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We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory…

Molecular Networks · Quantitative Biology 2018-01-30 Tomislav Plesa , Radek Erban , Hans G. Othmer

Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…

Systems and Control · Computer Science 2019-05-27 Milan Češka , Jan Křetínský

Recently, hybrid models have emerged that combine microscopic and mesoscopic regimes in a single stochastic reaction-diffusion simulation. Microscopic simulations track every individual molecule and are generally more accurate. Mesoscopic…

Emerging Technologies · Computer Science 2015-11-20 Adam Noel , Karen C. Cheung , Robert Schober

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…

Quantitative Methods · Quantitative Biology 2010-05-06 Thomas A. Henzinger , Maria Mateescu , Linar Mikeev , Verena Wolf

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…

Biological Physics · Physics 2024-07-22 Mohamed Swailem , Uwe C. Täuber

We introduce the notion of corresponding a chemical reaction network to a split network translation, and use this novel process to extend the scope of existing network-based theory for characterizing the steady state set of mass-action…

Dynamical Systems · Mathematics 2021-04-09 Matthew D. Johnston

Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large…

Molecular Networks · Quantitative Biology 2025-12-16 Jiayu Weng , Xinyi Zhu , Jing Liu , Linyuan Lü , Pan Zhang , Ying Tang

We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…

Analysis of PDEs · Mathematics 2026-01-07 Romina Travaglini , João Miguel Oliveira

Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…

Probability · Mathematics 2026-04-29 Louis Faul , Linard Hoessly , Panqiu Xia

Computational systems biology has provided plenty of insights into cell biology. Early on, the focus was on reaction networks between molecular species. Spatial distribution only began to be considered mostly within the last decade.…

Quantitative Methods · Quantitative Biology 2016-05-13 Atsushi Miyauchi , Kazunari Iwamoto , Satya Nanda Vel Arjunan , Koichi Takahashi

The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of…

Analysis of PDEs · Mathematics 2020-06-30 Martin Burger

We take up the challenge of designing realistic computational models of large interacting cell populations. The goal is essentially to bring Gillespie's celebrated stochastic methodology to the level of an interacting population of cells.…

Computational Engineering, Finance, and Science · Computer Science 2018-10-26 Stefan Engblom

The graph-related symmetries of a reaction network give rise to certain special equilibria (such as complex balanced equilibria) in deterministic models of dynamics of the reaction network. Correspondingly, in the stochastic setting, when…

Probability · Mathematics 2018-05-21 Daniele Cappelletti , Badal Joshi

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic…

Statistical Mechanics · Physics 2023-03-29 Praful Gagrani , Eric Smith

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Statistics Theory · Mathematics 2026-01-26 Lasse Leskelä , Maximilien Dreveton

Motivated by the study of social insects, we introduce a stochastic model based on interacting particle systems in order to understand the effect of communication on the division of labor. Members of the colony are located on the vertex set…

Probability · Mathematics 2016-01-07 Alesandro Arcuri , Nicolas Lanchier

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…

Dynamical Systems · Mathematics 2014-07-15 Matthew D. Johnston

A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…

Probability · Mathematics 2010-01-14 Florian Simatos , Danielle Tibi

To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction-diffusion master equations or deterministic, macroscopic reaction-diffusion system. The connection between these two models is not…

Analysis of PDEs · Mathematics 2023-06-21 Malcolm Egan , Bao Quoc Tang

We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…

Applications · Statistics 2025-07-01 Ricardo F. Ferreira , Matheus E. Pacola , Vitor G. Schiavone , Rodrigo F. O. Pena