The Gompertz model revisited and modified using reaction networks: Mathematical analysis
SM Markov - Biomath, 2021 - biomath.math.bas.bg
In the present work we discuss the usage of the framework of chemical reaction networks for
the construction of dynamical models and their mathematical analysis. To this end, the …
the construction of dynamical models and their mathematical analysis. To this end, the …
Reaction networks reveal new links between Gompertz and Verhulst growth functions
SM Markov - Biomath, 2019 - biomath.math.bas.bg
New reaction network realizations of the Gompertz and logisticВ growth models are
proposed. The proposed reaction networks involve an additional species interpreted as …
proposed. The proposed reaction networks involve an additional species interpreted as …
On some classes of growth functions and their links to reaction network theory
In this work we study some characteristics of sigmoidal growth functions that are solutions to
dynamical systems induced by reaction networks. The studied dynamical systems are close …
dynamical systems induced by reaction networks. The studied dynamical systems are close …
On the chemical meaning of some growth models possessing Gompertzian‐type property
Growth models are often used when modelling various processes in life sciences, ecology,
demography, social sciences, etc. Dynamical growth models are usually formulated in terms …
demography, social sciences, etc. Dynamical growth models are usually formulated in terms …
On a class of generalized Gompertz-Bateman growth-decay models
SM Markov - Biomath Communications, 2019 - biomath.math.bas.bg
A recently proposed reaction network induces the classical Gompertz equations. The
network consist of two reactions, one reaction for a decaying species $ S $ and another …
network consist of two reactions, one reaction for a decaying species $ S $ and another …
The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family
KMC Tjørve, E Tjørve - PloS one, 2017 - journals.plos.org
The Gompertz model is well known and widely used in many aspects of biology. It has been
frequently used to describe the growth of animals and plants, as well as the number or …
frequently used to describe the growth of animals and plants, as well as the number or …
The Gompertz model and its applications in microbial growth and bioproduction kinetics: Past, present and future
J Wang, X Guo - Biotechnology Advances, 2024 - Elsevier
The Gompertz model, initially proposed for human mortality rates, has found various
applications in growth analysis across the biotechnological field. This paper presents a …
applications in growth analysis across the biotechnological field. This paper presents a …
Varieties of stochastic model: a comparative study of the Gompertz effect.
P Holgate - Journal of theoretical Biology, 1989 - europepmc.org
A comparative study is made of various models for the Gompertz phenomenon, which is a
form of growth rate limitation in population dynamics. Deterministic, Markov birth-death …
form of growth rate limitation in population dynamics. Deterministic, Markov birth-death …
On Gompertz growth model and related difference equations
AG Nobile, LM Ricciardi, L Sacerdote - Biological Cybernetics, 1982 - Springer
Within the context of the dynamics of populations described by first order difference
equations a datailed study of the Gompertz growth model is performed. This is mainly …
equations a datailed study of the Gompertz growth model is performed. This is mainly …
A generalization of Gompertz law compatible with the Gyllenberg–Webb theory for tumour growth
A d'Onofrio, A Fasano, B Monechi - Mathematical Biosciences, 2011 - Elsevier
We present a new extension of Gompertz law for tumour growth and anti-tumour therapy.
After discussing its qualitative and analytical properties, we show, in the spirit of [16], that …
After discussing its qualitative and analytical properties, we show, in the spirit of [16], that …