Statistical Ensemble Theory of Gompertz Growth Model

Yamano, Takuya

doi:10.3390/e11040807

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…It should be pointed out that some works [36] – [38] , which analyzed the microscopic picture leading to the Gompertz growth law, argued that this kind of dynamics originates from stochasticity in the system of multiplying agents. This stochasticity can include a probabilistic distribution of the instant growth stages in the ensemble or arise from small fluctuations in growth rates.…”

Section: Resultsmentioning

confidence: 99%

Ensemble density-dependent synchronization of mycobacterial growth: BACTEC MGIT 960 fluorescence-based analysis and mathematical modelling of coupled biophysical and chemical processes

et al. 2022

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<abstract> <p>This study presents an analysis of <italic>M. tuberculosis</italic> growth data obtained using the BACTEC MGIT 960 system and respective mathematical models. The system is based on the detection of a decrease in oxygen level in the broth due to the bacterial respiration. It is shown that recordings sampled with a 1 hour rate provide an opportunity to distinguish between the oxygen consumption of growing cells and active cells division when the density of micro-organisms is sufficient to enter into the synchronized division mode. More specifically, the growth of culture is continuous only with large initial dilutions; otherwise, there are jumps between different growth stages with a time interval of 13–15 h. The combination of the oxygen-quenching kinetics for an analytic reagent and the population growth kinetics resulted in a mathematical model, which consists of mixing Verhulst's and Gompertz's models. The parameters of such mixing and switching between the models' prevalences are discussed with respect to oxygen uptake reactions reflected in the changes in the experimentally registered fluorescence level.</p> </abstract>

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Section: Resultsmentioning

confidence: 99%

Ensemble density-dependent synchronization of mycobacterial growth: BACTEC MGIT 960 fluorescence-based analysis and mathematical modelling of coupled biophysical and chemical processes

et al. 2022

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“…Biologically, the Gompertz model indicates an increase in mortality rate with increasing age, representing an increased vulnerability towards causes of death suffered by young adults. How rapidly this vulnerability enhances with age is depicted by the exponential term of the Gompertz function, where it is assumed that increasing age implies a greater probability of death 50 . Figure 9 shows the proposed re-parameterized Gompertz function, where the independent variable ‘ x ’ represents the predicted confidence score for a test sample by a classifier.…”

Section: Methodsmentioning

confidence: 99%

Fuzzy rank-based fusion of CNN models using Gompertz function for screening COVID-19 CT-scans

Kundu

Basak

Singh

et al. 2021

Sci Rep

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COVID-19 has crippled the world’s healthcare systems, setting back the economy and taking the lives of several people. Although potential vaccines are being tested and supplied around the world, it will take a long time to reach every human being, more so with new variants of the virus emerging, enforcing a lockdown-like situation on parts of the world. Thus, there is a dire need for early and accurate detection of COVID-19 to prevent the spread of the disease, even more. The current gold-standard RT-PCR test is only 71% sensitive and is a laborious test to perform, leading to the incapability of conducting the population-wide screening. To this end, in this paper, we propose an automated COVID-19 detection system that uses CT-scan images of the lungs for classifying the same into COVID and Non-COVID cases. The proposed method applies an ensemble strategy that generates fuzzy ranks of the base classification models using the Gompertz function and fuses the decision scores of the base models adaptively to make the final predictions on the test cases. Three transfer learning-based convolutional neural network models are used, namely VGG-11, Wide ResNet-50-2, and Inception v3, to generate the decision scores to be fused by the proposed ensemble model. The framework has been evaluated on two publicly available chest CT scan datasets achieving state-of-the-art performance, justifying the reliability of the model. The relevant source codes related to the present work is available in: GitHub.

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“…The generalized Seikkala differentiability approach and the Zadeh extension rule are used to determine deterministic solutions in another attempt to solve fuzzy differential equations [20][21][22][23][24][25][26][27]. This study discusses the influence of fuzzy uncertainty in the Gompertz growth equation, which is used in a variety of fields, including statistical mechanics, medicine (tumor growth rate), chemistry (response models), and ecology (population growth) [28,29]. The Gompertz model, probably second only to the logistic model, is amongst the most widely utilized sigmoid models for fitting growth data and other data.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Sheergojri

Iqbal

Agarwal

et al. 2022

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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For treating cancer, tumor growth models have shown to be a valuable resource, whether they are used to develop therapeutic methods paired with process control or to simulate and evaluate treatment processes. In addition, a fuzzy mathematical model is a tool for monitoring the influences of various elements and creating behavioral assessments. It has been designed to decrease the ambiguity of model parameters to obtain a reliable mathematical tumor development model by employing fuzzy logic.The tumor Gompertz equation is shown in an imprecise environment in this study. It considers the whole cancer cell population to be vague at any given time, with the possibility distribution function determined by the initial tumor cell population, tumor net population rate, and carrying capacity of the tumor. Moreover, this work provides information on the expected tumor cell population in the maximum period. This study examines fuzzy tumor growth modeling insights based on fuzziness to reduce tumor uncertainty and achieve a degree of realism. Finally, numerical simulations are utilized to show the significant conclusions of the proposed study.

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Statistical Ensemble Theory of Gompertz Growth Model

Cited by 8 publications

References 22 publications

Ensemble density-dependent synchronization of mycobacterial growth: BACTEC MGIT 960 fluorescence-based analysis and mathematical modelling of coupled biophysical and chemical processes

Ensemble density-dependent synchronization of mycobacterial growth: BACTEC MGIT 960 fluorescence-based analysis and mathematical modelling of coupled biophysical and chemical processes

Fuzzy rank-based fusion of CNN models using Gompertz function for screening COVID-19 CT-scans

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

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