Analysis and Approximation of a Stochastic Growth Model with Extinction

Campillo, Fabien; Joannides, Marc; Larramendy–Valverde, Irène

doi:10.1007/s11009-015-9438-7

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…We recall the well-known approach based on diffusion processes for the stochastic model of tumor growth, such as that exploited in Albano and Giorno [1], Giorno et al [17], Giorno and Nobile [15], Hanson and Tier [19], Spina et al [29]. Other studies including Gompertz and logistic growth models based on stochastic diffusions can be found in Campillo et al [8], Himadri Ghosh and Prajneshu [21], and Yoshioka et al [36]. Recent advances involving fractional Gompertz growth models in biological contexts have been analyzed in Ascione and Pirozzi [4], Dewanji et al [11], Frunzo et al [14], and in Meoli et al [24].…”

Section: Introductionmentioning

confidence: 99%

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

Asadi

Crescenzo

Sajadi

et al. 2020

Preprint

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In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $d_2$-distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process.

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Section: Introductionmentioning

confidence: 99%

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

Asadi

Crescenzo

Sajadi

et al. 2020

Preprint

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“…There exist many different ways of modeling stochasticity and/or randomness in some deterministic model, see e.g. [4,5,6,18,22,28,29,30,32,33]. Considerations of stochastic processes in the chemostat model have already been tackled in the literature, but mainly on the growth function (see, for instance, [7]).…”

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confidence: 99%

Modeling and analysis of random and stochastic input flows in the chemostat model

Caraballo¹,

Garrido-Atienza²,

López‐de‐la‐Cruz³

et al. 2019

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.

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“…There are many different ways to introduce stochasticity and/or randomness in some deterministic model, see e.g. Campillo et al (2011Campillo et al ( , 2014Campillo et al ( , 2016; Grasman et al (2005); Imhof and Walcher (2005); Wang and Jiang (2017); ; Xu and Yuan (2015); Yuan (2016, 2017). Concerning the chemostat model, the authors in Caraballo et al (2017a) have already analyzed the simplest chemostat model ( 1)-( 2) in which a stochastic perturbation of the payoff function in continuous-time replicator dynamics is introduced, following the idea developed in Fudenberg and Harris (1992) or in Foster and Young (1990).…”

Section: Discussionmentioning

confidence: 99%

MATHMOD 2018 Extended Abstract Volume

2018

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ARGESIM is a non-profit scientific society generally aiming for dissemination of information on system simulation -from research via development to applications of system simulation. ARGESIM's primary publication is the journal SNE -Simulation Notes Europe with open access to all contributions; generally, the authors retain the copyright of their SNE contributions. This copyright regulation holds also for other ARGESIM publications, as conference volumes of ASIM conferences, MATHMOD conferences, and special EUROSIM conferences, in consideration of copyright regulations for related conference publications. About ARGESIMARGESIM is a non-profit society generally aiming for dissemination of information on system simulation from research via development to applications of system simulation. ARGESIM is closely co-operating with EUROSIM, the Federation of European Simulation Societies, and with ASIM, the German Simulation Society. ARGESIM is an 'outsourced' activity from the Mathematical Modelling and Simulation Group of TU Wien, there is also close co-operation with TU Wien

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Analysis and Approximation of a Stochastic Growth Model with Extinction

Cited by 12 publications

References 16 publications

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

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

Modeling and analysis of random and stochastic input flows in the chemostat model

MATHMOD 2018 Extended Abstract Volume

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Analysis and Approximation of a Stochastic Growth Model with Extinction

Cited by 12 publications

References 16 publications

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

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

Modeling and analysis of random and stochastic input flows in the chemostat model

MATHMOD 2018 Extended Abstract Volume

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

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