37 citations · 68 across the 20 of their papers we have counts for
21 papers
Reduced-Precision Stochastic Simulation for Mathematical Biology
Tom Kimpson, Mark B. Flegg, Jennifer A. Flegg
The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by…
Mathematical modeling of biochemical signal propagation in many-stage enzymatic pathways
Chathranee Jayathilaka, Mark B. Flegg
Biochemical signalling cascades transduce extracellular stimuli into cellular responses through sequences of discrete, node-to-node activations. While signal fidelity depends criti…
Multiscale Modelling of Birth-Death Processes
Tom Kimpson, Domenic P. J. Germano, Jennifer A. Flegg +1
Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approa…
Particle-based simulation of non-elementary bimolecular kinetics
Taylor Kearney, Mark B. Flegg
Particle-based simulations are an essential tool for the study of biochemical systems for scales between molecular/Brownian dynamics and the reaction-diffusion master equation. The…
Evaluating interventions for Plasmodium vivax forest malaria using a three-scale mathematical model
Shoshana Elgart, Mark B. Flegg, Jennifer A. Flegg
The rising proportion of Plasmodium vivax cases concentrated in forest-fringe areas across the Greater Mekong Subregion highlights the importance of pharmaceutical and mosquito con…
Accurate stochastic simulation of nonlinear reactions between closest particles
Taylor Kearney, Ricardo Ruiz-Baier, Mark B. Flegg
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles sati…
Accurate stochastic simulation algorithm for multiscale models of infectious diseases
Yuan Yin, Jennifer A. Flegg, Mark B. Flegg
In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dyna…
A hybrid framework for compartmental models enabling simulation-based inference
Domenic P. J. Germano, Alexander E. Zarebski, Sophie Hautphenne +3
Multi-scale systems often exhibit a combination of stochastic and deterministic dynamics. In compartmental models, low occupancy compartments tend to exhibit stochastic dynamics wh…
A spatial multiscale mathematical model of Plasmodium vivax transmission
Shoshana Elgart, Mark B. Flegg, Somya Mehra +1
The epidemiological behavior of Plasmodium vivax malaria occurs across spatial scales including within-host, population, and metapopulation levels. On the within-host scale, P. viv…
Reduction of a biochemical network mathematical model by means of approximating activators and inhibitors as perfect inverse relationships
Chathranee Jayathilaka, Robyn Araujo, Lan Nguyen +1
Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. Th…
Optimal interruption of P. vivax malaria transmission using mass drug administration
Md Nurul Anwar, Roslyn I. Hickson, Somya Mehra +4
\textit{Plasmodium vivax} is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driv…
Enzyme kinetics simulation at the scale of individual particles
Taylor Kearney, Mark B. Flegg
Enzyme-catalysed reactions involve two distinct timescales. There is a short timescale on which enzymes bind to substrate molecules to produce bound complexes, and a comparatively…
Turing pattern or system heterogeneity? A numerical continuation approach to assessing the role of Turing instabilities in heterogeneous reaction-diffusion systems
Jacob C. Vandenberg, Mark B. Flegg
Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practi…
An activation-clearance model for Plasmodium vivax malaria
Somya Mehra, James M. McCaw, Mark B. Flegg +2
Malaria is an infectious disease with an immense global health burden. Plasmodium vivax is the most geographically widespread species of malaria. Relapsing infections, caused by th…
Multi-resolution dimer models in heat baths with short-range and long-range interactions
Ravinda Gunaratne, Daniel Wilson, Mark Flegg +1
This work investigates multi-resolution methodologies for simulating dimer models. The solvent particles which make up the heat bath interact with the monomers of the dimer either…
Smoluchowski reaction kinetics for reactions of any order
Mark B. Flegg
In 1917, Marian von Smoluchowski presented a simple mathematical description of diffusion-controlled reactions on the scale of individual molecules. His model postulated that a rea…
The pseudo-compartment method for coupling PDE and compartment-based models of diffusion
Christian A. Yates, Mark B. Flegg
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature impl…
Adaptive two-regime method: application to front propagation
Martin Robinson, Mark Flegg, Radek Erban
The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics s…
Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
Mark B Flegg, Stefan Hellander, Radek Erban
In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated.…
Analysis of the two-regime method on square meshes
Mark B. Flegg, S. Jonathan Chapman, Likun Zheng +1
The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations. It is a multiscale (hybrid) algorithm which uses stochastic reacti…
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Benjamin Franz, Mark B. Flegg, S. Jonathan Chapman +1
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) method…