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It is necessary to accurately capture the growth trajectory of fluorescence where the best fit, precision, and relative efficiency are essential. Having this in mind, a new family of growth functions called TWW (Tabatabai, Wilus, Wallace) was introduced. This model is capable of accurately analyzing quantitative polymerase chain reaction (qPCR). This new family provides a reproducible quantitation of gene copies and is less labor-intensive than current quantitative methods. A new cycle threshold based on TWW that does not need the assumption of equal reaction efficiency was introduced. The performance of TWW was compared with 3 classical models (Gompertz, logistic, and Richard) using qPCR data. TWW models the relationship between the cycle number and fluorescence intensity, outperforming some state-of-the-art models in performance measures. The 3-parameter TWW model had the best model fit in 68.57% of all cases, followed by the Richard model (28.57%) and the logistic (2.86%). Gompertz had the worst fit in 88.57% of all cases. It had the best precision in 85.71% of all cases followed by Richard (14.29%). For all cases, Gompertz had the worst precision. TWW had the best relative efficiency in 54.29% of all cases, while the logistic model was best in 17.14% of all cases. Richard and Gompertz tied for the best relative efficiency in 14.29% of all cases. The results indicate that TWW is a good competitor when considering model fit, precision, and efficiency. The 3-parameter TWW model has fewer parameters when compared to the Richard model in analyzing qPCR data, which makes it less challenging to reach convergence. [ABSTRACT FROM AUTHOR]

The study of damage and failure in fractured rock masses is crucial. This study employs the representative volume element (RVE) method to develop a microscale rock model. The model simulates the propagation and rupture of fractures by integrating factors including actual mineralogical composition, the Weibull distribution function, the Mohr–Coulomb damage criterion, and strain softening. Results indicate that fractures reduce the uniaxial compressive strength of the rock and that peak strength is significantly correlated with crack geometries. Plastic damage in rocks was categorized into three stages: elastic, rapid growth, and postpeak softening. A logistic growth model describes the plastic volume change curves for rocks with various fracture geometries, establishing the relationship between plastic damage volume and damage variables. Constitutive models for rocks with varying fracture geometries under uniaxial compression were formulated. The accuracy and applicability of these models were validated, providing a theoretical basis for rock engineering applications. Highlights: A heterogeneous plastic damage model based on representative volume elements is developed.A logistic growth model was used to describe the plastic volume change curves for rocks containing different fracture geometries.The relationship between rock plastic damage volume and damage variables was established.Plastic damage constitutive models of rocks containing different fracture geometries under uniaxial compression were obtained and validated. [ABSTRACT FROM AUTHOR]

This paper presents numerical works on estimating some logistic models using particle swarm optimization (PSO). The considered models are the Verhulst model, Pearl and Reed generalization model, von Bertalanffy model, Richards model, Gompertz model, hyper-Gompertz model, Blumberg model, Turner et al. model, and Tsoularis model. We employ data on commercial and rural banking assets in Indonesia due to their tendency to correspond with logistic growth. Most banking asset forecasting uses statistical methods concentrating solely on short-term data forecasting. In banking asset forecasting, deterministic models are seldom employed, despite their capacity to predict data behavior for an extended time. Consequently, this paper employs logistic model forecasting. To improve the speed of the algorithm execution, we use the Cauchy criterion as one of the stopping criteria. For choosing the best model out of the nine models, we analyze several considerations such as the mean absolute percentage error, the root mean squared error, and the value of the carrying capacity in determining which models can be unselected. Consequently, we obtain the best-fitted model for each commercial and rural bank. We evaluate the performance of PSO against another metaheuristic algorithm known as spiral optimization for benchmarking purposes. We assess the robustness of the algorithm employing the Taguchi method. Ultimately, we present a novel logistic model which is a generalization of the existence model. We evaluate its parameters and compare the result with the best-obtained model. [ABSTRACT FROM AUTHOR]

This study focused on evaluating the growth and productivity of Coffea arabica var. Esperanza L4A5 in different agroforestry systems in the Caribbean region of Costa Rica, a non-traditional area for coffee cultivation due to its low altitude and challenging climatic conditions. Three tree coverages were investigated, in combination with two types of differentiated fertilization (physical and chemical), comparing the results with full sun coffee plots as a control: (1) Albizia saman, (2) Hymenaea courbaril + Erythrina poeppigiana, and (3) Anacardium excelsum + Erythrina poeppigiana. The results showed that tree associations significantly reduced the mortality of coffee plants and increased both the height and mature cherry production compared to full sun treatments. In particular, the tree coverages associated with chemical and physical fertilization achieved the highest growth and production rates, with A. excelsum + E. poeppigiana and H. courbaril + E. poeppigiana standing out with maximum mature cherry productions of 3.35 t/ha and 3.28 t/ha, respectively. Growth analysis revealed that rapid initial growth, especially under chemical fertilization, is crucial for maximizing productivity, although a rapid slowdown in growth was also observed after reaching the peak. These findings underscore the importance of combining tree coverages with appropriate fertilization strategies to optimize coffee production in agroforestry systems, particularly in low-altitude areas like the Costa Rican Caribbean. This study concludes that agroforestry systems not only improve the resilience of coffee crops to adverse environmental conditions but can also be a viable strategy for increasing productivity in non-conventional regions. This suggests the need for further research to assess the long-term impacts on soil health, biodiversity, and the economic viability of these systems. [ABSTRACT FROM AUTHOR]

Apple tree productivity is influenced by the quantity of water and nutrients that are supplied during planting. To enhance resource utilization efficiency and optimize yields, a suitable strategy for supplying water and nitrogen must be established. A field experiment was conducted using a randomized block group design on five-year-old apple trees in Ningxia, with two irrigation lower limit levels (55%FC (W1) and 75%FC (W2)) and four N application levels (0 (N1), 120 (N2), 240 (N3), and 360 (N4) kg·ha−1). Our findings showed that leaf N content increased with a higher irrigation lower limit, but the difference was not statistically significant. However, the leaf N content significantly increased with increasing N application. The growth pattern of new shoots followed logistic curve characteristics, with the maximum new shoot growth rate and time of new shoot growth being delayed under high water and high nitrogen treatments. Apple yield and yield components (weight per fruit and number of fruits per plant) were enhanced under N application compared to no N application. The maximum apple yields were 19,405.3 kg·ha−1 (2022) and 29,607 kg·ha−1 (2023) at the N3 level. A parabolic relationship was observed between apple yield and N application level, with the optimal range of N application being 230–260 kg⸱ha−1. Apple quality indicators were not significantly affected by the irrigation lower limit but were significantly influenced by N application levels. The lower limit of irrigation did not have a significant impact on the quality indicators of the apples. Water and N utilization efficiencies improved with the W2 treatment at the same N application level. A negative relationship was observed between the amount of nitrogen applied and the biased productivity of nitrogen fertilizer. The utilization of nitrogen fertilizer was 127.6 kg·kg−1 (2022) and 200.3 kg·kg−1 (2023) in the W2N2 treatment. The apple yield was sustained, the quality of the fruit improved, and a substantial increase in water productivity was achieved with the W2N3 treatment. The findings of this study can be used as a reference for accurate field irrigation. [ABSTRACT FROM AUTHOR]

This study investigates the depressive effects of diode laser radiation on commonly found weed species in the Northwest Anatolian conditions. Unlike previous laboratory-based experiments, this pilot study conducted in natural environments aims to understand weed reactions to laser application under field conditions. Cleavers (Galium aparine), small scabious (Scabiosa columbaria), and sun spurge (Euphorbia helioscopia) were selected for observation. A diode laser (5500 mW power, 450 nm wavelength) was applied to plant apical meristems and stems at four doses for each species. Regression analyses using dry-based remaining biomass and laser doses were performed with the logistic growth model. The ED90 values, indicating a 90% reduction in plant growth on the stem, were determined as 14.42 J for cleavers, 11.04 J for scabious, and 18.04 J for sun spurge. For apical meristem applications, plant growth reduction was less than 90% at maximum energy doses, with rates of 72.18% for cleavers and 41.64% for scabious. These results support the thesis that laser application to the apical meristem region of the weed may not be sufficiently effective beyond the cotyledon period. However, the study concludes that laser application to the plant stem can successfully control all three weed species. [ABSTRACT FROM AUTHOR]

The simulation and early warning of cyanobacterial blooms in lakes are of great significance. Controlling the growth of cyanobacteria in plateau lakes is challenging due to the unique geographical environment, climatic conditions, and impact of anthropogenic activities. Therefore, conducting simulations and early warning is crucial to effectively control cyanobacterial blooms in plateau lakes. This study aimed to investigate Xingyun Lake, a representative plateau lake in China, using the logistic growth model to analyze cyanobacterial growth patterns and assess the effects of control projects, along with the influence of meteorological and environmental factors. Moreover, the study proposed a method for establishing control curves and ranges for managing cyanobacterial blooms. The results demonstrated that the chlorophyll-a concentration in the effluent decreased by an average of 97.74% compared with that in the influent after implementing the integrated “deep-well pressure algal control” and “ecological purification for algae-water separation” processes in Xingyun Lake. The total annual decrease in chlorophyll-a was approximately 3.40 times the lake's total chlorophyll-a content. The growth of cyanobacteria in Xingyun Lake followed a logistic pattern during the blooming period, before and after implementing control projects (from 2018 to 2022), with the overall growth trend from 2010 to 2022 aligning with the logistic growth model. The study identified lower temperatures and precipitation, reduced nitrogen and phosphorus loads, and a higher nitrogen-to‑phosphorus ratio as the main environmental factors inhibiting cyanobacterial growth. Establishing logistic control curves for cyanobacterial blooms and sustaining the algal control project before the transition point effectively reduced the maximum chlorophyll-a concentration and attenuated cyanobacterial growth rate throughout the year. This study offered novel perspectives for preventing and controlling cyanobacterial blooms, offering practical guidance for lake management, especially in plateau regions.

With the increased market penetration of electric vehicles (EVs), energy consumption is growing at a quicker rate. Electric vehicles are slowly but surely gaining a foothold in India’s rapidly expanding market. With more EVs on the road, there will be more demand for charging and more energy use in some places, which can put a lot of stress on the power grid. In the absence of sufficient planning, there is a risk of power system interruption and failure. Therefore, the need for energy in cities will shift in light of the advent of EVs in the next decade or two. Accordingly, Surat has been chosen as the research region for the planning of charging infrastructure in the current study. After reviewing the literature, primary data was acquired to estimate citizen travel demands. Vehicle registration statistics were compiled from the Regional Transport Office (RTO) for the purpose of EV forecasting. After collecting data, the EV population and demand for public charging stations by 2025 and 2030 were calculated. This study aims to meet the public charging demand in the city of Surat by analyzing the electric vehicle growth rate and vehicle forecast. This anticipated data was then utilized to compute the energy demand consumption for Surat city by calculating vehicle kilometers traveled. The demand for public charging comes out to be 42.4 MWh/day in 2025 and 358.05 MWh/day in 2030, respectively. The study’s objective is to determine energy demand per region in order to better understand grid planning due to the imbalance in electricity demand.

This study concerns with the production and partial characterization of alkaline cellulase from alkaliphilic cellulolytic (AC) fungi isolated fromsoil in Perlis, Malaysia. The best fungi strain was selected on the basis of producing the highest cellulase at high pH conditions. Cellulase from the selected fungi strain was further characterized under saccharification but varies in operating parameters. Finally, the kinetic model describing the growth of the AC fungi strain was studied by employing the logistic model. Among the tested fungi strains, Basidiomycetes strain (BK1) showed high potentiality for the production of maximum alkaline cellulase production at pH 9 after 72 h of incubation at 30°C containing 6 g·L−1 carboxyl methyl cellulose. The saccharification process showed that the enzyme favour high alkaline condition and proves thermotolerant properties, while 15% (v/v) enzyme loading and 1% substrate concentration recorded the highest glucose production at about 1.2–1.3 mg·mL−1. The novelty of the study is to identify and optimize a unique indigenous fungi that emit alkaliphilic cellulase as alternative usage in biotechnology industries due to its capacity to adapt to the extreme conditions of specific industrial processes. There are revolutionary options for use in biotechnological businesses that involve high pH and therefore have substantial biotechnological promise.

Abstract Background With the global spread of COVID-19, detecting high-risk countries/regions timely and dynamically is essential; therefore, we sought to develop automatic, quantitative and scalable analysis methods to observe and estimate COVID-19 spread worldwide and further generate reliable and timely decision-making support for public health management using a comprehensive modeling method based on multiple mathematical models. Methods We collected global COVID-19 epidemic data reported from January 23 to September 30, 2020, to observe and estimate its possible spread trends. Countries were divided into three outbreak levels: high, middle, and low. Trends analysis was performed by calculating the growth rate, and then country grouping was implemented using group-based trajectory modeling on the three levels. Individual countries from each group were also chosen to further disclose the outbreak situations using two predicting models: the logistic growth model and the SEIR model. Results All 187 observed countries' trajectory subgroups were identified using two grouping strategies: with and without population consideration. By measuring epidemic trends and predicting the epidemic size and peak of individual countries, our study found that the logistic growth model generally estimated a smaller epidemic size than the SEIR model. According to SEIR modeling, confirmed cases in each country would take an average of 9–12 months to reach the outbreak peak from the day the first case occurred. Additionally, the average number of cases at the peak time will reach approximately 10–20% of the countries’ populations, and the countries with high trends and a high predicted size must pay special attention and implement public health interventions in a timely manner. Conclusions We demonstrated comprehensive observations and predictions of the COVID-19 outbreak in 187 countries using a comprehensive modeling method. The methods proposed in this study can measure COVID-19 development from multiple perspectives and are generalizable to other epidemic diseases. Furthermore, the methods also provide reliable and timely decision-making support for public health management.

Apple tree productivity is influenced by the quantity of water and nutrients that are supplied during planting. To enhance resource utilization efficiency and optimize yields, a suitable strategy for supplying water and nitrogen must be established. A field experiment was conducted using a randomized block group design on five-year-old apple trees in Ningxia, with two irrigation lower limit levels (55%FC (W1) and 75%FC (W2)) and four N application levels (0 (N1), 120 (N2), 240 (N3), and 360 (N4) kg·ha−1). Our findings showed that leaf N content increased with a higher irrigation lower limit, but the difference was not statistically significant. However, the leaf N content significantly increased with increasing N application. The growth pattern of new shoots followed logistic curve characteristics, with the maximum new shoot growth rate and time of new shoot growth being delayed under high water and high nitrogen treatments. Apple yield and yield components (weight per fruit and number of fruits per plant) were enhanced under N application compared to no N application. The maximum apple yields were 19,405.3 kg·ha−1 (2022) and 29,607 kg·ha−1 (2023) at the N3 level. A parabolic relationship was observed between apple yield and N application level, with the optimal range of N application being 230–260 kg⸱ha−1. Apple quality indicators were not significantly affected by the irrigation lower limit but were significantly influenced by N application levels. The lower limit of irrigation did not have a significant impact on the quality indicators of the apples. Water and N utilization efficiencies improved with the W2 treatment at the same N application level. A negative relationship was observed between the amount of nitrogen applied and the biased productivity of nitrogen fertilizer. The utilization of nitrogen fertilizer was 127.6 kg·kg−1 (2022) and 200.3 kg·kg−1 (2023) in the W2N2 treatment. The apple yield was sustained, the quality of the fruit improved, and a substantial increase in water productivity was achieved with the W2N3 treatment. The findings of this study can be used as a reference for accurate field irrigation.

Since the COVID-19 epidemic, mathematical and simulation models have been extensively utilized to forecast the virus's progress. In order to more accurately describe the actual circumstance surrounding the asymptomatic transmission of COVID-19 in urban areas, this research proposes a model called Susceptible-Exposure-Infected-Asymptomatic-Recovered-Quarantine in a small-world network. In addition, we coupled the epidemic model with the Logistic growth model to simplify the process of setting model parameters. The model was assessed through experiments and comparisons. Simulation results were analyzed to explore the main factors affecting the spread of the epidemic, and statistical analysis that was applied to assess the model's accuracy. The results are consistent well with epidemic data from Shanghai, China in 2022. The model can not only replicate the real virus transmission data, but also anticipate the development trend of the epidemic based on available data, so that health policy-makers can better understand the spread of the epidemic.

Background: With the global spread of COVID-19, detecting high-risk countries/regions timely and dynamically is essential; therefore, we sought to develop automatic, quantitative and scalable analysis methods to observe and estimate COVID-19 spread worldwide and further generate reliable and timely decision-making support for public health management using a comprehensive modeling method based on multiple mathematical models. Methods: We collected global COVID-19 epidemic data reported from January 23 to September 30, 2020, to observe and estimate its possible spread trends. Countries were divided into three outbreak levels: high, middle, and low. Trends analysis was performed by calculating the growth rate, and then country grouping was implemented using group-based trajectory modeling on the three levels. Individual countries from each group were also chosen to further disclose the outbreak situations using two predicting models: the logistic growth model and the SEIR model. Results: All 187 observed countries' trajectory subgroups were identified using two grouping strategies: with and without population consideration. By measuring epidemic trends and predicting the epidemic size and peak of individual countries, our study found that the logistic growth model generally estimated a smaller epidemic size than the SEIR model. According to SEIR modeling, confirmed cases in each country would take an average of 9–12 months to reach the outbreak peak from the day the first case occurred. Additionally, the average number of cases at the peak time will reach approximately 10–20% of the countries' populations, and the countries with high trends and a high predicted size must pay special attention and implement public health interventions in a timely manner. Conclusions: We demonstrated comprehensive observations and predictions of the COVID-19 outbreak in 187 countries using a comprehensive modeling method. The methods proposed in this study can measure COVID-19 development from multiple perspectives and are generalizable to other epidemic diseases. Furthermore, the methods also provide reliable and timely decision-making support for public health management. [ABSTRACT FROM AUTHOR]

There is a 'coffee ring' in the Bacillus subtilis biofilm center, and the colony biofilm morphologies are distinct inside and outside the 'coffee ring'. In this paper, we study this morphological difference and explain the reasons of the 'coffee ring' formation and further the causes to the morphological variation. We developed a quantitative method to characterize the surface morphology, the outer area is thicker than the inner area of the 'coffee ring', and the thickness amplitude in outer area is larger than inner area of the 'coffee ring'. We adopt a logistic growth model to obtain how the environmental resistance influence the colony biofilm thickness. Dead cells provide gaps for stress release and make folds formation in colony biofilm. we developed a technique for optical imaging and matching cells with the BRISK algorithm to capture the distribution and movement of motile cells and matrix producing cells in the colony biofilm. Matrix producing cells are mainly distribute in the outside of the 'coffee ring', and the extracellular matrix (ECM) prevents the motile cells moving outward from center. Motile cells mainly locate inside the ring, a small amount of dead motile cells outside the 'coffee ring' give rise to radial folds formation. There are no ECM blocking cell movements inside the ring, which result in uniform folds formation. The distribution of ECM and different phenotypes lead to the formation of the 'coffee ring', which is verified by using eps and flagellar mutants. [ABSTRACT FROM AUTHOR]

As cities become increasingly interconnected in production and lifestyles, metropolitan areas have become the main areas for carbon dioxide (CO2) emissions. This article is the first to investigate the potential for peak CO2 emissions in China's metropolitan areas. Specifically, this study constructs logistic growth models using time series data of CO2 emissions from 1997 to 2017 for 26 metropolitan areas. Secondly, this study combines scenario analysis and the STIRPAT model for projection. Moreover, using the grid search method, this study optimizes ridge regression's penalty term coefficient (alpha). The results show that most metropolitan areas in China entered the saturation stage of carbon emission in 2016, but it is still challenging to achieve the goal of peak carbon dioxide emission by 2030. Per capita GDP, the proportion of the secondary industry, population, and urbanization positively affects CO2 emissions, and green technology innovation negatively affects CO2 emissions. Therefore, to achieve the peak CO2 emissions target, China should develop differentiated carbon reduction strategies for metropolitan areas and focus on the optimization and upgrading of industrial structure, the improvement of green technology level, and the low carbonization of residents' lifestyles in metropolitan areas. The significance of this study is that it helps policymakers to project potential peak CO2 emission trajectories from a bottom-up perspective, and its findings provide insights into China's peak CO2 emissions pathway. [ABSTRACT FROM AUTHOR]

In response to significant shifts in dietary and lifestyle preferences, the global demand for fruits has increased dramatically, especially for apples, which are consumed worldwide. Growing apple orchards of more productive and higher quality with limited land resources is the way forward. Precise planting age identification and yield prediction are indispensable for the apple market in terms of sustainable supply, price regulation, and planting management. The planting age of apple trees significantly determines productivity, quality, and yield. Therefore, we integrated the time-series spectral endmember and logistic growth model (LGM) to accurately identify the planting age of apple orchard, and we conducted planting age-driven yield prediction using a neural network model. Firstly, we fitted the time-series spectral endmember of green photosynthetic vegetation (GV) with the LGM. By using the four-points method, the environmental carrying capacity (ECC) in the LGM was available, which serves as a crucial parameter to determine the planting age. Secondly, we combined annual planting age with historical apple yield to train the back propagation (BP) neural network model and obtained the predicted apple yields for 12 counties. The results show that the LGM method can accurately estimate the orchard planting age, with Mean Absolute Error (MAE) being 1.76 and the Root Mean Square Error (RMSE) being 2.24. The strong correlation between orchard planting age and apple yield was proved. The results of planting age-driven yield prediction have high accuracy, with the MAE up to 2.95% and the RMSE up to 3.71%. This study provides a novel method to accurately estimate apple orchard planting age and yields, which can support policy formulation and orchard planning in the future. [ABSTRACT FROM AUTHOR]

Waste generated from electric and electronic equipment (WEEE) is increasing rapidly due to the high demand for appliances, rapid product obsolescence, coupled with rapid economic growth, urbanization and technology advancement. Setting up a proper WEEE management system, which ensures better collection, treatment, recycling and control of transboundary movement of waste is crucial to increasing resource efficiency, improving sustainable production, use and consumption, and promoting the circular economy in Jordan. However, this system requires proper assessment of WEEE generation rates and reliable figures. Estimation of historical and future electric and electronic equipment put on market (EEE POM) and WEEE generation rates in Jordan have been achieved using the population balance model (PBM), logistic growth model (LGM) and Weibull distribution from 2000 to 2050. It is expected that the total disposal of appliances will reach about 1.6 million units (53 kt) in 2022, double this figure by 2044 and hit around 5 million units (175 kt) in 2050, with increasing WEEE generation rates. This is combined with the changing composition of WEEE with time. Thus, a rapid increase of WEEE in the near future is expected; this increase requires close monitoring and immediate response to tackle this hazardous waste. [ABSTRACT FROM AUTHOR]

It is urgent to identify the development of the Corona Virus Disease 2019 (COVID‐19) in countries around the world. Therefore, visualization is particularly important for monitoring the COVID‐19. In this paper, we visually analyze the real‐time data of COVID‐19, to monitor the trend of COVID‐19 in the form of charts. At present, the COVID‐19 is still spreading. However, in the existing works, the visualization of COVID‐19 data has not established a certain connection between the forecast of the epidemic data and the forecast of the epidemic. To better predict the development trend of the COVID‐19, we establish a logistic growth model to predict the development of the epidemic by using the same data source in the visualization. However, the logistic growth model only has a single feature. To predict the epidemic situation in an all‐round way, we also predict the development trend of the COVID‐19 based on the Susceptible Exposed Infected Removed epidemic model with multiple features. We fit the data predicted by the model to the real COVID‐19 epidemic data. The simulation results show that the predicted epidemic development trend is consistent with the actual epidemic development trend, and our model performs well in predicting the trend of COVID‐19. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of a discrete fractional-order logistic growth model with infectious disease. We obtain the discrete model by applying the piecewise constant arguments to the fractional-order model. This model contains three fixed points namely the origin point, the disease-free point, and the endemic point. We confirm that the origin point is always exists and unstable, the disease-free point is always exists and conditionally stable, and the endemic point is conditionally exists and stable. We also investigate the existence of forward, period-doubling, and Neimark-Sacker bifurcation. The numerical simulations are also presented to confirm the analytical results. We also show numerically the existence of period-3 solution which leads to the occurrence of chaotic behavior.

Abstract Background The rising burden of the ongoing COVID-19 epidemic in South Africa has motivated the application of modeling strategies to predict the COVID-19 cases and deaths. Reliable and accurate short and long-term forecasts of COVID-19 cases and deaths, both at the national and provincial level, are a key aspect of the strategy to handle the COVID-19 epidemic in the country. Methods In this paper we apply the previously validated approach of phenomenological models, fitting several non-linear growth curves (Richards, 3 and 4 parameter logistic, Weibull and Gompertz), to produce short term forecasts of COVID-19 cases and deaths at the national level as well as the provincial level. Using publicly available daily reported cumulative case and death data up until 22 June 2020, we report 5, 10, 15, 20, 25 and 30-day ahead forecasts of cumulative cases and deaths. All predictions are compared to the actual observed values in the forecasting period. Results We observed that all models for cases provided accurate and similar short-term forecasts for a period of 5 days ahead at the national level, and that the three and four parameter logistic growth models provided more accurate forecasts than that obtained from the Richards model 10 days ahead. However, beyond 10 days all models underestimated the cumulative cases. Our forecasts across the models predict an additional 23,551–26,702 cases in 5 days and an additional 47,449–57,358 cases in 10 days. While the three parameter logistic growth model provided the most accurate forecasts of cumulative deaths within the 10 day period, the Gompertz model was able to better capture the changes in cumulative deaths beyond this period. Our forecasts across the models predict an additional 145–437 COVID-19 deaths in 5 days and an additional 243–947 deaths in 10 days. Conclusions By comparing both the predictions of deaths and cases to the observed data in the forecasting period, we found that this modeling approach provides reliable and accurate forecasts for a maximum period of 10 days ahead.

Background: Ever since the Coronavirus disease (COVID-19) outbreak emerged in China, there has been several attempts to predict the epidemic across the world with varying degrees of accuracy and reliability. This paper aims to carry out a short-term projection of new cases; forecast the maximum number of active cases for India and selected high-incidence states; and evaluate the impact of three weeks lock down period using different models. Methods: We used Logistic growth curve model for short term prediction; SIR models to forecast the maximum number of active cases and peak time; and Time Interrupted Regression model to evaluate the impact of lockdown and other interventions. Results: The predicted cumulative number of cases for India was 58,912 (95% CI: 57,960, 59,853) by May 08, 2020 and the observed number of cases was 59,695. The model predicts a cumulative number of 1,02,974 (95% CI: 1,01,987, 1,03,904) cases by May 22, 2020. As per SIR model, the maximum number of active cases is projected to be 57,449 on May 18, 2020. The time interrupted regression model indicates a decrease of about 149 daily new cases after the lock down period, which is statistically not significant. Conclusion: The Logistic growth curve model predicts accurately the short-term scenario for India and high incidence states. The prediction through SIR model may be used for planning and prepare the health systems. The study also suggests that there is no evidence to conclude that there is a positive impact of lockdown in terms of reduction in new cases.

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. • Proposed a generalized SIR (GSIR) framework for pandemic modeling and prediction. • An integrative model that captures the pandemic data via distinct waves emerging at different times. • Explicit expressions are derived for the susceptible, infected and removed populations. • Dynamic modeling of system parameters that can capture the impact of policy decisions. • GSIR model is tested on COVID-19 data and can serve as a good alternative to existing methods. [ABSTRACT FROM AUTHOR]

This paper aims to explore the transmission dynamics of COVID-19 with dengue co-infection using mathematical modeling. In this study, SIR model is developed that explains the trajectory of the epidemic to boost a plan for an effective control strategy for COVID-19 in Bangladesh. The model is extended to optimal control strategies. Pontryagin's Principle is used to establish the appropriate conditions for the existence of optimal control and the optimality system for the co-infection model. Coinfected cases were reduced with control greater than without control. Using Omicron incidence cases from 1st January – 13th April 2022, the maximum likelihood estimate of R0 with a 95% confidence interval is1.89 [ 95% CI: 1.88, 1.91]. The R0 estimated from the exponential growth method is 2.08 [95% CI: 2.07,2.09]and time-dependent estimate is 2.10[95% CI: 1.72,2.58]. The generalized logistic growth model predicted 19, 52,131 cumulative cases on day 103 (April 13, 2022), and a relatively flat curve of cumulative growth of COVID-19 cases implies a declining trend of new cases. The study also found from sensitivity analysis that, R0 is proportional to the mean generation time. This paper attempted to focus on suppressing the COVID-19 co-infections by preventing dengue and COVID-19. The results of the study show that by implementing optimal control spread of dengue and COVID-19 could be minimized. The logistic growth model suggests that the infection rate of COVID-19 is decreasing. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Objective: As the coronavirus disease 2019 (COVID-19) pandemic continues to proliferate globally, this paper shares the findings of modelling the outbreak in China at both provincial and national levels. This paper examines the applicability of the logistic growth model, with implications for the study of the COVID-19 pandemic and other infectious diseases. Methods: An NLS (Non-Linear Least Squares) method was employed to estimate the parameters of a differentiated logistic growth function using new daily COVID-19 cases in multiple regions in China and in other selected countries. The estimation was based upon training data from January 20, 2020 to March 13, 2020. A restriction test was subsequently implemented to examine whether a designated parameter was identical among regions or countries, and the diagnosis of residuals was also conducted. The model's goodness of fit was checked using testing data from March 14, 2020 to April 18, 2020. Results: The model presented in this paper fitted time-series data exceedingly well for the whole of China, its eleven selected provinces and municipalities, and two other countries - South Korea and Iran - and provided estimates of key parameters. This study rejected the null hypothesis that the growth rates of outbreaks were the same among ten selected non-Hubei provinces in China, as well as between South Korea and Iran. The study found that the model did not provide reliable estimates for countries that were in the early stages of outbreaks. Furthermore, this study concured that the R2 values might vary and mislead when compared between different portions of the same non-linear curve. In addition, the study identified the existence of heteroskedasticity and positive serial correlation within residuals in some provinces and countries. Conclusions: The findings suggest that there is potential for this model to contribute to better public health policy in combatting COVID-19. The model does so by providing a simple logistic framework for retrospectively analyzing outbreaks in regions that have already experienced a maximal proliferation in cases. Based upon statistical findings, this study also outlines certain challenges in modelling and their implications for the results.

Abstract Background Many studies have modeled and predicted the spread of COVID-19 (coronavirus disease 2019) in the U.S. using data that begins with the first reported cases. However, the shortage of testing services to detect infected persons makes this approach subject to error due to its underdetection of early cases in the U.S. Our new approach overcomes this limitation and provides data supporting the public policy decisions intended to combat the spread of COVID-19 epidemic. Methods We used Centers for Disease Control and Prevention data documenting the daily new and cumulative cases of confirmed COVID-19 in the U.S. from January 22 to April 6, 2020, and reconstructed the epidemic using a 5-parameter logistic growth model. We fitted our model to data from a 2-week window (i.e., from March 21 to April 4, approximately one incubation period) during which large-scale testing was being conducted. With parameters obtained from this modeling, we reconstructed and predicted the growth of the epidemic and evaluated the extent and potential effects of underdetection. Results The data fit the model satisfactorily. The estimated daily growth rate was 16.8% overall with 95% CI: [15.95, 17.76%], suggesting a doubling period of 4 days. Based on the modeling result, the tipping point at which new cases will begin to decline will be on April 7th, 2020, with a peak of 32,860 new cases on that day. By the end of the epidemic, at least 792,548 (95% CI: [789,162, 795,934]) will be infected in the U.S. Based on our model, a total of 12,029 cases were not detected between January 22 (when the first case was detected in the U.S.) and April 4. Conclusions Our findings demonstrate the utility of a 5-parameter logistic growth model with reliable data that comes from a specified period during which governmental interventions were appropriately implemented. Beyond informing public health decision-making, our model adds a tool for more faithfully capturing the spread of the COVID-19 epidemic.

In this paper, we deal with the non-autonomous logistic growth model with time-dependent intrinsic growth rate and carrying capacity. Accounting for errors in recorded data, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty of the model output is quantified by approximations of the first probability density function via the random variable transformation method. A numerical example illustrates the results. [ABSTRACT FROM AUTHOR]

The simulation and early warning of cyanobacterial blooms in lakes are of great significance. Controlling the growth of cyanobacteria in plateau lakes is challenging due to the unique geographical environment, climatic conditions, and impact of anthropogenic activities. Therefore, conducting simulations and early warning is crucial to effectively control cyanobacterial blooms in plateau lakes. This study aimed to investigate Xingyun Lake, a representative plateau lake in China, using the logistic growth model to analyze cyanobacterial growth patterns and assess the effects of control projects, along with the influence of meteorological and environmental factors. Moreover, the study proposed a method for establishing control curves and ranges for managing cyanobacterial blooms. The results demonstrated that the chlorophyll-a concentration in the effluent decreased by an average of 97.74% compared with that in the influent after implementing the integrated "deep-well pressure algal control" and "ecological purification for algae-water separation" processes in Xingyun Lake. The total annual decrease in chlorophyll-a was approximately 3.40 times the lake's total chlorophyll-a content. The growth of cyanobacteria in Xingyun Lake followed a logistic pattern during the blooming period, before and after implementing control projects (from 2018 to 2022), with the overall growth trend from 2010 to 2022 aligning with the logistic growth model. The study identified lower temperatures and precipitation, reduced nitrogen and phosphorus loads, and a higher nitrogen-to‑phosphorus ratio as the main environmental factors inhibiting cyanobacterial growth. Establishing logistic control curves for cyanobacterial blooms and sustaining the algal control project before the transition point effectively reduced the maximum chlorophyll-a concentration and attenuated cyanobacterial growth rate throughout the year. This study offered novel perspectives for preventing and controlling cyanobacterial blooms, offering practical guidance for lake management, especially in plateau regions. • Case study of cyanobacteria management in plateau lakes was performed. • The effectiveness of cyanobacterial control project was evaluated. • The growth of cyanobacteria followed a logistic pattern during the bloom period. • Temperature, precipitation, and total phosphorus influenced cyanobacterial growth. • The cyanobacterial bloom control curves and ranges were established. [ABSTRACT FROM AUTHOR]

Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different $(N, M) $ values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems.

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.

As the outbreak of coronavirus disease 2019 (COVID-19) is rapidly spreading in different parts of India, a reliable forecast for the cumulative confirmed cases and the number of deaths can be helpful for policymakers in making the decisions for utilizing available resources in the country. Recently, various mathematical models have been used to predict the outbreak of COVID-19 worldwide and also in India. In this article we use exponential, logistic, Gompertz growth and autoregressive integrated moving average (ARIMA) models to predict the spread of COVID-19 in India after the announcement of various unlock phases. The mean absolute percentage error and root mean square error comparative measures were used to check the goodness-of-fit of the growth models and Akaike information criterion for ARIMA model selection. Using COVID-19 pandemic data up to 20 December 2020 from India and its five most affected states (Maharashtra, Karnataka, Andhra Pradesh, Tamil Nadu and Kerala), we report 15-days-ahead forecasts for cumulative confirmed cases and the number of deaths. Based on available data, we found that the ARIMA model is the best-fitting model for COVID-19 cases in India and its most affected states. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population X (t). In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate r , carrying capacity K , intensity of Gaussian noise λ , noise intensity σ and stability index α vary. The MET from the interval (0 , 1) at the right boundary is finite if λ < 2 . For λ > 2 , the MET from (0 , 1) at this boundary is infinite. A larger stability index α is less likely leading to the extinction of the fish population. [ABSTRACT FROM AUTHOR]

In this study, in addition to classical Logistic and Gompertz models with three parameters, their growth models with four parameters were given. After that it is searched the effect of these growth models on the choice of appropriate growth model by using two separate data sets. For this purpose, classical Logistic and Gompertz growth models and their growth models with four parameters are compared with some model selection criteria such as such as error sum of squares, coefficient of determination, adjusted coefficient of determination and akaike information criteria. For the data set used in this study, it is found that the results of these growth models with four parameters are better than the results of these growth models. Thus, it is considered that these growth models with four parameters can be used in addition to these classical growth models. In addition, some other growth models with four parameters can be investigated for getting the best model choice. Even Logistic and Gompertz models with five and more parameters can be investigated for getting the best model choice. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic differential equation driven by multiplicative Gaussian noise. With the help of the associated Fokker–Planck equation, we analyze the population extinction probability and the probability of reaching a large population size before reaching a small one. We further study the impact of the harvest rate, noise intensity and the Allee effect on population evolution. The analysis and numerical experiments show that if the noise intensity and harvest rate are small, the population grows exponentially, and upon reaching the carrying capacity, the population size fluctuates around it. In the stochastic logistic-harvest model without the Allee effect, when noise intensity becomes small (or goes to zero), the stationary probability density becomes more acute and its maximum point approaches one. However, for large noise intensity and harvest rate, the population size fluctuates wildly and does not grow exponentially to the carrying capacity. So as far as biological meanings are concerned, we must catch at small values of noise intensity and harvest rate. Finally, we discuss the biological implications of our results. [ABSTRACT FROM AUTHOR]

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

The COVID-19 global pandemic has rapidly expanded, with the UK being one of the countries with the highest number of cases and deaths in proportion to its population. Major clinical and human behavioural measures have been taken by the UK government to control the spread of the pandemic and to support the health system. It remains unclear how exactly human mobility restrictions have affected the virus spread in the UK. This research uses driving, walking and transit real-time data to investigate the impact of government control measures on human mobility reduction, as well as the connection between trends in human-mobility and severe COVID-19 outcomes. Human mobility was observed to gradually decrease as the government was announcing more measures and it stabilized at a scale of around 80% after a lockdown was imposed. The study shows that human-mobility reduction had a significant impact on reducing COVID-19-related deaths, thus providing crucial evidence in support of such government measures.

Background: The rising burden of the ongoing COVID-19 epidemic in South Africa has motivated the application of modeling strategies to predict the COVID-19 cases and deaths. Reliable and accurate short and long-term forecasts of COVID-19 cases and deaths, both at the national and provincial level, are a key aspect of the strategy to handle the COVID-19 epidemic in the country.Methods: In this paper we apply the previously validated approach of phenomenological models, fitting several non-linear growth curves (Richards, 3 and 4 parameter logistic, Weibull and Gompertz), to produce short term forecasts of COVID-19 cases and deaths at the national level as well as the provincial level. Using publicly available daily reported cumulative case and death data up until 22 June 2020, we report 5, 10, 15, 20, 25 and 30-day ahead forecasts of cumulative cases and deaths. All predictions are compared to the actual observed values in the forecasting period.Results: We observed that all models for cases provided accurate and similar short-term forecasts for a period of 5 days ahead at the national level, and that the three and four parameter logistic growth models provided more accurate forecasts than that obtained from the Richards model 10 days ahead. However, beyond 10 days all models underestimated the cumulative cases. Our forecasts across the models predict an additional 23,551-26,702 cases in 5 days and an additional 47,449-57,358 cases in 10 days. While the three parameter logistic growth model provided the most accurate forecasts of cumulative deaths within the 10 day period, the Gompertz model was able to better capture the changes in cumulative deaths beyond this period. Our forecasts across the models predict an additional 145-437 COVID-19 deaths in 5 days and an additional 243-947 deaths in 10 days.Conclusions: By comparing both the predictions of deaths and cases to the observed data in the forecasting period, we found that this modeling approach provides reliable and accurate forecasts for a maximum period of 10 days ahead. [ABSTRACT FROM AUTHOR]

Vegetation community plays a pivotal role in various geomorphic processes. The growth of vegetation intrinsically depends on the effective shear stresses exerted by the flow of material (e.g., water or soil) along the slope. We comparatively assess the growth and decay of vegetation using linear and logistic growth model coupled with a runoff erosion model. The linear growth model predicts a sharp decrease in the non-dimensional vegetation profile from the upper reach to the lower part along the slope. However, the logistic growth model delivers a smooth gradual decrease in the vegetation extent. Additionally, we propose a stochastic model to capture the role of internal and external factors in the dynamics of vegetation growth using two Gaussian noises. The steady probability distribution functions from the stochastic model provide insights about the role of different noises on the reaction of the system and suggest that bio-environmental factors are difficult to segregate from one another. Highlights: Comparative study between logistic and linear vegetation growth model coupled with a surface erosion model. Steady-state equilibrium vegetation profile along any slope suggests that the logistic growth model is more realistic. Effect of Gaussian noises in vegetation growth has been demonstrated with the aid of stationary probability distribution. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the logistic growth model with a time-dependent carrying capacity that was proposed in the literature for the study of the total bacterial biomass during occlusion of healthy human skin. Accounting for data and model errors, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty is quantified by approximations of the solution stochastic process via truncated series solution together with the random variable transformation method. Numerical examples illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The logistic growth model and the Susceptible-Infectious-Recovered (SIR) framework are utilized for the mathematical modelling of the Coronavirus disease (COVID-19) outbreak in India. Karnataka, Kerala and Maharashtra, three states of India, are selected based on the pattern of the disease spread and the prominence in being affected in India. The parameters of the models are estimated by utilizing real-time data. The models predict the ending of the pandemic in these states and estimate the number of people that would be affected under the prevailing conditions. The models classify the pandemic into five stages based on the nature of the infection growth rate. According to the estimates of the models it can be concluded that Kerala is in a stable situation whereas the pandemic is still growing in Karnataka and Maharashtra. The infection rate of Karnataka and Kerala are lesser than 5% and reveal a downward trend. On the other hand, the infection rate and the high predicted number of infectives in Maharashtra calls for more preventive measures to be imposed in Maharashtra to control the disease spread. The results of this analysis provide valuable information regarding the disease spread in India. [ABSTRACT FROM AUTHOR]

A harvested logistic growth model that incorporates trapping of the adult banana weevils is formulated and solved both analytically and numerically. Key in the analysis of the model is the derivation of the critical trapping rate, that is, the threshold above which extinction of the banana weevils is a possibility. The existence of the saddle-node bifurcation is investigated. It is established that the stability of the equilibria is dependent on the relative sizes of the intrinsic growth rate and the carrying capacity. It is also found out that when the trapping rate exceeds the critical value, the model displays chaotic behavior and the trapping of the adult banana weevils in isolation can only provide short term relief. Thus a management package that targets all developmental stages of the banana weevils would be more effective. Numerical simulations are performed and agree with the analytical results. [ABSTRACT FROM AUTHOR]

The fast spreading of the COVID19 disease is overwhelming the hospitals, especially the intensive care units. And this is causing a scary crisis in the health care systems and is rising the fatality rate. The pandemic is increasing exponentially making more critical situations. To overcome the spread of the disease, the concerned countries are taking different measures even lockdowns. Unfortunately, even that the social distancing measures have showed a good effectiveness in reducing the transmission of the virus, countries such as Italy and Spain were kept struggling for weeks. Our aim in this paper, is to study the exponential progress of the outbreak, then fit the data to the logistic growth model which allows us to find the right time, with acceptable delay, the concerned country should take the lockdown decision. In this paper, we also discuss when countries such us Italy, Spain and France should have started the social distancing. The result show that when the number of confirmed cases reaches a threshold, the lockdown must have started 14 days earlier. The threshold is defined to not overwhelm the health care system. [ABSTRACT FROM AUTHOR]

Degradation of marine ecosystems through, e.g., eutrophication and climate change is a concern for sustainable fishery management worldwide, but studies on associated impacts on fish populations are rare. This study examines the effects of eutrophying nutrient loads on the economic value of perch populations along the Swedish east coast by estimating the effects of nutrient loads on the population of perch and, then, simulates the harvest value of future perch population under the changes in nutrient loads. A modified Gordon-Schaefer logistic growth model was used for econometric estimation of perch populations based on annual time series data for the period of 1970-2014. Regression analysis using the fully modified ordinary least square (FMOLS) estimator revealed that phosphorus loads had significant effects on the perch population. A 40% decrease in phosphorus loads, as suggested by the international HELCOM agreement, could increase the steady state perch population by 50%. Simple calculations showed that this could increase the total discounted recreational and commercial harvest value of the perch by 30% over a 30 year period.

Background: How many higher education researchers are there in the world? How many academic articles are published by researchers each year? This paper aims to answer these two questions by tracking the number of higher education teachers and the number of publications over the past four decades. Methods: We collected data on the number of higher education institutions and researchers from the United Nations, the World Bank, and the U.S., China, and U.K. governments (three countries with the largest number of academic publications in recent years). We used Scopus to obtain the number of publications per year. The growth of higher education researchers and academic publications were characterized using 4-parameter logistic models. Results: The number of higher education teachers-cum-researchers increased from 4 million in 1980 to 13.1 million in 2018 worldwide. Concurrently, the number of academic publications increased from 0.65 million in 1980 to 3.16 million in 2018 based on data from Scopus. At the country level, the number of academic publications from the U.S. increased from 0.15 million in 1980 to 0.70 million in 2018, while that from China increased by almost 1,000 times from 629 in 1980 to 0.60 million in 2018. Conclusions: The number of higher education researchers would reach 13.6 million and they would publish 3.21 million academic articles in 2020, imposing enormous pressure to publishers, peer-reviewers, and people who want to understand emerging scientific development. Additionally, not all academic publications are easily assessable because most articles are behind pay-walls. In addition, unethical research practices including falsification, fabrication, plagiarism, slicing publication, publication in a predatory journal or conference, etc. may hinder scientific and human development.

Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different (N , M) values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems. [ABSTRACT FROM AUTHOR]

The paper takes the industrial coupling symbiosis network (ICSN) of oil and gas resource-based urban eco-industrial parks (EIPs) as the research object. The purpose is to judge the stability of a symbiotic, one-way relying and two-way symbiosis model applied to oil and gas resource-based cities through constructing a logistic growth symbiotic network model. Through identifying and analyzing the stability model, the research concludes the stability conditions. The analytic results are as follows: In the symmetric ICSN system, it is important to maintain equal status and balanced benefit distribution among the coupled symbiotic enterprises. In the one-way-based ICSN system, the core enterprise significantly promotes the improvement of ecological efficiency the satellite enterprise while the satellite enterprise less effectively promotes the improvement of ecological efficiency of the core enterprise. In the two-way ICSN system, the core enterprise and the satellite enterprise are easily affected by the symbiotic enterprises within the network, and the stability is extremely poor. These conditions and analytic results will serve as a basis for constructing an efficient closed-loop system for ICSN of the oil and gas resource-based urban EIPs.Through the stability analysis of the industrial coupling symbiotic network of the oil and gas resource-based urban eco-industrial park, it can determine the stability conditions that affect the overall performance of the industrial park. Studies have shown that increasing network stability and improving energy efficiency in the park can improve the overall sustainability of the eco-industrial park and accelerate the effective transformation of resource-based cities. • Constructing an industrial coupling symbiotic network model. • Given stability conditions for three symbiotic modes. • Extremely poor stability of Two-way relying industry coupling symbiotic network. • Logistic growth model for network stability analysis. [ABSTRACT FROM AUTHOR]

Scratch assays are in vitro methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. Typically, scratch assays are modelled by reaction diffusion equations depicting cell migration by Fickian diffusion and proliferation by a logistic term. In a recent paper (Jin et al. in Bull Math Biol 79(5):1028–1050, 2017), the authors observed experimentally that during the early stage of the recolonisation process, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The authors did not identify the precise mechanism that causes the disturbance phase but showed that ignoring it can lead to incorrect parameter estimates. The aim of this work is to show that a nonlinear age-structured population model can account for the two phases of proliferation in scratch assays. The model consists of an age-structured cell cycle model of a cell population, coupled with an ordinary differential equation describing the resource concentration dynamics in the substrate. The model assumes a resource-dependent cell cycle threshold age, above which cells are able to proliferate. By studying the dynamics of the full system in terms of the subpopulations of cells that can proliferate and the ones that can not, we are able to find conditions under which the model captures the two-phase behaviour. Through numerical simulations, we are able to show that the interplay between the resource concentration in the substrate and the cell subpopulations dynamics can explain the biphasic dynamics. [ABSTRACT FROM AUTHOR]

The present paper deals with the logistic equation having harvesting factor by a new approach. This approach is an attempt to sketch the solutions to the model Rahmani Doust and Saraj (1).