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Автор: Grafiati

Опубліковано: 6 вересня 2023

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1

Awadalla, Muath, Yves Yannick Yameni Noupoue, and Kinda Abu Asbeh. "Psi-Caputo Logistic Population Growth Model." Journal of Mathematics 2021 (July 26, 2021): 1–9. http://dx.doi.org/10.1155/2021/8634280.

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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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2

T. Alkahtani, Badr Saad, Abdon Atangana, and Ilknur Koca. "New nonlinear model of population growth." PLOS ONE 12, no. 10 (October 24, 2017): e0184728. http://dx.doi.org/10.1371/journal.pone.0184728.

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3

Montiel-Arzate, Elia, Hector Echavarrı́a-Heras, and Cecilia Leal-Ramı́rez. "A functionally diverse population growth model." Mathematical Biosciences 187, no. 1 (January 2004): 21–51. http://dx.doi.org/10.1016/j.mbs.2003.08.009.

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4

Rodin, E. Y., and R. T. Williams. "A matrix model of population growth." Mathematical and Computer Modelling 10, no. 4 (1988): 299–306. http://dx.doi.org/10.1016/0895-7177(88)90007-6.

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5

Vance, R. R., and E. A. Coddington. "A nonautonomous model of population growth." Journal of Mathematical Biology 27, no. 5 (September 1989): 491–506. http://dx.doi.org/10.1007/bf00288430.

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6

Mohamad Radzi, Nurul Ashikin, Haliza Abd Rahman, Shariffah Suhaila Syed Jamaludin, and Arifah Bahar. "Exponential Growth Model and Stochastic Population Models: A Comparison via Population Data." Malaysian Journal of Fundamental and Applied Sciences 18, no. 1 (February 28, 2022): 60–69. http://dx.doi.org/10.11113/mjfas.v18n1.2402.

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Анотація:

A population dynamic model explains the changes of a population in the near future, given its current status and the environmental conditions that the population is exposed to. In modelling a population dynamic, deterministic model and stochastic models are used to describe and predict the observed population. For modelling population size deterministic model may provide sufficient biological understanding about the system, but if the population numbers do become small, then a stochastic model is necessary with certain conditions. In this study, both types of models such exponential, discrete-time Markov chain (DTMC), continuous-time Markov chain (CTMC) and stochastic differential equation (SDE) are applied to goat population data. Results from the simulations of stochastic realisations as well as deterministic counterparts are shown and tested by root mean square error (RMSE). The SDE model gives the smallest RMSE value which indicate the best model in fitting the data.

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7

O. Aiyedogbon, John, Sarah O. Anyanwu, Grace Hezekiah Isa, Yuriy Petrushenko, and Olena Zhuravka. "Population growth and food security: Evidence from Nigeria." Problems and Perspectives in Management 20, no. 2 (June 14, 2022): 402–10. http://dx.doi.org/10.21511/ppm.20(2).2022.33.

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Анотація:

The average agriculture output growth between 2011–2020, which stood at 3.5% against the backdrop of over 2.6% population growth rate, accounts for the present food insecurity, hunger, and malnutrition in Nigeria. The study aims to examine the impact of population growth on food security in Nigeria with data covering 1986–2020. The study employed two models: the first model analyzed agriculture output as a function of population growth rate. The second model examined the impact of population growth and agriculture productivity on economic growth. The Cochrane-Orcutt iterative method on an ordinary least squared (OLS) was employed. The study results found that population growth had a significant impact on agriculture output. However, the paper further substantiated that economic growth is significantly and positively responsive to changes in agriculture output and population growth rate in Nigeria. Among other things, the study recommended the government consider an increase in budget allocation to the agriculture sector so as to boost food output. Finally, the government may also consider introducing a policy that would encourage small families, thereby reducing the country’s population growth rate.

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8

Khodabin, Morteza, and Neda Kiaee. "Stochastic Dynamical Theta-Logistic Population Growth Model." SOP Transactions on Statistics and Analysis 2014, no. 3 (October 31, 2014): 1–15. http://dx.doi.org/10.15764/stsa.2014.03001.

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9

Tiebout, Charles M. "COMMUNITY INCOME MULTIPLIERS: A POPULATION GROWTH MODEL‡." Journal of Regional Science 2, no. 1 (July 28, 2006): 75–84. http://dx.doi.org/10.1111/j.1467-9787.1960.tb00836.x.

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10

Kajanovičová, Viktória, Branislav Novotný, and Michal Pospíšil. "Ramsey model with non-constant population growth." Mathematical Social Sciences 104 (March 2020): 40–46. http://dx.doi.org/10.1016/j.mathsocsci.2020.01.004.

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11

Ribeiro, Fabiano L., and Kayo N. Ribeiro. "A one dimensional model of population growth." Physica A: Statistical Mechanics and its Applications 434 (September 2015): 201–10. http://dx.doi.org/10.1016/j.physa.2015.03.021.

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12

DE, S. "Stochastic model of population growth and spread." Bulletin of Mathematical Biology 49, no. 1 (1987): 1–11. http://dx.doi.org/10.1016/s0092-8240(87)80032-0.

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13

Jablanovic, Vesna, and Nada Lakic. "A chaotic growth model of agricultural population." Journal of Agricultural Sciences, Belgrade 47, no. 1 (2002): 97–103. http://dx.doi.org/10.2298/jas0201097j.

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Анотація:

Using the autoregression models, the paper considers movement of agricultural population. Irregular movement of agricultural population can be analyzed within the formal framework of the chaotic growth model. The basic aims of this paper are: firstly, to set up a chaotic growth model of agricultural population; and secondly, to analyze the stability of agricultural population movement according to the presented logistic growth model in the world and eight group of countries in the period 1967-1997.

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14

Xuan, Hai Yan, An Qi Zhang, and Na Na Yang. "A Model in Chinese Population Growth Prediction." Applied Mechanics and Materials 556-562 (May 2014): 6811–14. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.6811.

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Firstly, we calculated several statistics relating to the population forecast. Secondly, ba-sed on the Logistic prediction models, against Logistic model defects, we obtained the improved prediction model. Finally, using China's total population in 2004 as the initial population, we predict the total population of China in the next 30 years and in 2050 year by applying the model.

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15

De, S. S. "Stochastic model of population growth and spread." Bulletin of Mathematical Biology 49, no. 1 (January 1987): 1–11. http://dx.doi.org/10.1007/bf02459957.

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16

Simpson, Matthew J., Alexander P. Browning, David J. Warne, Oliver J. Maclaren, and Ruth E. Baker. "Parameter identifiability and model selection for sigmoid population growth models." Journal of Theoretical Biology 535 (February 2022): 110998. http://dx.doi.org/10.1016/j.jtbi.2021.110998.

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17

Diez, Pedro J. Gutiérrez. "Population, immigration and growth in a Romer endogenous growth model." Global Business and Economics Review 20, no. 5/6 (2018): 679. http://dx.doi.org/10.1504/gber.2018.094433.

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18

Gutiérrez Diez, Pedro J. "Population, immigration and growth in a Romer endogenous growth model." Global Business and Economics Review 20, no. 5/6 (2018): 679. http://dx.doi.org/10.1504/gber.2018.10014905.

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19

Pratama, Rian Ade, A. Muh Amil Siddik, Oswaldus Dadi, and Kasbawati Kasbawati. "Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator." Desimal: Jurnal Matematika 5, no. 3 (December 20, 2022): 279–88. http://dx.doi.org/10.24042/djm.v5i3.13160.

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Анотація:

Bazykin's predator-prey population model is considered to represent the exchange stability condition of population growth. The existence of the hydra effect and, at the same time, analyzing its influence on population growth. The condition of the model divides the species into a stage structure, namely, prey, immature predators, and mature predators. The population growth of the three species has its own characteristics. This research revealed that the Holling type II and intraspecific predatory function responses together induce the Hydra effect. In the model formed, there are 12 equilibrium points, with details for every seven points of negative imaginary equilibrium and five points of non-negative equilibrium. The findings of research studies center on five points of non-negative equilibrium. All real roots that interpret the species population's growth conditions are taken and tested for long-term stability. The test results show one point of equilibrium that meets the Routh-Hurwitz criteria and their characteristic equations. In numerical simulations, the maximum sustained yield is in the local asymptotic stable state. The growth of prey trajectories increased significantly, although at the beginning of the interaction there was a slowdown in population growth. Meanwhile, the population of immature predators and mature predators was not significantly different. Both populations grow steadily toward the point of population stability. It turns out that the two populations grow inversely, the faster the rate of predation by predators, the faster the growth rate of the prey population.

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20

Laila, Umi, Rifa Nurhayati, Tyas Utami, and Endang Sutriswati Rahayu. "Prediction of Microbial Population in Sorghum Fermentation through Mathematical Models." Reaktor 19, no. 4 (December 31, 2019): 152–61. http://dx.doi.org/10.14710/reaktor.19.4.152-161.

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The mathematical models can be used as a tool in predicting microbial population in sorghum fermentation, either spontaneous fermentation or fermentation with the addition of lactic acid bacteria (LAB) inoculum. Gompertz model modified by Gibson, Gompertz model modified by Zwietering, Baranyi-Robert model, Fujikawa model, Richards model, Schnute model were used in predicting the growth of lactic acid bacteria (LAB) and coliform bacteria during spontaneous fermentation, and also the growth of LAB during fermentation with the addition of inoculum. Meanwhile, there was death (inactivation) of coliform bacteria during sorghum fermentation with the addition of LAB inoculum. The Geeraerd model and the Gompertz model modified by Gil et al. were used to predict the inactivation. The accuracy and precision of models were evaluated based on the Root Mean of Sum Square Error (RMSE), coefficient of determination (R2), and curve fitting. Gompertz model modified by Gibson had the highest accuracy and precision, which was followed by the accuracy of the Fujikawa model and Baranyi-Robert model in predicting the growth of LAB and the growth of coliform bacteria during spontaneous fermentation. Meanwhile, in predicting LAB growth during fermentation with the addition of inoculum, high accuracy and precision was obtained from Richards and Schnute models. In predicting the inactivation of coliform bacteria, Geeraerd model provided higher accuracy and precision compared to Gompertz model modified by Gil et al. Keywords: fermentation; inoculum; mathematical; model; sorghum; spontaneous

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21

Jiao, Yan, Richard Neves, and Jess Jones. "Models and model selection uncertainty in estimating growth rates of endangered freshwater mussel populations." Canadian Journal of Fisheries and Aquatic Sciences 65, no. 11 (November 2008): 2389–98. http://dx.doi.org/10.1139/f08-141.

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Appropriate inference of population status for endangered species is extremely important. Using a single model for estimating population growth rates is typically inadequate for assessing endangered species because inferences based on only one “best” model ignore model uncertainty. In this study, the endangered dromedary pearlymussel ( Dromus dromas ) in the Clinch and Powell rivers of eastern Tennessee, USA, was used as an example to demonstrate the importance of multiple models, with consideration of environmental noises for evaluating population growth. Our results showed that more than one model deserves consideration in making inferences of population growth rate. A Bayesian model averaging approach was used to make inferences by weighting each model using the deviance information criterion. To test the uncertainty resulting from model selection and the efficiency of the Bayesian averaging approach, a simulation study was conducted on the dromedary pearlymussel populations, which showed that model selection uncertainty is very high. The results of these tests lead us to recommend using Bayesian model averaging to assess population growth status for endangered species, by balancing goodness-of-fit and selection uncertainty among alternate models.

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22

LEMOS, CARLOS GENTIL ORO, and MARCIO SANTOS. "SEXUAL REPRODUCTION IN A SIMPLE GROWTH POPULATION MODEL." International Journal of Modern Physics C 23, no. 05 (May 2012): 1250022. http://dx.doi.org/10.1142/s0129183112500222.

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One of the most important characteristics in the survival of a species is related to the kind of reproduction responsible for the offspring generation. However, only in the last years the role played by sexual reproduction has been investigated. Then, for a better understanding of this kind of process we introduce, in this work, a surface reaction model that describes the role of the sexual reproduction. In our model two different elements of the species, representing male and female, can interact to reproduce a new element. The sex of this new element is chosen with a given probability and in order to take into account the mortality rate we introduce another kind of individual. The value of the spatial density of this element remains constant during the time evolution of the system. The model is studied using Monte Carlo simulations and mean field approximation. Depending on the values of the control parameters of the model, the system can attain two stationary states: In one of them the population survives and in the other it can be extinguished. Besides, accordingly to our results, the phase diagram of the model shows a discontinuous transition between these two states.

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23

Ariza-Hernandez, Francisco J., Jorge Sanchez-Ortiz, Martin P. Arciga-Alejandre, and Luis X. Vivas-Cruz. "Bayesian Analysis for a Fractional Population Growth Model." Journal of Applied Mathematics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9654506.

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Анотація:

We implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. We estimate the parameters in the model and we make a comparison between this model and an exponential one, based on an approximation of Bayes factor. A simulation study is carried out to show the performance of the estimators and the Bayes factor. Finally, we present a real data example to illustrate the effectiveness of the method proposed here and the pertinence of using a fractional model.

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24

Cayssials, Gaston, and Santiago Picasso. "The Solow-Swan model with endogenous population growth." Journal of Dynamics & Games 7, no. 3 (2020): 197–208. http://dx.doi.org/10.3934/jdg.2020014.

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25

Pedro, Francielle Santo, Laécio Carvalho de Barros, and Estevão Esmi. "Population growth model via interactive fuzzy differential equation." Information Sciences 481 (May 2019): 160–73. http://dx.doi.org/10.1016/j.ins.2018.12.076.

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26

Bucci, Alberto, and Xavier Raurich. "Population and Economic Growth Under Different Growth Engines." German Economic Review 18, no. 2 (May 1, 2017): 182–211. http://dx.doi.org/10.1111/geer.12092.

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Abstract Using a growth model with physical capital accumulation, human capital investment and horizontal R&D activity, this paper proposes an alternative channel through which an increase in the population growth rate may yield a non-uniform (i.e., a positive, negative, or neutral) impact on the long-run growth rate of per-capita GDP, as available empirical evidence seems mostly to suggest. The proposed mechanism relies on the nature of the process of economic growth (whether it is fully or semi-endogenous), and the peculiar engine(s) driving economic growth (human capital investment, R&D activity, or both). The model also explains why in the long term the association between population growth and productivity growth may ultimately be negative when R&D is an engine of economic growth.

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27

BINTZ, JASON, and SUZANNE LENHART. "OPTIMAL RESOURCE ALLOCATION FOR A DIFFUSIVE POPULATION MODEL." Journal of Biological Systems 28, no. 04 (December 2020): 945–76. http://dx.doi.org/10.1142/s0218339020500230.

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The spatial distribution of resources for diffusive populations can have a strong effect on population abundance. We investigate the optimal allocation of resources for a diffusive population. Population dynamics are represented by a parabolic partial differential equation with density-dependent growth and resources are represented through their space- and time-varying influence on the growth function. We consider both local and integral constraints on resource allocation. The goal is to maximize the abundance of the population while minimizing the cost of resource allocation. After characterizing the optimal control in terms of the population solution and the adjoint functions, we illustrate several scenarios numerically. The effects of initial and boundary conditions are important for the optimal allocation of resources.

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28

BINTZ, JASON, and SUZANNE LENHART. "OPTIMAL RESOURCE ALLOCATION FOR A DIFFUSIVE POPULATION MODEL." Journal of Biological Systems 28, no. 04 (December 2020): 945–76. http://dx.doi.org/10.1142/s0218339020500230.

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Анотація:

The spatial distribution of resources for diffusive populations can have a strong effect on population abundance. We investigate the optimal allocation of resources for a diffusive population. Population dynamics are represented by a parabolic partial differential equation with density-dependent growth and resources are represented through their space- and time-varying influence on the growth function. We consider both local and integral constraints on resource allocation. The goal is to maximize the abundance of the population while minimizing the cost of resource allocation. After characterizing the optimal control in terms of the population solution and the adjoint functions, we illustrate several scenarios numerically. The effects of initial and boundary conditions are important for the optimal allocation of resources.

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29

Wei Bin, Zhang. "Population growth and gender time distribution in a small-open growth model." Journal of Economics and International Finance 7, no. 6 (June 30, 2015): 144–50. http://dx.doi.org/10.5897/jeif2015.0643.

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30

Karras, Georgios. "Land and population growth in the Solow growth model: Some empirical evidence." Economics Letters 109, no. 2 (November 2010): 66–68. http://dx.doi.org/10.1016/j.econlet.2010.08.019.

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31

Loibel, Selene, Marinho G. Andrade, João B. R. do Val, and Alfredo R. de Freitas. "Richards growth model and viability indicators for populations subject to interventions." Anais da Academia Brasileira de Ciências 82, no. 4 (December 2010): 1107–26. http://dx.doi.org/10.1590/s0001-37652010000400028.

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Анотація:

In this work we study the problem of modeling identification of a population employing a discrete dynamic model based on the Richards growth model. The population is subjected to interventions due to consumption, such as hunting or farming animals. The model identification allows us to estimate the probability or the average time for a population number to reach a certain level. The parameter inference for these models are obtained with the use of the likelihood profile technique as developed in this paper. The identification method here developed can be applied to evaluate the productivity of animal husbandry or to evaluate the risk of extinction of autochthon populations. It is applied to data of the Brazilian beef cattle herd population, and the the population number to reach a certain goal level is investigated.

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32

Zhulego, Vladimir, Artem Balyakin, and Mikhail Sorokin. "Convergence and depopulation processes in the Center-Periphery system." Population 26, no. 2 (June 27, 2023): 30–39. http://dx.doi.org/10.19181/population.2023.26.2.3.

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The paper proposes advancement of a stratum demographic model characterized by the presence of two strata — the Center and the Periphery, which are different in respects of their way of life, development level and social values. The processes of convergence and depopulation in the heterogeneous system of the Center-Periphery type were studied. Various variants of “catch-up development” of the Periphery are considered within the framework of numerical simulation. Modes of economic growth that contribute to the convergence of income levels in the countries of the Center and the Periphery are indicated, depending on the value of the characteristic time of convergence. There are identified the regimes of a stable and supposedly irreversible depopulation of the Periphery. It is shown that economic participation of the Center in changing the situation in the Periphery countries might be necessary to achieve economic convergence for maintaining the stability of the entire system. As an explanatory principle of the observed phenomena, the institutional trap concept is proposed. A number of socio-economic interpretations of the dynamics of the Center-Periphery system as well as the possibility of the System behavior control by appropriate management decisions are discussed on the results of computer modeling. Further development of the proposed model may include studying other scenarios of economic interaction and taking into account additional demographic and migration parameters in the equations of economic growth.

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33

Moen, Ron, Yosef Cohen, and John Pastor. "Linking Moose Population and Plant Growth Models with a Moose Energetics Model." Ecosystems 1, no. 1 (January 1, 1998): 52–63. http://dx.doi.org/10.1007/s100219900005.

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34

Haliki, Emir. "A dynamic network model for population growth and urbanization." Cumhuriyet Science Journal 40, no. 4 (December 31, 2019): 896–901. http://dx.doi.org/10.17776/csj.632996.

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35

Luo, Yi Hong, and Shu Guang Zhang. "Resource Allocation Optimization Problem on the Population Growth Model." Applied Mechanics and Materials 291-294 (February 2013): 1507–13. http://dx.doi.org/10.4028/www.scientific.net/amm.291-294.1507.

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Анотація:

In this paper we mainly investigated the resource allocation optimization problem in three population models: death process, PDE model and birth and density-independent growth model. Considering the inﬂuence on population growth from different factors, ﬁnd the best proportion of population to obtain the biggest economic beneﬁt. Furthermore, we consider the effect on resource allocation from one more industrial structure on density-independent growth model. Finally, we compared the above models.

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36

Banasiak, Jacek, Katarzyna Pichór, and Ryszard Rudnicki. "Asynchronous Exponential Growth of a General Structured Population Model." Acta Applicandae Mathematicae 119, no. 1 (December 30, 2011): 149–66. http://dx.doi.org/10.1007/s10440-011-9666-y.

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37

Mathur, Vijay K., Sheldon H. Stein, and Rishi Kumar. "A DYNAMIC MODEL OF REGIONAL POPULATION GROWTH AND DECLINE*." Journal of Regional Science 28, no. 3 (August 1988): 379–95. http://dx.doi.org/10.1111/j.1467-9787.1988.tb01089.x.

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38

Boarnet, Marlon G. "AN EMPIRICAL MODEL OF INTRAMETROPOLITAN POPULATION AND EMPLOYMENT GROWTH." Papers in Regional Science 73, no. 2 (January 14, 2005): 135–52. http://dx.doi.org/10.1111/j.1435-5597.1994.tb00607.x.

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39

asgari, mahnaz. "Extended Operational Matrix For Solving Fractional Population Growth Model." Mathematical Researches 6, no. 1 (May 1, 2020): 89–98. http://dx.doi.org/10.52547/mmr.6.1.89.

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40

Momota, Akira. "A population-macroeconomic growth model for currently developing countries." Journal of Economic Dynamics and Control 33, no. 2 (February 2009): 431–53. http://dx.doi.org/10.1016/j.jedc.2008.07.001.

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41

Khodabin, M., K. Maleknejad, M. Rostami, and M. Nouri. "Interpolation solution in generalized stochastic exponential population growth model." Applied Mathematical Modelling 36, no. 3 (March 2012): 1023–33. http://dx.doi.org/10.1016/j.apm.2011.07.061.

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42

Vlad, Marcel O., and Vlad T. Popa. "A new nonlinear model of age-dependent population growth." Mathematical Biosciences 76, no. 2 (October 1985): 161–84. http://dx.doi.org/10.1016/0025-5564(85)90003-3.

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43

Guerrini, Luca. "The Ramsey model with a bounded population growth rate." Journal of Macroeconomics 32, no. 3 (September 2010): 872–78. http://dx.doi.org/10.1016/j.jmacro.2009.08.004.

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44

Muliyani, N., R. Ratianingsih, and N. Nacong. "ANALISIS KESTABILAN MODEL MATEMATIKA PENYEBARAN PENYAKIT SIFILIS PADA MANUSIA." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 15, no. 1 (May 14, 2018): 1–10. http://dx.doi.org/10.22487/2540766x.2018.v15.i1.10189.

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Анотація:

Syphilis is a sexually transmitted infection caused by the bacterium Treponema pallidum spiroset subspecies pallidum. Transmitted through sexual contact, the infection can also be transfered from mother to fetus during pregnancy or at birth, that causes congenital syphilis. The mathematical model that represents the spread of the disease was adapted from a mathematical model SEI. The model classifiles human population into vulnerable suscepted women and men, Exposed , and Infected , sub-populations of women vulnerable , sub-populations women incubation period , sub-populations of women infected and a sub-population of men vulnerable , sub-populations incubation period male , sub-populations laki- infected men considered in the model. The derived models gives two critical point that is free disease and endemic critical point. The existence of a critical point must satisfye and . The model was analyzed by the linierized method and Routh-Hurwitz criteria to determine the system stability. The simulation shows that, in case of free-disease syphilis spread condition, the population of women and men has increased. The growth of women population is higher than the men population. it means that the spread of syphilis occurs faster in the men sub-population. In endemic condition of syphilis disease spread, the women population will growth rapidly than the men population.

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45

Horowitz, Joseph, Mark D. Normand, Maria G. Corradini, and Micha Peleg. "Probabilistic Model of Microbial Cell Growth, Division, and Mortality." Applied and Environmental Microbiology 76, no. 1 (November 13, 2009): 230–42. http://dx.doi.org/10.1128/aem.01527-09.

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ABSTRACT After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability Pd (t)δt, dead with probability Pm (t)δt, or alive but undivided with the probability 1 − [Pd (t) + Pm (t)]δt, where t is time, Pd (t) expresses the probability of division for an individual cell per unit of time, and Pm (t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat's properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population's size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With Pd (t) and Pm (t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data.

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46

Shakirova, Alisa, and Elena Demkina. "Conceptualization of the efficiency model of the institution of social protection of population (Part 1)." Population 24, no. 1 (March 30, 2021): 66–76. http://dx.doi.org/10.19181/population.2021.24.1.7.

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Анотація:

Today, we are faced with the coronavirus (COVID-19) pandemic, which directly or indirectly affected all countries and regions of the world. The State policy of all countries is aimed at containing the spread of the virus and meeting the basic needs of people in forced isolation. This situation has once again proved the importance of the institution of social protection of population (hereinafter—ISPP) and the need to ensure the efficiency of its functioning. The high rates of growth of social changes, in turn, cause a certain lag behind the process of their scientific comprehension accumulation of issues unsolved by means of sociological science. Thus, the current system for assessing efficiency of the ISPP functioning in terms of the actually obtained result against the normative / planned one, as well as the system for assessing economic costs, do not meet the challenges faced by modern science and management. Many problems concerning assessment of the ISPP functioning remain unresolved. In particular, the entire range of difficulties faced by consumers of social services has not been fully disclosed; the issues of achieving a consistently high satisfaction of vulnerable groups of the population with various quantitative and qualitative parameters of service provision are acute. The article discusses the scientific concepts and approaches to assessing the effectiveness of social protection of population used in domestic and foreign social science and practice, and outlines the developed model for assessing effectiveness of the ISPP functioning on the example of the Republic of Tatarstan, which is based on an integrated approach that consists in fixing the temporal and spatial aspects of assessing effectiveness of the ISPP functioning.

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47

Shakirova, Alisa, and Elena Demkina. "Conceptualization of the efficiency model of the institution of social protection of population (Part 2)." Population 24, no. 2 (June 29, 2021): 97–108. http://dx.doi.org/10.19181/population.2021.24.2.9.

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Анотація:

Today we are faced with the coronavirus (COVID-19) pandemic, which directly or indirectly has affected all countries and regions of the world. The state policy of all countries is aimed at containing the spread of the virus and meeting the basic needs of people in forced isolation. This situation has once again proved the importance of the institution of social protection of population (hereinafter—ISPP) and the need to ensure the efficiency of its functioning. The high growth rates of social changes, in turn, cause a certain lagging behind the process of their scientific comprehension — piling up issues unresolved by means of sociological science. Thus, the current system for assessing the ISPP functioning in terms of the actually obtained result against the normative/planned one, as well as the system for estimating economic costs, do not meet the challenges that modern science and management face. Many problems related to assessment of the ISPP functioning remain unresolved. In particular, the entire range of difficulties faced by consumers of social services has not been fully disclosed; the issues of achieving a consistently high satisfaction of vulnerable population groups with various quantitative and qualitative parameters of service provision are acute. The article discusses the scientific concepts and approaches to assessing effectiveness of the social protection of population used in domestic and foreign social science and practice. It outlines the authors' model for assessing effectiveness of the ISPP functioning on the example of the Republic of Tatarstan, which is based on an integrated approach that consists in fixing the temporal and spatial aspects of assessing effectiveness of the ISPP functioning.

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48

Nurkholipah, N. S., Z. Amarti, N. Anggriani, and A. K. Supriatna. "A fuzzy mathematical model of West Java population with logistic growth model." IOP Conference Series: Materials Science and Engineering 332 (March 2018): 012035. http://dx.doi.org/10.1088/1757-899x/332/1/012035.

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49

AGARWAL, MANJU, and SAPNA DEVI. "A RESOURCE-DEPENDENT COMPETITION MODEL: EFFECTS OF POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION." International Journal of Modeling, Simulation, and Scientific Computing 03, no. 02 (May 10, 2012): 1250003. http://dx.doi.org/10.1142/s1793962312500031.

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In this paper, a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource. It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass. Further, it is assumed that the resource biomass too is growing logistically in the environment and its carrying capacity decreases with the increase in densities of competing species and industrialization. The growth rate of population pressure is assumed to be proportional to the densities of competing species. Stabilities of all equilibria and conditions which influence the permanence of the system are carried out using theory of differential equations. Numerical simulations are performed to accomplish our analytical findings. It is shown that the equilibrium density of resource biomass decreases as (i) the growth rate coefficient of population pressure increases (ii) the growth rate coefficient of industrialization due to population pressure increases and (iii) the growth rate coefficient of industrialization due to resource biomass increases. It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure. Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.

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50

Zeng, Yingxin, Peiting Zhu, and Zhitian Hou. "Analysis on the growth of fungal population and the interaction between population." Highlights in Science, Engineering and Technology 6 (July 27, 2022): 242–48. http://dx.doi.org/10.54097/hset.v6i.967.

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The carbon cycle is an important part of the geochemical cycle of the Earth. As the primary decomposers of organic material in terrestrial ecosystems, fungi are critical agents of the global carbon cycle. Based on the two characteristics of a fungus, the growth rate of the fungus and the fungus’ tolerance to moisture, this article will establish a mathematical model to describe fungi and their role in the decomposition of ground litter (dead plant material) and woody fibers. First of all, the growth rate of a single fungus population was determined by modifying the Logistic population growth model. According to the hyphal extension rate of a fungus comprehensively measured by temperature and humidity changes, the effect of hyphal extension rate on wood decomposition rate is obtained. Next, this article uses the competitive ranking of fungi and the moisture niche width to determine the moisture tolerance of fungi and the influence of fungus moisture tolerance on wood decomposition rate. Integrating the hyphal extension rate and moisture tolerance of fungi, we established a wood decomposition rate model for a single fungus community. Based on this model and Lotka-Volterra model, this paper quantified and described the interaction between different types of fungi, and constructed a model of wood decomposition rate under the interaction of multiple fungal populations. Finally, the sensitivity and stability of the model are analyzed and tested. For the role and importance of biodiversity in the ecosystem, we conducted a more comprehensive study, and analyzed the role and principle of biodiversity in the process of environmental factors change.

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