70 citations · 332 across the 25 of their papers we have counts for
27 papers
A coupled geometric surface and surface reaction-diffusion framework for modelling nuclear mechanics during confined cell migration
Francesca Ballatore, Silvia Comunian, Anotida Madzvamuse +2
Confined cell migration is governed by nuclear and cellular deformation. In this work, we formulate a two-dimensional mathematical framework in which the cell and nuclear membranes…
A Predictive Model for Synergistic Oncolytic Virotherapy: Unveiling the Ping-Pong Mechanism and Optimal Timing of Combined Vesicular Stomatitis and Vaccinia Viruses
Joseph Malinzi, Amina Eladdadi, Rachid Ouifki +3
We present a mathematical model that describes the synergistic mechanism of combined Vesicular Stomatitis Virus (VSV) and Vaccinia Virus (VV). The model captures the dynamic interp…
The evolving surface morphochemical reaction-diffusion system for battery modeling
Benedetto Bozzini, Massimo Frittelli, Anotida Madzvamuse +1
It is well known that phase formation by electrodeposition yields films of poorly controllable morphology. This typically leads to a range of technological issues in many fields of…
Parameter spaces for cross-diffusive-driven instability in a reaction-diffusion system on an annular domain
Gulsemay Yigit, Wakil Sarfaraz, Raquel Barreira +1
In this work, the influence of geometry and domain size on spatiotemporal pattern formation is investigated to establish parameter spaces for a cross-diffusive reaction-diffusion m…
Pattern formation of bulk-surface reaction-diffusion systems in a ball
Edgardo Villar-Sepúlveda, Alan R. Champneys, Davide Cusseddu +1
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, u…
Numerical investigations of the bulk-surface wave pinning model
Davide Cusseddu, Anotida Madzvamuse
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk dif…
Virtual element method for elliptic bulk-surface PDEs in three space dimensions
Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura
In this work we present a novel bulk-surface virtual element method (BSVEM) for the numerical approximation of elliptic bulk-surface partial differential equations (BSPDEs) in thre…
Reformulating the SIR model in terms of the number of COVID-19 detected cases: well-posedness of the observational model
Eduard Campillo-Funollet, Hayley Wragg, James Van Yperen +2
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problem…
A hospital demand and capacity intervention approach for COVID-19 in the UK
James Van Yperen, Eduard Campillo-Funollet, Rebecca Inkpen +2
The mathematical interpretation of interventions for the mitigation of epidemics and pandemics in the literature often involves finding the optimal time to initiate an intervention…
Bulk-surface virtual element method for systems of PDEs in two-space dimension
Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura
In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general…
Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain
Nikos. I. Kavallaris, Raquel Barreira, Anotida Madzvamuse
The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt model on an isotropically evolv…
A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration
Laura Murphy, Anotida Madzvamuse
This work presents the development, analysis and numerical simulations of a biophysical model for 3D cell deformation and movement, which couples biochemical reactions and biomecha…
A coupled bulk-surface model for cell polarisation
Davide Cusseddu, Leah Edelstein-Keshet, John A. Mackenzie +2
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which…
Stability analysis and parameter classification of a reaction-diffusion model on non-compact circular geometries
Wakil Sarfaraz, Anotida Madzvamuse
This work explores the influence of domain size of a non-compact two dimensional annular domain on the evolution of pattern formation that is modelled by an \textit{activator-deple…
A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix
Nikolaos Sfakianakis, Anotida Madzvamuse, Mark A. J. Chaplain
The ability to locally degrade the extracellular matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a criti…
Domain-dependent stability analysis and parameter classification of a reaction-diffusion model on spherical geometries
Wakil Sarfaraz, Anotida Madzvamuse
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of doma…
Classification of parameter spaces for reaction-diffusion systems on stationary domains
Wakil Sarfaraz, Anotida Madzvamuse
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored bot…
Lumped finite element method for reaction-diffusion systems on compact surfaces
Massimo Frittelli, Anotida Madzvamuse, Ivonne Sgura +1
We propose and analyse a novel surface finite element method that preserves the invariant regions of systems of semilinear parabolic equations on closed compact surfaces in $\mathb…
A Bayesian approach to parameter identification with an application to Turing systems
Eduard Campillo-Funollet, Chandrasekhar Venkataraman, Anotida Madzvamuse
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a ri…
A computational approach for mode isolation for reaction-diffusion systems on arbitrary geometries
Laura Murphy, Chandrasekhar Venkataraman, Anotida Madzvamuse
In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model…
Whole cell tracking through the optimal control of geometric evolution laws
Konstantinos N. Blazakis, Anotida Madzvamuse, Constantino-Carlos Reyes-Aldasoro +2
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular…
Keratin Dynamics: Modeling the Interplay between Turnover and Transport
Stephanie Portet, Anotida Madzvamuse, Andy Chung +2
Keratin are among the most abundant proteins in epithelial cells. Functions of the keratin network in cells are shaped by their dynamical organization. Using a collection of experi…
Fully implicit time-stepping schemes and non-linear solvers for systems of reaction-diffusion equations
Anotida Madzvamuse, Andy H. W. Chung
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications o…
Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems
Anotida Madzvamuse, Andy H. W. Chung, Chandrasekhar Venkataraman
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to…