Methods in Mathematical Modeling for Stem Cells

Eby, Wayne M.; Tabatabai, Mohammad

doi:10.1007/978-94-017-8032-2_18

Cited by 6 publications

(1 citation statement)

References 32 publications

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“…See also in [10], where hyperbolastic curves are used to introduce a model of wound healing. All of these models are the starting point for the development of others, such as the oscillabolastic, which aim to model oscillatory growth (Eby and Tabatabai [11]). Similarly, T-type models (Tabatabai et al [12]) are capable of representing biphasic sigmoidal growths characterized by stages of growth and decrease, that is, multisigmoidal patterns of behavior.…”

Section: Introductionmentioning

confidence: 99%

Hyperbolastic Models from a Stochastic Differential Equation Point of View

2021

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A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

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Section: Introductionmentioning

confidence: 99%