An Improved Logistic Model Illustrating Microcystis aeruginosa Growth Under Different Turbulent Mixing Conditions

To overcome the limitations of the normal logistic equation, we aimed to improve the logistic model under hydrodynamic conditions for the examination of the responses of cyanobacterium, coupled turbulence mixing, and growth of cyanobacterium in population dynamics models. Selecting Microcystis aeruginosa and experimenting with the ideal conditions in a laboratory beaker, the chlorophyll-a concentration reached the corresponding maximum under each turbulent condition compared with the control. According to the experiment results, the theory of mass transfer, turbulence mixing, and the logistic equation are organically combined. The improved logistic growth model of Microcystis aeruginosa and competition growth model in the symbiont Scenedesmus quadricauda under turbulent conditions were established. Using the MATLAB multi-parameter surface fitting device, both models produced good fitting effects, with R > 0.95, proving that the results fit the models, and demonstrating the relationship of the unity of nutrient transfer and algae growth affected by turbulence mixing. With continuous increases in turbulent mixing, the fitted curve became smoother and steadier. Algae stimulated by turbulence accelerate reproduction and fission to achieve population dominance. The improved logistic model quantitatively explains the Microcystis aeruginosa response to turbulence and provides a basis to represent ecological and biogeochemical processes in enclosed eutrophic water bodies.

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Psi-Caputo Logistic Population Growth Model

Journal of Mathematics ◽

10.1155/2021/8634280 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Muath Awadalla ◽

Yves Yannick Yameni Noupoue ◽

Kinda Abu Asbeh

Keyword(s):

Population Growth ◽

Fractional Derivative ◽

Carrying Capacity ◽

Chinese Population ◽

Logistic Model ◽

Logistic Equation ◽

Logistic Growth ◽

Growth Equation ◽

Uniqueness Of The Solution ◽

Better Than

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.

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Fitting a logistic growth model to yield traits of lettuce cultivars growing in summer

Revista Colombiana de Ciencias Hortícolas ◽

10.17584/rcch.2020v14i1.8955 ◽

2020 ◽

Vol 14 (1) ◽

Author(s):

Fernanda Carini ◽

Alberto Cargnelutti-Filho ◽

Jéssica Maronez De Souza ◽

Rafael Vieira Pezzini ◽

Cassiane Ubessi ◽

...

Keyword(s):

Confidence Intervals ◽

Growth Model ◽

Iterative Process ◽

Logistic Model ◽

Goodness Of Fit ◽

Least Squares Method ◽

Logistic Growth ◽

Model Parameters ◽

Yield Traits ◽

Logistic Growth Model

The objective of this study was to fit a logistic model to fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars to describe growth in summer. Cultivars Crocantela, Elisa, Rubinela, and Vera were evaluated in the summer of 2017 and 2018, in soil in protected environment and in soilless system. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters of 8 plants were weighed every 4 days. The model parameters were estimated using the software R, using the least squares method and iterative process of Gauss-Newton. We also estimated the confidence intervals of the parameters, verified the assumptions of the models, calculated the goodness-of-fit measures and the critical points, and quantified the parametric and intrinsic nonlinearities. The logistic growth model fitted well to fresh and dry leaf and shoot matters of cultivars Crocantela, Elisa, Rubinela, and Vera and is indicated to describe the growth of lettuce.

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Science Students’ Spontaneous Utilization of School Library with Logistic Growth Model: A Focus on Gender

Malikussaleh Journal of Mathematics Learning (MJML) ◽

10.29103/mjml.v4i1.2894 ◽

2021 ◽

Vol 4 (1) ◽

pp. 20

Author(s):

Chinedu Victor Obasi

Keyword(s):

Growth Model ◽

School Library ◽

Logistic Equation ◽

Male Students ◽

Logistic Growth ◽

Science Students ◽

Imo State ◽

Library Resources ◽

Logistic Growth Model ◽

Do So

In this paper the logistic growth model of spontaneous utilization of school library in Imo State, is presented. First‐order variables separable logistic equation is solved. The parameters that gave the best logistic curve for the data were determined. The number of male and female science students who utilized school library spontaneously also is presented. The logistic equation allows rigorous estimation of 2.34% growth rate of male science students’ spontaneous utilization of school library in Imo State. While that of female students is decreasing by 2.71%. The results revealed that male students are experiencing upward trend in the spontaneous utilization of school library while their female counterparts are experiencing downward trend. Therefore, it is recommended that science students should utilize the school library resources spontaneously without being induced to do so. They should also develop passion for reading because reading books pushes readers to use their imaginations and encourages creativity for scientific endeavours.

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The poststagnation stage for mature tourism areas

Tourism Economics ◽

10.5367/te.2015.0533 ◽

2016 ◽

Vol 23 (2) ◽

pp. 387-402 ◽

Cited By ~ 6

Author(s):

Isabel P. Albaladejo ◽

María Pilar Martínez-García

Keyword(s):

Life Cycle ◽

Growth Model ◽

Logistic Model ◽

Temporal Evolution ◽

Growth Models ◽

Life Cycles ◽

Logistic Growth ◽

Tourism Sector ◽

Passenger Flows ◽

Logistic Growth Model

The tourism area life cycle (TALC) model of Butler explains the temporal evolution of a tourism resort. Lundtorp and Wanhill find that the logistic growth model represents the first phases of the TALC model. However, since the logistic model assumes a fixed tourism market ceiling, it fails to explain the poststagnation stage, where rejuvenation, decline, or any other intermediate possibility may arise. Taking into account the data of passenger flows to Bornholm from 1912 to 2001 collected by Lundtorp and Wanhill, the authors find that the superposition of several logistic growth models fits better with these data. Then they propose a multilogistic growth model, where investment or innovation in the tourism sector boosts the addition of new logistic curves which superpose the old ones. The continuous birth and superposition of these new life cycles is not free; it requires the purposive effort of entrepreneurs and governments seeking new markets and the improvement of infrastructures.

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Application of Logistic Model in Container Throughput Prediction

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.401-403.2163 ◽

2013 ◽

Vol 401-403 ◽

pp. 2163-2165

Author(s):

Pan Zheng ◽

Shou Jiang Zhao ◽

Hao Fan

Keyword(s):

Growth Model ◽

Logistic Model ◽

Logistic Growth ◽

Real Situation ◽

The Real ◽

Limited Space ◽

Logistic Growth Model

Logistic growth model is important for studying the increasing laws in limited space. In this paper, the container throughput of Wuhan xingang has been studied by using logistic model. Compared with the actual throughput, container throughput prediction using logistic growth model is in accordance with the real situation on the whole.

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Malthusian Catastrophe: Species Extinction Caused by Oversized Population

10.1101/134221 ◽

2017 ◽

Author(s):

Xubin Pan

Keyword(s):

Lower Limit ◽

Growth Model ◽

Logistic Model ◽

Allee Effect ◽

Extinction Risk ◽

Logistic Growth ◽

Extinction Debt ◽

Species Extinction ◽

Upper Limit ◽

Logistic Growth Model

AbstractThere is one pseudo-extinction debt and four occurring conditions for real extinction debt. Since small and oversized populations have a high extinction risk, Pan threshold (upper limit) was calculated for Verhulst-Pear “logistic” growth model and logistic model with the Allee effect, an important parameter corresponding to Allee threshold (lower limit).

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Models and data Analysis of the Outbreak Risk of COVID-19

International Journal of Coronaviruses ◽

10.14302/issn.2692-1537.ijcv-20-3383 ◽

2020 ◽

Vol 1 (4) ◽

pp. 26-32

Author(s):

Jinming Cao ◽

Xia Jiang ◽

Bin Zhao

Keyword(s):

Growth Model ◽

Prevention And Control ◽

Logistic Model ◽

Virus Transmission ◽

Rapid Expansion ◽

Chinese Patients ◽

Mathematical Representation ◽

Logistic Growth ◽

Cumulative Number ◽

And Control

With the spread of the new coronavirus around the world, governments of various countries have begun to use the mathematical modeling method to construct some virus transmission models assessing the risks of spatial spread of the new coronavirus COVID-19, while carrying out epidemic prevention work, and then calculate the inflection point for better prevention and control of epidemic transmission. This work analyzes the spread of the new coronavirus in China, Italy, Germany, Spain, and France, and explores the quantitative relationship between the growth rate of the number of new coronavirus infections and time. In investigating the dynamics of a disease such as COVID-19, its mathematical representation can be constructed at many levels of details, guided by the questions the model tries to help answer. Mathematical sophistication may have to yield to a more pragmatic approach closer to the ability to make predictions that inform public health policies. Background In December 2019 , the first Chinese patients with pneumonia of unknown cause is China admitted to hospital in Wuhan, Hubei Jinyintan , since then, COVID-19 in the rapid expansion of China Wuhan, Hubei, in a few months time, COVID-19 is Soon it spread to a total of 34 provincial-level administrative regions in China and neighboring countries, and Hubei Province immediately became the hardest hit by the new coronavirus. In an emergency situation, we strive to establish an accurate infectious disease retardation growth model to predict the development and propagation of COVID-19, and on this basis, make some short-term effective predictions. The construction of this model has Relevant departments are helpful for the prevention and monitoring of the new coronavirus, and also strive for more time for the clinical trials of Chinese researchers and the research on vaccines against the virus to eliminate the new corona virus as soon as possible. Methods According to the original data change law, Establish a Logistic growth model, we collect and compare and integrate the spread of COVID-19 in China, Italy, France, Spain and Germany, record the virus transmission trend among people in each country and the protest measures of relevant government departments. Findings Based on the analysis results of the Logistic model model, the Logistic model has a good fitting effect on the actual cumulative number of confirmed cases, which can bring a better effect to the prediction of the epidemic situation and the prevention and control of the epidemic situation. Interpretation In the early stage of the epidemic, due to inadequate anti-epidemic measures in various countries, the epidemic situation in various countries spread rapidly. However, with the gradual understanding of COVI D -19, the epidemic situation began to be gradually controlled, thereby retarding growth

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