A generalized Gompertz growth model with applications and related birth-death processes

Asadi, Majid; Crescenzo, Antonio Di; Sajadi, Farkhondeh Alsadat; Spina, Serena

doi:10.1007/s11587-020-00548-y

Cited by 18 publications

(13 citation statements)

References 35 publications

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“…Concerning to the COVID-19 we refer the readers to [33][34][35][36][37][38]. Finally, we also recommend readers see [39] where authors propose a generalized Gompertz growth model. Remarking its limitations we will find that the Gompertz model does not address the core issues of epidemiological models, namely, the well-mixing hypothesis and lack of spatial influences.…”

Section: The Modelmentioning

confidence: 99%

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

Sánchez-Sánchez

Suárez‐Llorens

2021

Mathematics

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The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain.

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Section: The Modelmentioning

confidence: 99%

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

Sánchez-Sánchez

Suárez‐Llorens

2021

Mathematics

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“…It has already been established that dealing with parameter inaccuracy is not always suitable due to a lack of comprehensive knowledge or estimation failure. A basic technique of coping with Gompertz equation uncertainties ( 6) is utilized to obtain these parameter estimations by utilizing the equation (7) to calculate the average approximations and to assess the complexity [42,43,[45][46][47].…”

Section: Tumor Growth In a Fuzzy Environment Using The Gompertz Modelmentioning

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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“…Examples of the observable variables are the body weight and body size, while the latent variables include the history-dependent maximum body weight [19,35] and dynamically changing energetic variables [36][37]. Temporally inhomogeneous models can also be seen as open-ended growth models where time-dependent parameters add a flexibility in modeling the growth curves [38][39][40][41]. Hence, we need to find a mathematical framework that depends only on the observable variables.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

Yoshioka

Tanaka

Aranishi

et al. 2021

Math Methods in App Sciences

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In inland fisheries, transporting fishery resource individuals from a habitat to spatially apart habitat(s) has recently been considered for fisheries stock management in the natural environment. However, its mathematical optimization, especially finding when and how much of the population should be transported, is still a fundamental unresolved issue. We propose a new impulse control framework to tackle this issue based on a simple but new stochastic growth model of individual fishes. The novel growth model governing individuals' body weights uses a Wright-Fisher model as a latent driver to reproduce plausible growth dynamics. The optimization problem is formulated as an impulse control problem of a cost-benefit functional constrained by a degenerate parabolic Fokker-Planck equation of the stochastic growth dynamics.Because the growth dynamics have an observable variable and an unobservable variable (a variable difficult or impossible to observe), we consider both full-information and partial-information cases. The latter is more involved but more realistic because of not explicitly using the unobservable variable in designing the controls. In both cases, resolving an optimization problem reduces to solving the associated Fokker-Planck and its adjoint equations, the latter being non-trivial. We present a derivation procedure of the adjoint equation and its internal boundary conditions in time to efficiently derive the optimal transporting strategy.We finally provide a demonstrative computational example of a transporting problem of Ayu sweetfish (Plecoglossus altivelis altivelis) based on the latest real data set.

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A generalized Gompertz growth model with applications and related birth-death processes

Cited by 18 publications

References 35 publications

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

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

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

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