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In topological dynamical systems (TDS), recurrence (periodic–like recurrence) is one of the important concepts in its studies but one major problem is the inability to demonstrate and/or illustrate its formation in the orbit structure of system from a topological point of view. In this paper, the logistic function was applied to demonstrate the periodic point as a recurrent formation (periodic–like recurrence) in the topological dynamical system and dynamical system. The Wolfram Alpha computational knowledge engine was used in obtaining the tables and the figures for the study through various examples of the logistic function. The study shows that period – 2 recurrence is formed when the trajectory of the function is made up of two different values that keep repeating after successive iterations as a result of the period – 2 orbits when the parameter of the function is between 3 and 3.45. The study again shows that when the parameter of the function is greater than 3.83 there is a period – 3 point hence the formation of other periodic points. Convincingly, beyond this period – 3 is another subsequent period called the period-doubling cascade leading into chaos. This period-doubling asserts that other periodic–like recurrences are also present, hence period –n recurrent exists.

The aim of this paper is to establish the stability results based on the approach of Linear Matrix Inequality (LMI) for the addressed mathematical model using Caputo–Fabrizio operator (CF operator). Firstly, we extend some existing results of Caputo fractional derivative in the literature to a new fractional order operator without using singular kernel which was introduced by Caputo and Fabrizio. Secondly, we have created a mathematical model to increase Cytoplasmic Incompatibility (CI) in Aedes Aegypti mosquitoes by releasing Wolbachia infected mosquitoes. By this, we can suppress the population density of A.Aegypti mosquitoes and can control most common mosquito-borne diseases such as Dengue, Zika fever, Chikungunya, Yellow fever and so on. Our main aim in this paper is to examine the behaviours of Caputo–Fabrizio operator over the logistic growth equation of a population system then, prove the existence and uniqueness of the solution for the considered mathematical model using CF operator. Also, we check the α -exponential stability results for the system via linear matrix inequality technique. Finally a numerical example is provided to check the behaviour of the CF operator on the population system by incorporating the real world data available in the known literature.

RESUMEN La tarea de proyectar el número de los habitantes está basada en cálculos rigurosos, en el conocimiento previo sobre los comportamientos de las variables demográficas que implican entradas de población o salidas. El objetivo del presente artículo consistió en presentar un método estadístico para realizar estimaciones de proyecciones demográficas, mostrando sus aspectos metodológicos y técnicos, con el objeto de que los no demógrafos cuenten con los elementos necesarios para su estimación. Lo anterior se logró a través del uso de la Función Logística, llevando al lector paso por paso con el objeto de que sea claro el procedimiento a seguir; posteriormente, para ello se lleva a cabo un ejercicio de proyección utilizando como ejemplo datos para la población joven (15 a 29 años) en la Zona Metropolitana del Valle de México (ZMVM). Los resultados muestran que en 2050 el número de jóvenes en la ZMVM alcanzará la cifra de 5,2 millones, lo que corresponde a un decremento de 0,76%. Esto indica que, dentro de aproximadamente 30 años, todavía el número de jóvenes de la ZMVM será alto (22,27% del total de la población de dicha zona). Se concluye que al usar la función logística se puede obtener una buena estimación en las proyecciones de población, en general y por grandes grupos de edad. ABSTRACT The task of projecting the number of inhabitants is based on rigorous calculations, on prior knowledge about the behavior of demographic variables that imply population entries or exits. The objective of this article was to present a statistical method for estimating demographic projections, showing its methodological and technical aspects, so that non-demographers have the necessary elements for their estimation. The above was achieved through the use of the Logistics Function, taking the reader step by step in order to make the procedure to follow clear; Subsequently, for this purpose, a projection exercise is carried out using data for the young population (15 to 29 years old) in the Metropolitan Zone of the Valley of Mexico (ZMVM) as an example. The results show that in 2050 the number of young people in the ZMVM will reach 5.2 million, which corresponds to a decrease of 0.76%. This indicates that, within approximately 30 years, the number of young people in the ZMVM will still be high (22.27% of the total population of said area). It is concluded that by using the logistic function an acceptable estimate can be obtained in population projections, in general and by large age groups.

We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann condition that we take into account comprises, as a particular case, the one that has been recently introduced in [S. Dipierro, X. Ros-Oton, E. Valdinoci, Rev. Mat. Iberoam. (2017)]. Also, the results that we present here find a natural application to a logistic equation motivated by biological problems that has been recently considered in [S. Dipierro, E. Proietti Lippi, E. Valdinoci, preprint (2020)].

Novel coronavirus respiratory disease COVID-19 has caused havoc in many countries across the globe. In order to contain infection of this highly contagious disease, most of the world population is constrained to live in a complete or partial lockdown for months together with a minimal human-to-human interaction having far reaching consequences on countries' economy and mental well-being of their citizens. Hence, there is a need for a good predictive model for the health advisory bodies and decision makers for taking calculated proactive measures to contain the pandemic and maintain a healthy economy. This paper extends the mathematical theory of the classical Susceptible-Infected-Removed (SIR) epidemic model and proposes a Generalized SIR (GSIR) model that is an integrative model encompassing multiple waves of daily reported cases. Existing growth function models of epidemic have been shown as the special cases of the GSIR model. Dynamic modeling of the parameters reflect the impact of policy decisions, social awareness, and the availability of medication during the pandemic. GSIR framework can be utilized to find a good fit or predictive model for any pandemic. The study is performed on the COVID-19 data for various countries with detailed results for India, Brazil, United States of America (USA), and World. The peak infection, total expected number of COVID-19 cases and thereof deaths, time-varying reproduction number, and various other parameters are estimated from the available data using the proposed methodology. The proposed GSIR model advances the existing theory and yields promising results for continuous predictive monitoring of COVID-19 pandemic.

It is well known that the mathematical biology and dynamical systems give very important information for the study and research of viral infection models such as HIV, HBV, HCV, Ebola and Influenza. This paper deals with the global dynamics of generalized virus model with logistic growth rate for target cells, general incidence rate and cellular immunity. The results will be obtained by using Lyapunov’s second method and LaSalle’s invariance principle. We prove the global stability of the rest points of the system by the value of basic reproduction number ( R 0 ) and the immune response reproduction number ( R CTL ) . We have found that if R 0 1 , then the infection-free equilibrium is globally asymptotically stable. For R 0 > 1 and R CTL 1 , under certain conditions on incidence rate function, immune-free equilibrium is globally asymptotically stable. Finally, we prove that if R 0 > 1 and R CTL > 1 , then under certain conditions on incidence rate function the endemic equilibrium is globally asymptotically stable. Since the logistic growth rate for target cells and general incidence rate have been included in this manuscript, our obtained results are the generalization of those in the previous literatures. Moreover, the results have been obtained with weaker assumptions in comparison with the previous ones. Numerical simulations are presented to support and illustrate our analytical results.

Analysis of dose-response data is an important step in many scientific disciplines, including but not limited to pharmacology, toxicology, and epidemiology. The R package drda is designed to facilitate the analysis of dose-response data by implementing efficient and accurate functions with a familiar interface. With drda it is possible to fit models by the method of least squares, perform goodness-of-fit tests, and conduct model selection. Compared to other similar packages, drda provides in general more accurate estimates in the least-squares sense. This result is achieved by a smart choice of the starting point in the optimization algorithm and by implementing the Newton method with a trust region with analytical gradients and Hessian matrices. In this article, drda is presented through the description of its methodological components and examples of its user-friendly functions. Performance is evaluated using both synthetic data and a real, large-scale drug sensitivity screening dataset.

The growing amount of electronic waste (e-waste) poses considerable risks to the environment and human health, especially when treated inadequately. However, it is difficult to assess the significance of these issues without quantitative understanding of spatiotemporal patterns of e-waste generation. This paper proposes a new model to estimate in-use stock of electric household appliances (HAs) and e-waste generation at the level of 1 km × 1 km grids by coupling geographic information system (GIS) and material flow analysis (MFA). We took Xiamen, a rapidly urbanized city in China, as a case and the results showed that demands for HAs increased from 1980, peaked in 2016, and then declined. In-use HAs exhibited a logistic growth and significantly increased in both spatial extent and intensity. E-waste generation kept rising until 2019, and its spatial center expanded outward from downtown to suburban areas. Our study highlights that a dynamic and spatial model is useful for designing effective policies for e-waste management by providing spatiotemporal details of e-waste types and generation magnitudes and explicitly recognizing generation hotspots in cities.

The problem of testing in education is relevant for many countries. Testing solves three problems. The first task is to assess the quality of current training. The second task is to conduct a comparative analysis of learning outcomes. The third task is the management of the educational process in a particular educational institution and in the education sector. This determines the relevance of testing and the relevance of developing new methods for assessing test results. The article proposes a new method for assessing test results for different situations: “teacher– student”, computer test, virtual testing model, test on a mixed reality model and others. To solve the problem, a special quasi-sigmoidal function is introduced. It is analogous to the logistic function, but takes into account the peculiarities of real testing of students. The logistic function ranges from minus infinity to plus infinity. There are no negative assessments in education. The introduced function lies only in the positive range of the argument. It describes actual positive scores when testing students. The authors called this function the complexity function. With its help, the complexity of the subject is assessed according to the test results. To substantiate the method, the function of the logarithms of the odds, logistic regression and the resulting Rush method are investigated. The article notes two shortcomings of the Rush method. The testing principle has been defined for the new function, which is used to estimate complexity. The article introduces two new concepts: the test difficulty function and the integral test score. Integral assessment of testing is a smooth function and makes it possible to go from a stepwise dependence to a continuous one. The cumulative test score translates the point test results into a continuous function and creates a correlation between the scores. The results of an experiment with the participation of RTU MIREA students are presented. The experimental results are analyzed. The possibility of using the method in educational processes is shown. The method is an alternative to the Rush method.

Data of observations and published materials on linear and weight growth of pacific cod in the first year of life are analyzed for different habitats. The growth curve is approximated by logistic function. Monthly increments for the body length of larvae and fry are about 50 % in the first three months of life, when growth is the most intense. Absolute length increments increase in the first half of the year and reach the maximum of 25-30 mm per month in late summer — early autumn, then decrease in the rest of the year. Relative body length increments decrease in autumn and winter, too. The cod grow faster in southern areas. Weight growth patterns are different from the linear growth. The weight growth is the most intense in the first half of year, when relative weight increments exceed significantly the length increments — monthly weight increments decrease gradually form 142 % in the first month of life to 85 % in the sixth month. When the weight reaches app. 4 g, the relative weight increments decrease abruptly though the absolute increments continue to increase until the 7–9th months of life when they reach 8–10 g per month for fish with body length > 10 cm. The cod weight increases by 58 % in this short period of the highest growth. Time lag between the peaks of absolute increments of length (in the sixth month of life) and weight (in the eighth month) is about 2 months

In the present investigation, a prey–predator model consisting of phytoplankton, susceptible zooplankton, and infected zooplankton, incorporating the response function of Holling type II, has been explored. Logistic growth is assumed to be followed by the phytoplankton species. A combined effort ( E ) is applied to harvest all of the three populations. Environmental toxicity is considered to affect the phytoplankton species directly and the predating zooplankton indirectly. The dynamical behaviour of the model is examined for each of the possible steady states. Hopf-bifurcation analysis has been carried out with the combined harvesting effort E as the bifurcation parameter. The optimal control is characterized by using Pontryagin’s maximum principle. In the end, the analytical discoveries found so far have been established employing numerical simulations.

The literature contains different methods for estimating logistic functions parameters to fit the power‐speed characteristics of a wind turbine (WT). However, their disadvantages are: (1) they require a large amount of supervisory control and data acquisition data; (2) the parameter range needed for constrained optimization is not systematically determined; and/or (3) they do not guarantee monotonically increasing relationship between wind speed and predicted WT output power. This paper proposes a systematic approach to fitting the five‐ and the six‐parameter logistic functions to power‐speed data of WTs. The authors introduce new limits on the parameters of these functions, which guarantee their monotonicity. Most of these limits are determined analytically and are obtained from manufacturer datasheets. Afterwards, these limits are passed as optimization constraints for subspace trust region algorithm. The results show that the authors' method generally provides better accuracy with mean absolute percentage error values below 0.02 for the five‐parameter logistic function and below 0.005 for the six‐parameter logistic function. The authors present accurate fits for a group of WTs of different ratings (from 275 kW to 3000 kW) and 12 unique manufacturers, which proves the versatility of the authors' method.

Investigation of rumor spread dynamics and its control in social networking sites (SNS) has become important as it may cause some serious negative effects on our society. Here we aim to study the rumor spread mechanism and the influential factors using epidemic like model. We have divided the total population into three groups, namely, ignorant, spreader and aware. We have used delay differential equations to describe the dynamics of rumor spread process and studied the stability of the steady-state solutions using the threshold value of influence which is analogous to the basic reproduction number in disease model. Global stability of rumor prevailing state has been proved by using Lyapunov function. An optimal control system is set up using media awareness campaign to minimize the spreader population and the corresponding cost. Hopf bifurcation analyses with respect to time delay and the transmission rate of rumors are discussed here both analytically and numerically. Moreover, we have derived the stability region of the system corresponding to change of transmission rate and delay values.

What is the impact of COVID-19 on South Africa? This paper envisages to assist researchers in battling of the COVID-19 pandemic focusing on South Africa. This paper focuses on the spread of the disease by applying heatmap retrieval of hotspot areas, and spatial analysis is carried out using the Moran index. For capturing spatial autocorrelation between the provinces of South Africa, the adjacent as well as the geographical distance measures are used as weight matrix for both absolute and relative counts. Furthermore, generalized logistic growth curve modelling is used for prediction of the COVID-19 spread. We expect this data-driven modelling to provide some insights into hotspot identification and timeous action controlling the spread of the virus.

In the last 20 years, land and forest fires have become a phenomenon that occurs annually in South Sumatra and Kalimantan. More than 2.6 million ha of the area was burned only during very strong El Nino in 2015. Understanding the relation of fire indicators with various drivers such as dry spell, total precipitation, El Nino, and positive IOD is essential to prevent future fires. This study aims to propose a method that can be used to model and analyze the impact of El Nino and IOD on land and forest fires using polynomial and generalized logistic functions. Coefficients of the model are determined using the optimization method to maximize the correlation between climate and hotspot data. In analyzed regions, the model can represent the behavior of El Nino and IOD in influencing hotspot occurrence. In Kalimantan, the model is dominated by El Nino's impact with a coefficient value of 2.6, more than 3 × larger than the coefficient of IOD. South Sumatra's models show a balanced coefficient of ENSO (4.4) and IOD (3.25), while the highest impact occurred on the ENSO–IOD teleconnection coefficient with a value of 4.6. When used as a weight function, the model increases the correlation value of dry spell and hotspot at the center of the fire. Therefore, resulting in the more precise result of HCM analysis. A cross-validation test for weighted regression can increase the determination number (in %) of models with coefficient determination value more than 0.7 by around 28%–59% in Kalimantan and 0%–31% in South Sumatra. Moreover, the model can estimate hotspot data using monthly average data and ENSO/IOD index in the respective month. Using the copula-based joint distribution of estimate data and dry spell, we can estimate the conditional probability of 10% high extreme fire events close to the observed data conditional probability during El Nino in Kalimantan (less than 7% error average) and positive IOD in South Sumatra (around 26% error average).

This work aims at introducing a new discrete fractional order model based on Lotka-Volterra prey-predator model with logistic growth of prey species. The proposed model is a generalization of the standard integer order discrete-time Lotka-Volterra model to its fractional-order version while incorporating also logistic growth for prey population. The equilibrium points of the presented model are firstly obtained, and their stability analysis is conducted. Then, the nonlinear dynamics of the proposed model and possible occurrence of chaotic behavior are explored. The effects of fractional order along with other key parameters in the model are investigated using several techniques. Thorough numerical simulations are carried out where Lyapunov exponents, bifurcation diagrams, phase portraits and as well as $$C_{0}$$ complexity measure are obtained to analyze the dynamics of the proposed model and confirm theoretical results.

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.

This paper focuses on the stationary problem of the diffusive logistic equation on a bounded interval. We consider the ratio of a population size of a species to a carrying capacity which denotes a spatial heterogeneity of an environment. In one-dimensional case, Wei-Ming Ni proposed a variational conjecture that the supremum of this ratio varying a diffusion coefficient and a carrying function is 3. Recently, Xueli Bai, Xiaoqing He, and Fang Li [Proc. Amer. Math. Soc. 144 (2016), pp. 2161–2170] settled the conjecture by finding a special sequence of diffusion coefficients and carrying functions. Our interest is to derive a profile of the solutions corresponding to this maximizing sequence. Among other things, we obtain the exact order of the maximum and the minimum of solutions of the sequence. The proof is based on separating the stationary problem into two ordinary differential equations and smoothly adjoining each solution.

We are concerned with the existence of extremal solutions to a large class of first-order functional differential problems under weak regularity assumptions. Our technique involves multivalued analysis and the method of lower and upper solutions in order to obtain a new existence result to a scalar Cauchy problem. As a consequence of this result and a monotone iterative method for discontinuous operators, we derive our main existence result which is illustrated by several examples concerning well-known models: a generalized logistic equation or second-order problems in the presence of dry friction.

Containing the COVID-19 pandemic while balancing the economy has proven to be quite a challenge for the world. We still have limited understanding of which combination of policies have been most effective in flattening the curve; given the challenges of the dynamic and evolving nature of the pandemic, lack of quality data etc. This paper introduces a novel data mining-based approach to understand the effects of different non-pharmaceutical interventions in containing the COVID-19 infection rate. We used the association rule mining approach to perform descriptive data mining on publicly available data for 50 states in the United States to understand the similarity and differences among various policies and underlying conditions that led to transitions between different infection growth curve phases. We used a multi-peak logistic growth model to label the different phases of infection growth curve. The common trends in the data were analyzed with respect to lockdowns, face mask mandates, mobility, and infection growth. We observed that face mask mandates combined with mobility reduction through moderate stay-at-home orders were most effective in reducing the number of COVID-19 cases across various states.

Graphical abstract, Introduction The fusion of fractional order differential equations and fuzzy numbers has been widely used in modelling different engineering and applied sciences problems. In addition to these, the Allee effect, which is of high importance in field of biology and ecology, has also shown great contribution among other fields of sciences to study the correlation between density and the mean fitness of the subject. Objectives The present paper is intended to measure uncertain dynamics of an economy by restructuring the Cobb-Douglas paradigm of the renowned Solow-Swan model. The purpose of study is further boosted innovatively by subsuming the perception of logistic growth with Allee effect in the dynamics of physical capital and labor force. Methods Fractional order derivative and neutrosophic fuzzy (NF) theory are applied on the parameters of the Cobb-Douglas equation. Distinctively, cogitating fractional order derivative to study the change at each fractional stage; single-valued triangular neutrosophic fuzzy numbers (SVTNFN) to cope the uncertain situations; logistic growth function with Allee effect to analyze the factors in natural way, are the significant and novel features of this endeavor. Results The incorporation of the aforementioned theories and effects in the Cobb-Douglas equation, resulted in producing maximum sustainable capital investment and maximum capacity of labor force. The solutions in intervals located different possible solutions for different membership degrees, which accumulated the uncertain circumstances of a country. Conclusion Explicitly, these notions add new facts and figures not only in the dynamical study of capital and labor, which has been overlooked in classical models, but also left the door open for discussion and implementation on classical models of different fields.

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

Binary categorizations refer to the behaviour for which a decision maker puts the alternatives from a menu into binary categories (authorization category and rejection category). For example, a judge approves/denies parole for inmates, a doctor administers/withholds treatment to patients, and a teacher passes/fails essays. Categorizations are observed to exhibit randomness in various contexts, but the stochasticity in categorizations has received little attention in economic studies. We consider stochastic categorizations using a logit categorization function, which expresses the probability of authorizing an alternative from a menu in a ‘logit-like’ form. We characterize the model from a simple condition on authorization frequencies. Furthermore, we derive an empirical version of our model, which not only provides insight into applications of the model, but also gives an intuitive interpretation of the stochasticity in categorizations. We use simple examples to show that our model can bring new insights and research possibilities in the economic studies.

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.

We study the bifurcation diagrams and exact multiplicity of positive solutions for the one-dimensional prescribed mean curvature equation − u ′ 1 + u ′ 2 ′ = λ u 1 + u p , − L < x < L , u ( − L ) = u ( L ) = 0 , \left\{\begin{array}{l}-{\left(\frac{{u}^{^{\prime} }}{\sqrt{1+{u}^{^{\prime} 2}}}\right)}^{^{\prime} }=\lambda {\left(\frac{u}{1+u}\right)}^{p},\hspace{1.0em}-L\lt x\lt L,\\ u\left(-L)=u\left(L)=0,\end{array}\right. where λ \lambda is a bifurcation parameter, and L , p > 0 L,p\gt 0 are two evolution parameters. We prove that on the ( λ , ‖ u ‖ ∞ ) \left(\lambda ,\Vert u{\Vert }_{\infty }) -plane, for 0 < p ≤ 2 4 0\lt p\le \frac{\sqrt{2}}{4} , the bifurcation curve is ⊃ \supset -shaped bifurcation starting from ( 0 , 0 ) \left(0,0) . And for p = 1 , f ( u ) = u 1 + u p=1,f\left(u)=\frac{u}{1+u} is a logistic function, then the bifurcation curve is also ⊃ \supset -shaped bifurcation starting from π 2 4 L 2 , 0 \left(\frac{{\pi }^{2}}{4{L}^{2}},0\right) . While for p > 1 p\gt 1 , the bifurcation curve is reversed ε \varepsilon -like shaped bifurcation if L > L ∗ L\gt {L}^{\ast } , and is exactly decreasing for λ > λ ∗ \lambda \gt {\lambda }^{\ast } if 0 < L < L ∗ 0\lt L\lt {L}_{\ast } .

Background A novel coronavirus disease (COVID-19) has caused huge damage to public health around the world. Revealing the transmission dynamics of COVID-19 and control efficiency is important for containing the spread of the virus. Methods By using a logistic growth model, we estimated the transmission parameters of COVID-19 in China and six other countries (Republic of Korea, Iran, Italy, Spain, France and Germany). The transmission parameters represent the maximum daily increase rate in the early stages of the epidemic and the control efficiency under human intervention. The control efficiency was determined by the significant decrease of the daily increase rate in time and cumulative cases. Results We found the daily increase rate of cumulative cases of COVID-19 decreased significantly in both time and cumulative cases in all countries, but the decreasing trend was not further reduced in other countries except for China and Republic of Korea. The response of the daily increase rate to control measures was much earlier than the number of new cases. Conclusions Our results suggested that lockdown at the epicenter and social distancing effectively reduced the spread of COVID-19 in the early stage, but identification and isolation of patients, suspected cases and people with close contact at a community level is essential in further reduction of the daily increase rate of COVID-19.

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α = 1.6455.

In the present study, a time-delayed SIR epidemic model with a logistic growth of susceptibles, Crowley–Martin type incidence, and Holling type III treatment rates is proposed and analyzed mathematically. We consider two explicit time-delays: one in the incidence rate of new infection to measuring the impact of the latent period, and another in the treatment rate of infectives to analyzing the effect of late treatment availability. The stability behavior of the model is analyzed for two equilibria: the disease-free equilibrium (DFE) and the endemic equilibrium (EE). We derive the threshold quantity, the basic reproduction number $$R_0$$ , which determines the eradication or persistence of infectious diseases in the host population. Using the basic reproduction number, we show that the DFE is locally asymptotically stable when $$R_0< 1$$ , linearly neutrally stable when $$R_0= 1$$ , and unstable when $$R_0> 1$$ for the time-delayed system. We analyze the system without a latent period, revealing the forward bifurcation at $$R_0= 1$$ , which implies that keeping $$R_0$$ below unity can diminish the disease. Further, the stability behavior for the EE is investigated, demonstrating the occurrence of oscillatory and periodic solutions through Hopf bifurcation concerning every possible grouping of two time-delays as the bifurcation parameter. To conclude, the numerical simulations in support of the theoretical findings are carried out.

In this study, a nonlinear fractional logistic equations is proposed in the context of a modified form of the conformable fractional-order derivative. The analytical and approximate-analytical solutions are obtained for the proposed mathematical model via the method of conformable fractional differential transform method (CFDTM) and all obtained results have been analyzed and compared with homotopy perturbation method (HPM). With plotting the figures, we compared the CFDTM, HPM, and exact solution together and conclude that the CFDTM solution is closer than the exact solution in comparison with the HPM. The methods are illustrated by two examples of FOLE and solution is obtained. All obtained solutions have been analyzed and compared graphically to validate the effiency and applicability of all results.

In the present paper, we are interested in the nonlocal dispersal logistic equations in heterogeneous environment. This leads to study the spectrum theory and asymptotic behavior of nonlocal dispersal problems. We establish the existence and uniqueness of positive stationary solutions. By employing continuous lemma and nonlocal estimates, we obtain the limiting behavior of positive solutions when the dispersal rate is small or large. We also analyze the effect of spatial heterogeneity on the long time behavior of evolution equations.

The local dynamics of coupled chains of identical oscillators are considered. As a basic model of an oscillator, the well-known logistic equation with delay is proposed. The transition to studying a spatially distributed model is made. Two types of coupling of major interest are treated: diffusive coupling and unidirectional coupling. Critical cases are distinguished in the stability problem for the equilibrium state. It turns out that they are of infinite dimension: infinitely many roots of the characteristic equation tend to the imaginary axis as a small parameter characterizing the inverse of the number of elements in the chain tends to zero. The main result is the constructed special nonlinear boundary value problems whose nonlocal dynamics describes the behavior of all solutions for the chain in a neighborhood of the equilibrium state.

Long-non-coding RNA (lncRNA) is a transcription product that exerts its biological functions through a variety of mechanisms. The occurrence and development of a series of human diseases are closely related to abnormal expression levels of lncRNAs. Scientists have developed many computational models to identify the lncRNA-disease associations (LDAs). However, many potential LDAs are still unknown. In this paper, a novel method, namely MSF-UBRW (multiple similarities fusion based on unbalanced bi-random walk), is designed to explore new LDAs. First, two similarities (functional similarity and Gaussian Interaction Profile kernel similarity) of lncRNAs are calculated and fused linearly, also for disease data. Then, the known association matrix is preprocessed. Next, the linear neighbor similarities of lncRNAs and diseases are calculated, respectively. After that, the potential associations are predicted based on unbalanced bi-random walk. The fusion of multiple similarities improves the prediction performance of MSF-UBRW to a large extent. Finally, the prediction ability of the MSF-UBRW algorithm is measured by two statistical methods, leave-one-out cross-validation (LOOCV) and 5-fold cross-validation (5-fold CV). The AUCs of 0.9391 in LOOCV and 0.9183 (±0.0054) in 5-fold CV confirmed the reliable prediction ability of the MSF-UBRW method. Case studies of three common diseases also show that the MSF-UBRW method can infer new LDAs effectively.

Diferencialne enačbe z zamikom povezujejo odvod funkcije z njenimi vrednosti v preteklem času. Začetni pogoj je podan kot funkcija na ustreznem intervalu. Pogoji za obstoj in enoličnost rešitve takega začetnega problema so podobni kot pri navadnih diferencialnih enačbah, vendar pa rešitve pogosto niso zvezne in odvedlijve. V nalogi je predstavljenih nekaj standardnih metod za reševanje izbranih tipov enačb, analizirana pa sta tudi zamaknjena modela eksponentne in logistične rasti. Delay differential equations connect the derivative of a function with its value in a previous state. The initial condition is given as a function over a certain interval. The conditions for existence and uniqueness of a solution are similar to those for ordinary differential equations, yet the solution is often neither differentiable nor continuous. In this thesis I present some of the standard methods for solving certain types of delay differential equations and analyse delayed exponential and logistic growth models.

This paper seeks to establish a framework which operationalizes cognitive traits as a portion of the predefined mastery level, the highest level expected to successfully perform all of the relevant tasks of the target trait. This perspective allows us to use and interpret the cognitive trait levels in relative quantities (e.g., %s) of the mastery level instead of relative standings (i.e., rankings) on an unbounded continuum. To facilitate the proposed perspective, this paper presents an analytical framework that has support on the [0, 1] trait continuum with truncated logistic link functions. The framework provides a solution to cope with the chronic question of “relative standings or magnitudes of learning outcome?” in measuring cognitive traits. The proposed framework is articulated relative to the traditional models and is illustrated with both simulated and empirical datasets within the Bayesian framework, estimated with the Markov chain Monte Carlo method.

This study examines the mathematical characteristics of the logistic, the generalized logistic and the Gompertz growth function used in human population analysis. When a population growth is mathematically modeled, it starts with differential equations considered as a preliminary study. Then, a general solution equation is derived. This is the method followed by the mathematicians who developed these models. To prepare for the study, I used the framework of the objectives and adhered to the resources and approaches outlined by mathematicians who developed the growth function. In addition, I wanted to evaluate the methodologies that remain valid in contemporary applications using the current perspectives. Mathematician and actuary Benjamin Gompertz developed the first survivors’ function in 1825 which was used later as a population growth function while systematizing life tables. In his three published articles, the mathematician Pierre-François Verhulst developed a logistic human population growth function based on his economic analysis. In addition, he searched for test opportunities using the limited population statistics of France, Belgium, England, the USA, and Russia. Contemporary authors Richards and, ‘Ricketts and Head’ made very invaluable contributions to logistic growth function.

Background: Recent Coronavirus Disease 2019 (COVID-19) pandemic has inflicted the whole world critically. Although India has been listed amongst the top ten highly affected countries to date, one cannot rule out COVID-19 associated complications in the near future. Aim & Objective: We aim to build the COVID-19 severity model employing logistic function which determines the inflection point and help in the prediction of the future number of confirmed cases. Methods and Material: An empirical study was performed on the COVID-19 patient status in India. We performed the study commencing from 30 January 2020 to 12 July 2020 for the analysis. Exploratory data analysis (EDA) tools and techniques were applied to establish a correlation amongst the various features. The acute stage of the disease was mapped in order to build a robust model. We collected five different datasets to execute the study. Results: We found that men were more prone to get infected with the coronavirus disease as compared to women. On 165-days based analysis, we found a trending pattern of confirmed, recovered, deceased and active cases of COVID-19 in India. The as-developed growth model provided an inflection point of 72.0 days. It also predicted the number of confirmed cases as 17,80,000.0 in the future i.e. after 12th July. A growth rate of 32.0 percent was obtained. We achieved statistically significant correlations amongst growth rate and predicted COVID-19 confirmed cases. Conclusions: This study demonstrated the effective application of EDA and analytical modeling in building a mathematical severity model for COVID-19 in India. © 2021, Indian Association of Preventive and Social Medicine. All rights reserved.

Modelling stated preferences is an almost mystical science and as there is no data explaining how the sustainable feature in homes would effectively encourage homebuyers to invest in sustainable housing, it is important to investigate the buyers’ willingness to pay (WTP) for sustainable housing. The study of stated preferences often requires the use of specialised software or proprietary programs, which can be difficult and/or expensive to use. This study proposes to re-purpose the ‘support.CEs’ package, a program written in the R programming language, from its agronomic roots to measure home buyer preferences for sustainable housing. These are demonstrated through a stated preference discrete choice experiment of choosing model houses with differing levels of energy savings, renewable energy generation, landscaping, soundproofing, ventilation, and price differences. A pilot study was performed using an online survey, constructed using the LMA design tool provided in the ‘support.CEs’ package. The survey was also separated into six blocks of six questions each to reduce the cognitive burden on respondents. The survey was distributed through social media channels. Preliminary results with a limited sample of 20 respondents with mixed income, age, and occupational demographics, analysed using the package’s clogit function, that performs conditional logit estimations, have shown that the results have a statistically reliable adjusted rho-squared value and that all coefficients show the expected signs. From this study, it can be concluded that the ‘support.CEs’ package can be used to model home buyer preferences and that adequate blocking allows for the measurement of a higher number of variables despite having smaller sample sizes.

In this paper, a new dynamic traffic assignment (DTA) model is proposed for large-scale networks. Existing DTA merely describe traffic flow problems based on the travel time holographic principle, which is easy to distribute the bulk of traffic flows on the shortest path. Among the models examined in this respect, the solution method via estimating maximum correctness and expanding logarithmic correction is suggested. The given method is then validated on the Sioux Falls (SF) sample network, whose results indicate that the proposed solution method is appropriate. The findings also demonstrate a difference of less than 5% from the conventional DTA models. In addition, they show that the maximum log-likelihood (MLL) model has a significantly better performance than the multi-sentence logit function (MLF). After validating the proposed solution method, the large-scale road network in the city of Yazd, as one of the metropolises in Iran, is analyzed, using the method concerned and the DTA is performed at different times of the day and night.

Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation, the effects of quarantine strategies and stochasticity should be taken into account. Hence, our paper focuses on a stochastic susceptible-infected-quarantined-recovered-susceptible epidemic model with temporary immunity. First, by means of the Khas’minskii theory and Lyapunov function approach, we construct a critical value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0^S$$\end{document}R0S corresponding to the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document}R0 of the deterministic system. Moreover, we prove that there is a unique ergodic stationary distribution if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0^S>1$$\end{document}R0S>1. Focusing on the results of Zhou et al. (Chaos Soliton Fractals 137:109865, 2020), we develop some suitable solving theories for the general four-dimensional Fokker–Planck equation. The key aim of the present study is to obtain the explicit density function expression of the stationary distribution under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0^S>1$$\end{document}R0S>1. It should be noted that the existence of an ergodic stationary distribution together with the unique exact probability density function can reveal all the dynamical properties of disease persistence in both epidemiological and statistical aspects. Next, some numerical simulations together with parameter analyses are shown to support our theoretical results. Last, through comparison with other articles, results are discussed and the main conclusions are highlighted.

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.

To understand and approach the spread of the SARS-CoV-2 epidemic, machine learning offers fundamental tools. This study presents the use of machine learning techniques for projecting COVID-19 infections and deaths in Mexico. The research has three main objectives: first, to identify which function adjusts the best to the infected population growth in Mexico; second, to determine the feature importance of climate and mobility; third, to compare the results of a traditional time series statistical model with a modern approach in machine learning. The motivation for this work is to support health care providers in their preparation and planning. The methods compared are linear, polynomial, and generalized logistic regression models to describe the growth of COVID-19 incidents in Mexico. Additionally, machine learning and time series techniques are used to identify feature importance and perform forecasting for daily cases and fatalities. The study uses the publicly available data sets from the John Hopkins University of Medicine in conjunction with the mobility rates obtained from Google’s Mobility Reports and climate variables acquired from the Weather Online API. The results suggest that the logistic growth model fits best the pandemic’s behavior, that there is enough correlation of climate and mobility variables with the disease numbers, and that the Long short-term memory network can be exploited for predicting daily cases. Given this, we propose a model to predict daily cases and fatalities for SARS-CoV-2 using time series data, mobility, and weather variables.

A logistic equation with a delay depending on the state in the past is considered. We study the question of the existence of nonlocal relaxation periodic solutions of this equation for large values of the parameter. The characteristics (for example, period and extreme values) of solutions that we find are compared with similar characteristics of solutions of other modifications of this equation. Asymptotic estimates for the period and the maximum and minimum values are obtained. The study is carried out by the large parameter method.

This article uses precise and novel data on country-level Cloud IaaS and PaaS revenue to measure the intensive margin of technology diffusion across countries and within countries over time. We horse race diffusion models and find that cloud diffusion exhibits both Log-Log and Logistic Growth patterns. We use cross validation on nearly 100 features to determine what correlates with cross-country differences. We find that increases in features impacting Gross Domestic Product, Internet Connectivity, and Human Capital are associated with increases in intensity of cloud adoption. We finally compare the relative impacts of these variables using a random coefficients model. Although correlative, our algorithmic research design motivates data-driven hypothesis generation and further causal work regarding how policymakers can encourage more cloud computing adoption and technology adoption more broadly.

[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

Merging behavior requires multiple tasks such as cognition, decision-making, and driving operation. Previously, driving assistance systems, which instruct drivers on making accelerations, have been studied to support the decision-making task. The importance of improving driver comfort with adjusting system variables has been revealed through these studies. The present study aims to propose assistance methods for merging, which decreases driver’s workload and difficulty in decision-making. The proposed methods recognize drivers’ decision ambiguity using a decision-making model for respective drivers and instruct them on acceleration to decrease the ambiguity. First, we develop a decision-making model to predict where drivers merge based on a logistic function. Furthermore, we propose acoustic assistance methods, which instruct the acceleration and deceleration. The systems continuously calculate the optimal instruction based on driving history from the beginning of the assistance. Driving simulator experiments demonstrated that drivers’ workload and decision ambiguity decreased with our proposed methods.