-19 in Mexico from March 19th to September 30th were used. The data published in the month of October were included to carry out the prediction. The results show a satisfactory comparison between the real data and those obtained by both models with a R2 > 0.999. The Levenberg-Marquardt and BFGS quasi-Newton optimization algorithm were favorable for fitting the coefficients during learning in the ANN model due to their fast and precision, respectively. On the other hand, the Nelder-Mead simplex algorithm fitted the parameters of the Gompertz model faster by minimizing the sum of squares. Therefore, the ANN model better fits the real data using ten coefficients. However, the Gompertz model using three parameters converges in less computational time. In the prediction, the inverse ANN model was solved by a genetic algorithm obtaining the best precision with a maximum error of 2.22% per day, as opposed to the 5.48% of the Gompertz model with respect to the real data reported from November 1st to 15th. Finally, according to the coefficients and parameters obtained from both models with recent data, a total of 109,724 cumulative deaths for the inverse ANN model and 100,482 cumulative deaths for the Gompertz model were predicted for the end of 2020.

A Synergetic R-Shiny Portal for Modeling and Tracking of COVID-19 Data.

The purpose of this paper is to introduce a useful online interactive dashboard (https://mahdisalehi.shinyapps.io/Covid19Dashboard/) that visualize and follow confirmed cases of COVID-19 in real-time. The dashboard was made publicly available on 6 April 2020 to illustrate the counts of confirmed cases, deaths, and recoveries of COVID-19 at the level of country or continent. This dashboard is intended as a user-friendly dashboard for researchers as well as the general public to track the COVID-19 pandemic, and is generated from trusted data sources and built in open-source R software (Shiny in particular); ensuring a high sense of transparency and reproducibility. The R Shiny framework serves as a platform for visualization and analysis of the data, as well as an advance to capitalize on existing data curation to support and enable open science. Coded analysis here includes logistic and Gompertz growth models, as two mathematical tools for predicting the future of the COVID-19 pandemic, as well as the Moran's index metric, which gives a spatial perspective via heat maps that may assist in the identification of latent responses and behavioral patterns. This analysis provides real-time statistical application aiming to make sense to academic- and public consumers of the large amount of data that is being accumulated due to the COVID-19 pandemic.

Ensemble bootstrap methodology for forecasting dynamic growth processes using differential equations: application to epidemic outbreaks.

BACKGROUND: Ensemble modeling aims to boost the forecasting performance by systematically integrating the predictive accuracy across individual models. Here we introduce a simple-yet-powerful ensemble methodology for forecasting the trajectory of dynamic growth processes that are defined by a system of non-linear differential equations with applications to infectious disease spread. METHODS: We propose and assess the performance of two ensemble modeling schemes with different parametric bootstrapping procedures for trajectory forecasting and uncertainty quantification. Specifically, we conduct sequential probabilistic forecasts to evaluate their forecasting performance using simple dynamical growth models with good track records including the Richards model, the generalized-logistic growth model, and the Gompertz model. We first test and verify the functionality of the method using simulated data from phenomenological models and a mechanistic transmission model. Next, the performance of the method is demonstrated using a diversity of epidemic datasets including scenario outbreak data of the Ebola Forecasting Challenge and real-world epidemic data outbreaks of including influenza, plague, Zika, and COVID-19. RESULTS: We found that the ensemble method that randomly selects a model from the set of individual models for each time point of the trajectory of the epidemic frequently outcompeted the individual models as well as an alternative ensemble method based on the weighted combination of the individual models and yields broader and more realistic uncertainty bounds for the trajectory envelope, achieving not only better coverage rate of the 95% prediction interval but also improved mean interval scores across a diversity of epidemic datasets. CONCLUSION: Our new methodology for ensemble forecasting outcompete component models and an alternative ensemble model that differ in how the variance is evaluated for the generation of the prediction intervals of the forecasts.

Measuring differences between phenomenological growth models applied to epidemiology.

Phenomenological growth models (PGMs) provide a framework for characterizing epidemic trajectories, estimating key transmission parameters, gaining insight into the contribution of various transmission pathways, and providing long-term and short-term forecasts. Such models only require a small number of parameters to describe epidemic growth patterns. They can be expressed by an ordinary differential equation (ODE) of the type C'(t)=f(t,C;Θ) for t>0, C(0)=C0, where t is time, C(t) is the total size of the epidemic (the cumulative number of cases) at time t, C0 is the initial number of cases, f is a model-specific incidence function, and Θ is a vector of parameters. The current COVID-19 pandemic is a scenario for which such models are of obvious importance. In Bürger et al. (2019) it is demonstrated that some PGMs are better at fitting data of specific epidemic outbreaks than others even when the models have the same number of parameters. This situation motivates the need to measure differences in the dynamics that two different models are capable of generating. The present work contributes to a systematic study of differences between PGMs and how these may explain the ability of certain models to provide a better fit to data than others. To this end a so-called empirical directed distance (EDD) is defined to describe the differences in the dynamics between different dynamic models. The EDD of one PGM from another one quantifies how well the former fits data generated by the latter. The concept of EDD is, however, not symmetric in the usual sense of metric spaces. The procedure of calculating EDDs is applied to synthetic data and real data from influenza, Ebola, and COVID-19 outbreaks.

Impact of COVID-19 in Minas Gerais, Brazil: Excess deaths, sub-notified cases, geographic and ethnic distribution.

By analysing the evolution of the COVID-19 epidemic in the state of Minas Gerais, Brazil, we showed the importance of considering the sub-notification not only of deaths but also of infected cases. It was shown that the largely used criteria of a historical all-deaths baseline are not approachable in this case, where most of the deaths are associated with causes that should decrease due to social distancing and reduction of economic activities. A quite simple and intuitive model based on the Gompertz function was applied to estimate excess deaths and excess of infected cases. It fits well the data and predicts the evolution of the epidemic adequately. Based on these analyses, an excess of 21.638 deaths and 557.216 infected cases is predicted until the end of 2020, with an upper bound of the case fatality rate of around 2.4% and a prevalence of 2.6%. The geographical distribution of cases and deaths and its ethnic correlation are also presented. This study points out the necessity of governmental and private organizations working together to improve public awareness and stimulate social distancing to curb the viral infection, especially in critical places with high poverty.