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This study aimed to identify the productive cycle response of Italian zucchini genotypes grown under field conditions in two growing seasons using the nonlinear logistic model and its critical points. Two randomized block experiments were conducted, with three genotypes (Caserta, PX13067051, and Tronco) and two growing seasons (spring-summer and summer-fall), with eight replicates and each experimental unit consisting of 7 plants. The logistic nonlinear model was adjusted for the fruit mass variable, as a function of the accumulated thermal sum, and the critical points were estimated by the partial derivatives of the adjusted function. Adjustment by bootstrap resampling was performed to address the violation of assumptions. The results of intrinsic and parametric nonlinearity confirm the quality of the model fit. This experiment demonstrated that the zucchini genotypes evaluated were more productive in the spring-summer growing season, using the parameters and critical points obtained from the logistic nonlinear model. Genotypes PX13067051 and Caserta showed superior productivity to the Tronco genotype, and also fruited earlier and at a higher rate of production. The logistic growth model and its critical points characterized the production cycle of the zucchini genotypes in different growing seasons and allowed inferences to be made to differentiate the genotypes and the growing seasons. RESUMO O objetivo deste estudo foi identificar a resposta do ciclo produtivo de genótipos de abobrinha italiana cultivadas em condições de campo em duas épocas de cultivo por meio do modelo não linear logístico e seus pontos críticos. Para isso dois experimentos foram conduzidos em delineamento blocos ao acaso, com três genótipos (Caserta, PX13067051 e Tronco) e duas épocas de cultivo (primavera-verão e verão-outono) com oito repetições e a unidade experimental composta por 7 plantas. Ajustou-se o modelo não linear logístico para a variável massa de frutos, em função da soma térmica acumulada, e estimou-se os pontos críticos pelas derivadas parciais da função ajustada. Os pressupostos do modelo não linear não foram atendidos para nenhum genótipo em ambas as épocas avaliadas, e para contornar este problema foi realizado o ajuste por reamostragens bootstrap. Os resultados de não linearidade intrínseca e paramétrica confirmam a qualidade do ajuste do modelo. Pelos parâmetros e pontos críticos do modelo foi possível determinar que os genótipos de abobrinha italiana avaliados foram mais produtivos na primavera-verão. Os genótipos PX13067051 e Caserta apresentaram produtividade superior ao genótipo Tronco, além de serem mais precoces e apresentar maiores taxas de produção. O modelo de crescimento logístico e seus pontos críticos foram capazes de caracterizar o ciclo de produção dos genótipos de abobrinha italiana em diferentes épocas de cultivo, e permitiu que inferências fossem realizadas com vistas a diferenciar os genótipos e as épocas de cultivo avaliadas.

We apply a generalized logistic growth model, with time dependent parameters, to describe the fatality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. In the case of two waves only, the model parameters vary as a function of time according to a logistic function, whose two extreme values, i.e., for early and late times, characterize the first and second waves, respectively. For the multiple-wave model, the time-dependency of the parameters is likewise described by a multi-step logistic function with N intermediate plateaus, representing the N waves of the epidemic. We show that the theoretical curves are in excellent agreement with the empirical data for all countries considered here, namely: Brazil, Canada, Germany, Iran, Italy, Japan, Mexico, South Africa, Sweden, and US. The model also allows for predictions about the time of occurrence and severity of the subsequent waves. It is shown furthermore that the subsequent waves of COVID-19 can be generically classified into two main types, namely, standard and anomalous waves, according as to whether a given wave starts well after or well before the preceding one has subsided, respectively.

The paper is devoted to the forecasting of the COVID-19 epidemic by the novel method of randomized machine learning. This method is based on the idea of estimation of probability distributions of model parameters and noises on real data. Entropy-optimal distributions correspond to the state of maximum uncertainty which allows the resulting forecasts to be used as forecasts of the most “negative” scenario of the process under study. The resulting estimates of parameters and noises, which are probability distributions, must be generated, thus obtaining an ensemble of trajectories that considered to be analyzed by statistical methods. In this work, for the purposes of such an analysis, the mean and median trajectories over the ensemble are calculated, as well as the trajectory corresponding to the mean over distribution values of the model parameters. The proposed approach is used to predict the total number of infected people using a three-parameter logistic growth model. The conducted experiment is based on real COVID-19 epidemic data in several countries of the European Union. The main goal of the experiment is to demonstrate an entropy-randomized approach for predicting the epidemic process based on real data near the peak. The significant uncertainty contained in the available real data is modeled by an additive noise within 30%, which is used both at the training and predicting stages. To tune the hyperparameters of the model, the scheme is used to configure them according to a testing dataset with subsequent retraining of the model. It is shown that with the same datasets, the proposed approach makes it possible to predict the development of the epidemic more efficiently in comparison with the standard approach based on the least-squares method. © St. Petersburg Federal Research Center of the Russian Academy of Sciences.

At the end of 2019, the COVID-19 disease emerged in the city of Wuhan, China, and caused an outbreak of unusual viral pneumonia. Being highly transmissible, this novel coronavirus disease has spread fast all over the world. COVID-19 continues to challenge most developed countries in the search for an effective strategy to either prevent infection or to avoid the spreading of the disease. While several developed countries have managed to contain COVID-19, several countries in Latin America continue to report an increase in the daily number of infected people. Ecuador, particularly, became the epicenter of the COVID-19 outbreak in the region during March and April 2020. In this context, the present study shows a simple mathematical approach to understand the effect of the COVID-19 outbreak in Ecuador (and some Latin American countries such as Brazil, Peru, and Colombia). The proposed method is based on the exponential model, discrete logistic equation, and differential logistic model using one-year data from March 1, 2020, to February 28, 2021. This study presents the estimated growth rate coefficient (λ), the total number of cases (N), and the midpoint of maximum infection (t_0) as well as the variability of the λ coefficient as a function of total cases and time. The exponential model shows a high value of λ=0.185 which decreases to λ=0.014 and λ=0.056 according to the discrete and differential logistic models, respectively. An accurate value of the total number of cases of infected people was found by analyzing the number of daily cases as a function of the total of cases whose value (N~409 K) agrees with the data reported at the end of May 2021, validating the proposed approach. How to use the current mathematical approach for long-term prediction is also discussed here. Most importantly, the proposed method has two important characteristics: (i) the mathematical model is as simple as possible compared to other time-consuming approaches, and (ii) it can be used to study the effect of COVID-19 and predicts its consequences in other countries, allowing revenue new decisions against the COVID-19 disease. Doi: 10.28991/esj-2021-SPER-09 Full Text: PDF

Starting February 2020, COVID-19 was confirmed in 11,946 people worldwide, with a mortality rate of almost 2%. A significant number of epidemic diseases consisting of human Coronavirus display patterns. In this study, with the benefit of data analytic, we develop regression models and a Susceptible-Infected-Recovered (SIR) model for the contagion to compare the performance of models to predict the number of cases. First, we implement a good understanding of data and perform Exploratory Data Analysis (EDA). Then, we derive parameters of the model from the available data corresponding to the top 4 regions based on the history of infections and the most infected people as of the end of August 2020. Then models are compared, and we recommend further research.

Accurate prediction of tropical cyclone (TC) intensity remains a challenge due to the complex physical processes involved in TC intensity changes. A seven-day TC intensity prediction scheme based on the logistic growth equation (LGE) for the western North Pacific (WNP) has been developed using the observed and reanalysis data. In the LGE, TC intensity change is determined by a growth term and a decay term. These two terms are comprised of four free parameters which include a time-dependent growth rate, a maximum potential intensity (MPI), and two constants. Using 33 years of training samples, optimal predictors are selected first, and then the two constants are determined based on the least square method, forcing the regressed growth rate from the optimal predictors to be as close to the observed as possible. The estimation of the growth rate is further refined based on a step-wise regression (SWR) method and a machine learning (ML) method for the period 1982–2014. Using the LGE-based scheme, a total of 80 TCs during 2015–17 are used to make independent forecasts. Results show that the root mean square errors of the LGE-based scheme are much smaller than those of the official intensity forecasts from the China Meteorological Administration (CMA), especially for TCs in the coastal regions of East Asia. Moreover, the scheme based on ML demonstrates better forecast skill than that based on SWR. The new prediction scheme offers strong potential for both improving the forecasts for rapid intensification and weakening of TCs as well as for extending the 5-day forecasts currently issued by the CMA to 7-day forecasts.

[EN] This paper presents a methodology to deal with the randomness associated to ecological modelling. Data variability makes it necessary to analyse the impact of random perturbations on the fitted model parameters. We conduct such analysis for the logistic growth model with a certain sigmoid functional form of the carrying capacity, which was proposed in the literature for the study of parasite growth during infection. We show how the probability distributions of the parameters are set via the maximum entropy principle. Then the random variable transformation method allows for computing the density function of the population., Spanish Ministerio de Economia y Competitividad, Grant/Award Number: PID2020-115270GB-I00; Agencia Estatal de Investigacion

There are different models used for enrolment projection in the education system. Of them ARIMA, double exponential, logistic curve method, reconstructive cohort, and regression model, method are commonly used. Every model has its suitability under certain conditions and with prior assumptions. In India, no attempt was made to estimate enrolment except in 1996. The logistic curve method was adopted to estimate enrolment between 1996 – 2001. In the present situation, an attempt has been made to estimate school enrolment for the next years. The present paper discusses fitting the best model for estimating enrolment for the next few years.

The current study aimed to estimate the growth curve parameters through three non-linear models (logistic, Gompertz and Richards) to determine which model best fits the data. A total number of 1566 monthly live weight records of 87 Holstein- Friesian bulls collected between 2017-2019 from a Holstein-Friesian herd cattle that belongs to the Association of Livestock Development (EL- Lahhamy farm), located thirty kilometers west of Fayoum governrate. In this work, the parameters of studied models, asymptotic weight (A), Constant of integration (b), and the maturation rate (K) ranged from 626.15 kg to 879.82 kg, 2.708 to 11.08, and 0.0035 to 0.008, respectively. According to the studied parameters of growth functions, Gompertz reached the highest numerical estimated value for (A) and the Logistic function had the lowest value. Parameter (K) estimate by the Gompertz model was similar to that obtained by the Richards model; both values were lower than those attained through the Logistic model (0.008). The inflection point traits, time at Point of inflection (IPT) and weight at Point of inflection (IPW) estimates ranged from 300.64 kg to 314.59 kg and 323.92 days to 336.14 days, respectively. The Richards model has the highest estimates of IPW and IPT compared to the other models, also it had the best adjustment according to model goodness of fit criteria, by having the lowest values for Akaike information criterion (AIC), Schwarz Bayesian information criterion( BIC), Mean square error (MSE) and highest : coefficient of determination (R 2 ) 82236.80, 83265.51, 317.37 and 0.9983.

A kinetic model has been proposed for the spread of epidemics, describing the dynamics of the variation in the number of disease-free, infected, and recovered (SIR) cases, based on a lag logistic equation. It has been established that this model predicts the possibility of existence of a quasi-steady-state mode of an epidemic in which the number of infected cases is constant due to the balance of the daily increment of infections and recoveries. Conditions have been identified under which such a mode can be a source of the advance of the second epidemic wave. The COVID-19 pandemic data were used to show the possibility of reliable forecasts based on this model of the spread of an epidemic for a period of up to two months.

World is now experiencing the new pandemic caused by COVID-19 virus and all countries are affected by this disease specially Iran. From the beginning of the outbreak until April 30, 2020, over 90,000 confirmed cases of COVID-19 have been reported in Iran. Due to socio-economic problems of this disease, it is required to predict the trend of the outbreak and propose a beneficial method to find out the correct trend. In this paper, we compiled a dataset including the number of confirmed cases, the daily number of death cases and the number of recovered cases. Furthermore, by combining case number variables like behavior and policies that are changing over time and machine-learning (ML) algorithms such as logistic function using inflection point, we created new rates such as weekly death rate, life rate and new approaches to mortality rate and recovery rate. Gaussian functions show superior performance which is helpful for government to improve its awareness about important factors that have significant impacts on future trends of this virus.

The COVID-19 pandemics challenges governments across the world. To develop adequate responses, they need accurate models for the spread of the disease. Using least squares, we fitted Bertalanffy-Putter (BP) trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed. BP-models achieved excellent fits (R-squared above 99%) to all data. Using them to smoothen the data, in the median one could forecast that the final count (asymptotic limit) of infections and fatalities would be 2.48 times (95% confidence limits 2.42–2.6) and 2.67 times (2.39–2.765) the total count at the respective peak (inflection point). By comparison, using logistic growth would evaluate this ratio as 2.00 for all data. The case fatality rate, defined as the quotient of the asymptotic limits of fatalities and confirmed infections, was in the median 4.85% (confidence limits 4.4%–6.5%). Our result supports the strategies of governments that kept the epidemic peak low, as then in the median fewer infections and fewer fatalities could be expected.

In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay.

The objective of this study was to determine the best model that describe the pattern of cayenne pepper productivity in Magelang Regency. This study uses primary data which was obtained from the results of a survey of cayenne pepper production by the General Director of Horticulture on several sample plots in Magelang District, Central Java Province in 2018. The process of data analysis was divided into two parts: grouping the sample plots based on the similarity in productivity pattern and then fitting models in each group. The models used to fit data were Logistic Growth Model, Monomolecular Growth Model, Exponential Growth Model, Polynomial Model and Linear B-Spline Model. The best model was determined based on R2 and MAPE. The results showed that the pattern of cayenne pepper productivity in Magelang District had eight different characteristics. Characteristics of each groups were illustrated by the similarity of their productivity pattern. The best model in each group was B-Spline Linear Model.

The effect of temperature on the rate of spotted lanternfly, Lycorma delicatula (White) (Hemiptera: Fulgoridae), egg development was investigated for a population in Pennsylvania. Mean developmental duration (days ± SE) for egg hatch was evaluated at five constant temperatures of 19.9, 24.2, 25.1, 26.7, and 30°C using egg masses laid during the fall of 2018 and collected in 2019 from Berks Co., Pennsylvania. Base temperature thresholds for egg development were estimated using intercept and slope parameters by fitting a linear relationship between average temperature and developmental rate for the Pennsylvania study, two Korean studies, and the combined data sets. The base threshold estimates were then used to calculate seasonal accumulated degree-days (ADD) and construct logistic equations for predicting cumulative proportion of hatch in the spring. The fitted logistic prediction equations were then graphed against the egg hatch observations from field sites in Pennsylvania (2017) and Virginia (2019). When base temperature estimates from the three studies and combined studies were used to calculate ADD, the logistic models predicted similar timing for seasonal egg hatch. Because the slopes and intercepts for these four data sets were not statistically different, a base temperature threshold of 10.4°C derived from the combined model is a good estimate for computing ADD to predict spotted lanternfly spring emergence across a spatio-temporal scale. The combined model was linked with open source weather database and mapping programs to provide spatiotemporal prediction maps to aid pest surveillance and management efforts for spotted lanternfly.

Since the first cases of Covid-19 (Corona Virus Disease-19) infection were officially recognized and recorded in Indonesia on March 2, 2020 and March 1, 2020 in Armenia, the addition of new cases has not shown any indication of sloping. The relatively high number of new cases indicates that Indonesia has not yet passed the peak of the pandemic. As for Armenia, the addition of new cases indicates a new pandemic peak to be faced. In these conditions, an important question for decision makers (the Government) to find answers to is when and at what level of total cases will the COVID-19 pandemic end in Indonesia or the second wave in Armenia. Based on this, the forecasting method of Hybrid Nonlinear Regression With Modified Logistic Growth Model - Double Smoothing Exponential and Classical methods is used to predict the Covid-19 cases that occur in Indonesia and Armenia. Based on the model formed, the peak of Covid-19 cases in Indonesia is predicted to occur on November 26, 2020, with the number of cases reaching 5968 cases. As for Armenia, the peak of Covid-19 cases will occur on November 15, 2020, with the number of cases reaching 3098 cases. Covid-19 in both countries is predicted to decline and be constant in 2021. For the country, Indonesia is predicted to begin to stabilize and be controlled in July - August 2021. As for Armenia, Covid-19 is predicted to be under control and approaching 0 cases in February - March 2021.

This study presents a prediction model based on Logistic Growth Curve (LGC) to evaluate the effectiveness of Movement Control Order (MCO) on COVID-19 pandemic spread. The evaluation assesses and predicts the growth models. The estimated model is a forecast-based model that depends on partial data from the COVID-19 cases in Malaysia. The model is studied on the effectiveness of the three phases of MCO implemented in Malaysia, where the model perfectly fits with the R2 value 0.989. Evidence from this study suggests that results of the prediction model match with the progress and effectiveness of the MCO to flatten the curve, and thus is helpful to control the spike in number of active COVID-19 cases and spread of COVID-19 infection growth.

Developing a simplified estimation method without compromising the performance of the distribution is germane to forest modelling. Few estimation methods exist for the Log-Logistic distribution and are relatively complex. A simplified estimator for the Log-Logistic parameters will increase its application in diameter distribution yield systems. Therefore, in this study, a percentile-based estimator was applied for the Log-Logistic distribution. The Kolmogorov-Smirnov, Anderson-Darling and Cramer-von Mises statistics were used to evaluate the method in two natural forest stands and two monospecific plantations of Gmelina arborea Roxb. and Tectona grandis Linn. f. in Nigeria. The parameter recovery model (PRM) and parameter prediction model (PPM) were used to predict the diameter distributions of independent stands of G. arborea and T. grandis. The results showed that the percentile estimator did not compromise the quality of fits of the Log-Logistic function across the four forest stands and are comparable to the maximum likelihood estimator. The 25th and 75th, and 40th and 80th were the best sample percentiles for the estimator. The predicted diameter distributions of G. arborea and T. grandis stands from the PRM and PPM were reasonable and compare well with the observed distribution. Thus, either of the models can be incorporated into the growth and yield system of forest stand management.

This research aims to predict the end of the COVID-19 pandemic in Indonesia based on parametric growth models. The models are chosen by considering their fitness with the data of Taiwan which is believed to have passed over the peak of the pandemic and have gone through all phases in the growth curves. The models are parameterized using the nonlinear least squares method. The deviation and confidence interval of each parameter is estimated using the k-fold cross-validation and the bootstrap techniques. Using the total cases per million population data from March 2 to June 18, 2020, it was found that two growth models fit the data, i.e. logistic and modified Gompertz, where the latter performs better. Using the information about the deviation of each model parameter, a simulation model is developed to predict the time at which the total cases curve starts to flatten, which is an indication of the end of the pandemic. It was found with 95% confidence level that based on the modified Gompertz model the pandemic will end somewhere between March 9 – September 7, 2021 with total cases per million of 206 - 555. Meanwhile, based on the logistic growth model, the end of the pandemic is between August 28 – September 23, 2020 with total cases per million of 180 - 375. This model can be extended by making comparative scenario with Taiwan based on measures that represent the quality of the pandemic mitigation such as test ratio and the intensity of social restriction.

Backgrounds The novel coronavirus disease (COVID‐19) poses serious threat to global public health and economics. Serial interval (SI), time between the symptom onsets of a primary case and a second case, is a key epidemiological parameter. We estimated SI of COVID‐19 in Shenzhen, China based on 27 records of transmission chains. Methods We adopted three parametric models: Weibull, Lognormal and Gamma distributions and an interval censored likelihood framework. The three models were compared using the corrected Akaike information criterion (AICc). We also fitted the epidemic curve of COVID‐19 to the exponential growth to estimate the reproduction number. Findings Using a Weibull distribution, we estimated mean SI at 5.9 days (95%CI: 3.9−9.6) and a standard deviation (SD) at 4.8 days (95%CI: 3.1−10.1). Using a logistic growth model, we estimated the basic reproduction number in Shenzhen at 2.6 (95%CI: 2.4−2.8). Conclusion The SI of COVID‐19 is relative shorter than that of SARS and MERS, other two beta coronavirus diseases, which suggests the iteration of the transmission was rapid. It is crucial to isolate close contacts promptly to control the spread of COVID‐19 effectively.

A new growth modeling approach is proposed to can fit inherently nonlinear (i.e., logistic) function without constraint nor reparameterization. A simulation study is employed to investigate the feasibility and performance of a Markov chain Monte Carlo method within Bayesian estimation framework to estimate a fully random version of a logistic growth curve model under manipulated conditions such as the number and timing of measurement occasions and sample sizes.

The present study demonstrates the growth of Chemistry literature for the period 2005-2016. A total of 24322 records were extracted from the Scopus Database for twelve years which is used as main source of primary data for the present study. The growth models were applied for the literature of Chemistry. The result of the study indicates that, the Relative Growth Rate (RGR) of Chemistry publication found to be decreasing trend and Doubling Time (Dt) found to be increasing trend. The growth of literature in the field of Chemistry does not follow either Polynomial or Power growth model. The study concluded that there has consistent trend in the growth of Chemistry literature. The study can be concluded that chemical literature follows the moderately follows Linear growth, Exponential growth and Logistic growth model. Keywords: Scientometrics, Chemistry Literature, Relative Growth rate (RGR), Doubling Time (Dt), Growth Models Cite this Article Mahadevi R Nyamagoudar, Gavisiddappa Anandhalli. Modelling The Growth of Chemistry Literature from 2005-2016: A Scientometric Study. Journal of Advancements in Library Sciences. 2020; 7(1): 83–90p.

In this study, a new regression method called Kappa regression is introduced to model conditional probabilities. The regression function is based on Dombi’s Kappa function, which is well known in fuzzy theory. Here, we discuss how the Kappa function relates to the Logistic function as well as how it can be used to approximate the Logistic function. We introduce the so-called Generalized Kappa Differential Equation and show that both the Kappa and the Logistic functions can be derived from it. Kappa regression, like binary Logistic regression, models the conditional probability of the event that a dichotomous random variable takes a particular value at a given value of an explanatory variable. This new regression method may be viewed as an alternative to binary Logistic regression, but while in binary Logistic regression the explanatory variable is defined over the entire Euclidean space, in the Kappa regression model the predictor variable is defined over a bounded subset of the Euclidean space. We will also show that asymptotic Kappa regression is Logistic regression. The advantages of this novel method are demonstrated by means of an example, and afterwards some implications are discussed.

Cholera is an infection of the small intestine of humans caused by a gram-negative bacterium called Vibrio cholerae. It is spread through eating food or drinking water contaminated with faeces from an infected person. It causes rapid dehydration and general body imbalance, and can lead to death since untreated individuals suer severely from diarrhea and vomiting. Its dynamics involves multiple interaction between the human host, the pathogen and the environment which contributes to both human to human and indirect environment to human transmission pathways. Rehydration is critical in reducing cholera death. This has been studied by other scholars but they did not consider delay in rehydration on the spread of cholera. In this paper, I formulate a mathematical model based on system of ordinary differential equation with rehydration on the spread of cholera in a logistically growing population. The existence of the steady states and the basic reproduction number is established such that disease free equilibrium point exists. Determination of endemic equilibrium shows that the model has positive points. The findings will be signicant in the sense that timely rehydration should be done during cholera outbreak and will enable individuals with symptoms to seek immediate medical attention.

Avian Influenza, with a high mortality rate in human population, is considered to be one of the most significant potential threats to human beings. Based on a recent avian influenza SI-SIR model with logistic growth for birds, we propose a stochastic model with generalized incidence rate. For the stochastic avian-only system, sufficient conditions for the extinction of infected birds are established, and the existence of a unique ergodic stationary distribution is also obtained. For the stochastic avian-human system, a threshold number is established, and hence the extinction of disease is investigated. From the viewpoint of biology, the noise intensity in the infected birds plays a key role in the evolutionary dynamics. Moreover, we also analyze the asymptotic behavior around the endemic equilibrium of the corresponding deterministic model.

Coronavirus disease 2019 outbreak has spread as a pandemic since the end of year 2019 This situation has been causing a lot of problems of human beings such as economic problems, health problems The forecasting of the number of infectious people is required by the authorities of all countries including Southeast Asian countries to make a decision and control the outbreak This research is to investigate the suitable forecasting model for the number of infectious people in Southeast Asian countries A comparison of forecasting models between logistic growth curve which is symmetric and Gompertz growth curve which is asymmetric based on the maximum of Coefficient of Determination and the minimum of Root Mean Squared Percentage Error is also proposed The estimation of parameters of the forecasting models is evaluated by the least square method In addition, spreading of the outbreak is estimated by the derivative of the number of cumulative cases The findings show that Gompertz growth curve is a suitable forecasting model for Indonesia, Philippines, and Malaysia and logistic growth curve suits the other countries in South Asia © 2020 Tech Science Press All rights reserved

Lifetime analyses frequently apply a parametric functional description from measured data of the Kaplan-Meier non-parametric estimate (KM) of the survival probability. The cumulative Weibull distribution function (WF) is the primary choice to parametrize the KM. but some others (e.g. Gompertz, logistic functions) are also widely applied. We show that the cumulative two-parametric Weibull function meets all requirements. The Weibull function is the consequence of the general self-organizing behavior of the survival, and consequently shows self-similar death-rate as a function of the time. The ontogenic universality as well as the universality of tumor-growth fits to WF. WF parametrization needs two independent parameters, which could be obtained from the median and mean values of KM estimate, which makes an easy parametric approximation of the KM plot. The entropy of the distribution and the other entropy descriptions are supporting the parametrization validity well. The goal is to find the most appropriate mining of the inherent information in KM-plots. The two-parameter WF fits to the non-parametric KM survival curve in a real study of 1180 cancer patients offering satisfactory description of the clinical results. Two of the 3 characteristic parameters of the KM plot (namely the points of median, mean or inflection) are enough to reconstruct the parametric fit, which gives support of the comparison of survival curves of different patient’s groups.

In the spirit of punctuated equilibrium, complexity is quantified relatively in terms of the spacing between equally important evolutionary turning points (milestones). Thirteen data sets of such milestones, obtained from a variety of scientific sources, provide data on the most important complexity jumps between the big bang and today. Forecasts for future complexity jumps are obtained via exponential and logistic fits on the data. The quality of the fits and common sense dictate that the forecast by the logistic function should be retained. This forecast stipulates that we have already reached the maximum rate of growth for complexity, and that in the future, complexity's rate of change (and the rate of change in our lives) will be declining. One corollary is that we are roughly halfway through the lifetime of the universe. Another result is that complexity's rate of growth has built up to its present high level via seven evolutionary subprocesses, themselves amenable to logistic description.

BackgroundIt is shown that tumour volume distributions, can yield information on two aspects of cancer research: tumour induction and tumour control.Materials and methodsFrom the hypothesis that the intrinsic distribution of breast cancer volumes follows an exponential distribution, firstly the probability density function of tumour growth time was deduced via a mathematical transformation of the probability density functions of tumour volumes. In a second step, the distribution of tumour volumes was used to model the variation of the clonogenic cell number between patients in order to determine tumour control probabilities for radiotherapy patients.ResultsDistribution of lag times, i.e. the time from the appearance of the first fully malignant cell until a clinicaly observable cancer, can be used to deduce the probability of tumour induction as a function of patient age. The integration of the volume variation with a Poisson-TCP model results in a logistic function which explains population-averaged survival data of radiotherapy patients.ConclusionsThe inclusion of tumour volume distributions into the TCP formalism enables a direct link to be deduced between a cohort TCP model (logistic) and a TCP model for individual patients (Poisson). The TCP model can be applied to non-uniform tumour dose distributions.

Logistic growth regressions present high uncertainties when data are not past their inflection points. In such conditions, the uncertainty in the estimated carrying capacity K, for example, can be of the order of K. Here, we present a method for uncertainty reduction in logistic growth regression using data from a surrogate logistic growth process. We illustrate the method using Richards’ growth function to predict the inflection points of COVID-19 first-wave accumulated causalities in Brazilian cities. First waves of epidemics are known to be reasonably well modeled a posteriori by Richard’s growth function. Yet, we make predictions using early data that end before or around the inflection point. For that goal, we estimate K by logistic growth regression using data from surrogate international cities where the epidemics are clearly past their inflection points. The constraint stabilizes the logistic growth regression for the Brazilian cities, reducing the uncertainty in the prediction parameters even when the surrogate K is a rough estimate. The predictions for COVID-19 first-wave peaks in Brazilian cities agree with official data. The method may be used for other logistic models and logistic processes, in areas such as economics and biology, when surrogate populations or systems are identified.

This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

In this article, we study a fractional control problem that models the maximization of the profit obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this problem, we develop different resolution techniques, both for the classical case and for the fractional case. We perform several numerical simulations to make a comparison between both cases.

In this paper, we introduce the logit Pearson type III distribution and we utilize it, for first time in the literature, to investigate the statistical behavior of wireless power transfer, assuming that the harvested energy follows a well-established nonlinear energy harvesting (EH) model based on the logistic function. Specifically, we present closed-form expressions for the statistical properties of the introduced logit Pearson type III distribution, e.g., the cumulative distribution function (CDF), the probability density function and the moments and we utilize this distribution to define the logit gamma distribution. Furthermore, taking into account that the logit Pearson type III distribution is closely related to the considered nonlinear EH model the statistical properties of the distribution of the harvested power are derived. These expressions are of high practical value, since useful insights for the EH system can be extracted through the evaluation of the CDF, as well as the average harvested power and the variance.

The size will be approximately 5100 ± 130 cases. The discrepancy of actual and forecasted number of cases is within 3%. However, actual and predicted daily new cases are scattered and vary between 26% to 600%. Prediction is cumulative 3993 cases and 29 daily cases. The errors are 7.413% and 48.276% for cumulative and daily cases, respectively.

A simple model for predicting Coronavirus Disease 2019 (COVID-19) epidemic is presented in this study. The prediction model is presented based on the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to describe the epidemic time evolution of infectious diseases. The original version of the Kermack and McKendrick model is used in this study. This included the daily rates of infection spread by infected individuals when these individuals interact with a susceptible population, which is denoted by the parameter β, while the recovery rates to determine the number of recovered individuals is expressed by the parameter γ. The parameters estimation of the three-compartment SIR model is determined through using a mathematical sequential reduction process from the logistic growth model equation. As the parameters are the basic characteristics of epidemic time evolution, the model is always tested and applied to the latest actual data of confirmed COVID-19 cases. It seems that this simple model is still reliable enough to describe the dynamics of the COVID-19 epidemic, not only qualitatively but also quantitatively with a high degree of correlation between actual data and prediction results. Therefore, it is possible to apply this model to predict cases of COVID-19 in several countries. In addition, the parameter characteristics of the classic SIR model can provide information on how these parameters reflect the efforts by each country to prevent the spread of the COVID-19 outbreak. This is clearly seen from the changes of the parameters shown by the classic SIR model.

The novel coronavirus 2019 (COVID-19) pandemic was declared a global health crisis. The real-time accurate and predictive model of the number of infected cases could help inform the government of providing medical assistance and public health decision-making. This work is to model the ongoing COVID-19 spread in Thailand during the 1st and 2nd phases of the pandemic using the simple but powerful method based on the model-free and time series regression models. By employing the curve fitting, the model-free method using the logistic function, hyperbolic tangent function, and Gaussian function was applied to predict the number of newly infected patients and accumulate the total number of cases, including peak and viral cessation (ending) date. Alternatively, with a significant time-lag of historical data input, the regression model predicts those parameters from 1-day-ahead to 1-month-ahead. To obtain optimal prediction models, the parameters of the model-free method are fine-tuned through the genetic algorithm, whereas the generalized least squares update the parameters of the regression model. Assuming the future trend continues to follow the past pattern, the expected total number of patients is approximately 2,689 - 3,000 cases. The estimated viral cessation dates are May 2, 2020 (using Gaussian function), May 4, 2020 (using a hyperbolic function), and June 5, 2020 (using a logistic function), whereas the peak time occurred on April 5, 2020. Moreover, the model-free method performs well for long-term prediction, whereas the regression model is suitable for short-term prediction. Furthermore, the performances of the regression models yield a highly accurate forecast with lower RMSE and higher R2 up to 1-week-ahead. HIGHLIGHTS COVID-19 model for Thailand during the first and second phases of the epidemic The model-free method using the logistic function, hyperbolic tangent function, and Gaussian function applied to predict the basic measures of the outbreak Regression model predicts those measures from one-day-ahead to one-month-ahead The parameters of the model-free method are fine-tuned through the genetic algorithm GRAPHICAL ABSTRACT

This work explores how the Portuguese population fits a logistic growth model. The present study is divided into two main sections. The first one consists on the qualitative and quantitative study of the logistic equation. Qualitatively, I will look at various aspects of the differential equation, such as the equilibria and their stability and possible inflections of solutions. Quantitatively, I will use the separation of variables to find explicit solutions. Given the lack of accuracy in the linear fitting to the proportional growth rate against the population, in second chapter, I attempted a polynomial trendline fitting to the growth rate against the population. This led the focus to creating an adapted form of the logistic curve that fits the Portuguese population from 1850 to 2010. With a certain degree of accuracy, the adapted form of the logistic growth model fits the Portuguese population in the period mentioned.

Coronavirus disease 2019 (COVID-19) continues to spread worldwide since its emergence in December 2019 in Wuhan, China, and as of January 3, 2021 more than 84.4 million cases and 1.8 million deaths have been reported. To predict COVID-19 cases in Algeria, we applied two models—the logistic growth model and the polynomial regression model—using the data on COVID-19 cases reported by the Algerian Ministry of Health from February 25 to December 2, 2020. Results showed that the polynomial regression model better fitted the data of COVID-19 in Algeria compared with the logistic model. The first model estimated the number of cases on January 19, 2021 to reach 387,673. This model can help Algerian authorities in the fight against this disease.

Since December 2019, the world has been facing an emerging infectious disease named coronavirus disease 2019. Thailand has also been affected by the spread of the coronavirus. The Thai government have announced policies to protect people, based on the emergency decree and curfew law for flattening the curve of the number of the coronavirus disease 2019 cases without vaccination in Thailand. This research estimated of the number of total infectious cases of coronavirus disease 2019 in Thailand. Two growth curves, including an exponential growth curve under a non-flattened curve policy (herd immunity policy without vaccination), and a logistic growth curve under a flattened curve policy without vaccination, were selected to estimate the parameters of the curves by the least square method to represent the number of the total infectious cases in Thailand. Moreover, the maximum infectious cases of coronavirus disease 2019 and the speed of spreading for coronavirus disease 2019 in Thailand were also explored. Based on the number of the total infectious cases of coronavirus disease 2019 in Thailand, the findings demonstrated that the coefficient of determination of the logistic growth curve was greater than the exponential growth curve and the root means squared percentage error of the logistic growth curve was less than the exponential growth curve. These results suggest that the logistic growth curve is suitable for describing the number of total infectious cases of coronavirus disease 2019 in Thailand under the fattened curve policy. [ABSTRACT FROM AUTHOR] Copyright of Walailak Journal of Science & Technology is the property of Walailak Journal of Science & Technology 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 abstract 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 abstract. (Copyright applies to all Abstracts.)