A Neoclassical Growth Model for Population Dynamics in a Homogeneous Habitat

2001 ◽  
Author(s):  
Peter Vadasz ◽  
Alisa S. Vadasz
Keyword(s):  
Experimental Data ◽  
Growth Model ◽  
Logistic Growth ◽  
Lag Phase ◽  
Growth Stages ◽  
Initial Growth ◽  
Neoclassical Model ◽  
Wide Range ◽  
Logistic Growth Model ◽  
Special Case

Abstract A neoclassical model is proposed for the growth of cell and other populations in a homogeneous habitat. The model extends on the Logistic Growth Model (LGM) in a non-trivial way in order to address the cases where the Logistic Growth Model (LGM) fails short in recovering qualitative as well as quantitative features that appear in experimental data. These features include in some cases overshooting and oscillations, in others the existence of a “Lag Phase” at the initial growth stages, as well as an inflection point in the “In curve” of the population size. The proposed neoclassical model recovers also the Logistic Growth Curve as a special case. Comparisons of the solutions obtained from the proposed neoclassical model with experimental data confirm its quantitative validity, as well as its ability to recover a wide range of qualitative features captured in experiments.

POPULATION DYNAMICS FOR SPIN-POLARON-PAIRS IN HIGH-Tc SUPERCONDUCTORS

1993 ◽  
Vol 07 (05) ◽  
pp. 325-330
Author(s):  
RONALDO MOTA
Keyword(s):  
Experimental Data ◽  
Population Dynamics ◽  
Critical Temperature ◽  
Growth Model ◽  
Logistic Growth ◽  
Spin Polaron ◽  
High Tc Superconductors ◽  
High Tc ◽  
Logistic Growth Model ◽  
Good Concordance

A study of the population dynamics for spin-polaron-pairs in high-T c superconductors is presented. A particular population dynamical model and its appropriateness is discussed. Numerical results are obtained for the x-dependence of the critical temperature using the logistic growth model and a good concordance with experimental data has been obtained for T c as a function of x for La 2 − x Sr x CuO 4. A discussion of various aspects and implications of the model is given.

Development and Validation of a Dynamic Growth Model for Listeria monocytogenes in Fluid Whole Milk

1999 ◽  
Vol 62 (2) ◽  
pp. 170-176 ◽  
Author(s):  
S. H. ALAVI ◽  
V. M. PURI ◽  
S. J. KNABEL ◽  
R. H. MOHTAR ◽  
R. C. WHITING
Keyword(s):  
Experimental Data ◽  
Listeria Monocytogenes ◽  
Growth Model ◽  
Extreme Values ◽  
Exponential Growth Phase ◽  
Lag Phase ◽  
Maximum Relative Error ◽  
Whole Milk ◽  
Dynamic Growth ◽  
Fluid Milk

Listeria monocytogenes, a psychrotrophic microorganism, has been the cause of several food-borne illness outbreaks, including those traced back to pasteurized fluid milk and milk products. This microorganism is especially important because it can grow at storage temperatures recommended for milk (≤7°C). Growth of L. monocytogenes in fluid milk depends to a large extent on the varying temperatures it is exposed to in the postpasteurization phase, i.e., during in-plant storage, transportation, and storage at retail stores. Growth data for L. monocytogenes in sterilized whole milk were collected at 4, 6, 8, 10, 15, 20, 25, 30, and 35°C. Specific growth rate and maximum population density were calculated at each temperature using these data. The data for growth rates versus temperature were fitted to the Zwietering square root model. This equation was used to develop a dynamic growth model (i.e., the Baranyi dynamic growth model or BDGM) for L. monocytogenes based on a system of equations which had an intrinsic parameter for simulating the lag phase. Results from validation of the BDGM for a rapidly fluctuating temperature profile showed that although the exponential growth phase of the culture under dynamic temperature conditions was modeled accurately, the lag phase duration was overestimated. For an α0 (initial physiological state parameter) value of 0.137, which corresponded to the mean temperature of 15°C, the population densities were under-predicted, although the experimental data fell within the narrow band calculated for extreme values of α0. The maximum relative error between the experimental data and the curve based on an average α0 value was 10.42%, and the root mean square error was 0.28 log CFU/ml.

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

scholarly journals Outbreak analysis with a logistic growth model shows COVID-19 suppression dynamics in China

PLoS ONE ◽  
2020 ◽  
Vol 15 (6) ◽  
pp. e0235247 ◽  
Author(s):  
Yi Zou ◽  
Stephen Pan ◽  
Peng Zhao ◽  
Lei Han ◽  
Xiaoxiang Wang ◽  
...  
Keyword(s):  
Growth Model ◽  
Logistic Growth ◽  
Logistic Growth Model

scholarly journals Extended logistic growth model for heterogeneous populations

2018 ◽  
Vol 445 ◽  
pp. 51-61 ◽  
Author(s):  
Wang Jin ◽  
Scott W. McCue ◽  
Matthew J. Simpson
Keyword(s):  
Growth Model ◽  
Logistic Growth ◽  
Heterogeneous Populations ◽  
Logistic Growth Model

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chunyan Bai ◽  
Luchun Du ◽  
Dongcheng Mei
Keyword(s):  
Stochastic Resonance ◽  
Growth Model ◽  
Noise Intensity ◽  
Critical Phenomenon ◽  
Fixed Ratio ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Logistic Growth Model ◽  
Multiplicative Periodic Signal ◽  
Correlated Noises

AbstractThe stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

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