Anotida Madzvamuse #
- Anotida Madzvamuse DPhil. MSc, MSC (EDU), BSC (Hons), BSs Maths, is a Full Professor and Tier-1 Canada Research Chair in Theoretical and Computational Biology at UBC.
- His research integrates mathematics, physics, and computational methods to model biological systems, including pattern formation, cancer invasion, cell and nuclear mechanics. He has also researched COVID-19 transmission dynamics.
- He has received prestigious awards such as the Royal Society Wolfson Research Merit Award (2016–2021) and the Theodore von Kaman Fellowship (2013).
- Madzvamuse has published extensively in top-tier journals, focusing on pattern formation, reaction-diffusion systems, and cell motility.
- He actively engages in public outreach, including podcast interviews and speaker series, sharing his journey from rural Zimbabwe to international academia.
Credit: UBC
Introduction #
Anotida Madzvamuse is a distinguished mathematician and computational biologist who joined the University of British Columbia (UBC) as a Full Professor in the Department of Mathematics in October 2022. His work lies at the intersection of fundamental disciplines - mathematics, numerical analysis, physics, and scientific computing - and experimental sciences such as developmental, cellular, and plant biology, as well as biomedicine. Madzvamuse’s research focuses on developing novel mathematical and computational approaches to address complex biological phenomena, including pattern formation and cell migration. He is also deeply committed to teaching and mentoring at both undergraduate and graduate levels. His recent appointment as a Tier-1 Canada Research Chair in Theoretical and Computational Biology underscores his leadership in the field.
Professional Background and Achievements #
Anotida Madzvamuse’s academic journey began with a BSc (Hons) from the University of Zimbabwe (1994) and a Masters in Mathematics and Education from the University of Enrique Jose Varona, Cuba (1991). He earned his DPhil (2000) and MSc (1997) in Mathematical Modelling and Numerical Analysis from the University of Oxford. His early career included a postdoctoral fellowship at Oxford and an Assistant Professorship at Auburn University (2003–2006). He then joined the University of Sussex, where he rose through the ranks from Lecturer to Professor of Mathematical and Computational Biology (2006–2022).
Madzvamuse’s contributions have been recognized with several prestigious awards, including the Royal Society Wolfson Research Merit Award (2016–2021) and the Theodore von Kaman Fellowship from RWTH Aachen University (2013). He has also received multiple grants from the EPSRC and other international funding bodies, totaling over 5 million euros, supporting his research in spatial patterning, cell migration, and computational modeling.
Research Areas and Projects #
Madzvamuse’s research is characterized by its interdisciplinary nature, combining mathematical modeling, numerical analysis, and computational biology to tackle complex biological questions. His primary research areas include:
- Mathematical Modeling and Analysis: Development of bulk-surface-extracellular partial differential equations (PDEs) to model biological processes such as pattern formation and cell motility.
- Numerical Analysis and Computational Methods: Implementation of finite element and virtual element methods to simulate biological systems.
- Parameter Inference and Estimation: Techniques to infer parameters from experimental data, enhancing the predictive power of mathematical models.
- Applications in Biology and Medicine: Collaborations with health experts to model COVID-19 transmission dynamics and other biomedical phenomena.
One of his most notable projects involves collaborating with UK health authorities to predict COVID-19 outbreaks using advanced computational models, demonstrating the practical impact of his theoretical work. Additionally, he has organized and led a 6-month research program on Coupling geometric PDEs with physics for cell morphology, motility and pattern formation (2015) at the Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, and a 5-day workshop (2026) at Banff International Research Station (BIRS), Canada, in order to promote, foster and cultivate international collaborations in Mathematical Sciences and its Applications.
Major Publications #
| Title | Journal | Year | Link |
|---|---|---|---|
| Emergence of Bursting and Delay-Induced Spiral Patterns in Eco-Epidemiological Systems | Bulletin of Mathematical Biology | 2026 | link |
| Using Floquet theory to unravel far-from equilibrium dynamics in reaction-diffusion systems | PNAS Nexus | 2026 | link |
| Pattern Formation of Bulk-Surface Reaction-Diffusion Systems in a Ball | SIAM Journal on Applied Mathematics | 2026 | link |
| Exploring the spatio–temporal dynamics in activator–inhibitor systems through a dual approach of analysis and computation | Mathematical Biosciences | 2025 | link |
| Existence and convergence of stochastic processes underlying a thin layer approximation of a coupled bulk-surface PDE | Journal of Differential Equations | 2025 | link |
| Analysis of the spatio-temporal dynamics of a Rho-GEF-H1-myosin activator-inhibitor reaction-diffusion system | Royal Society Open Science | 2025 | link |
| Parameter Spaces for Cross-Diffusive-Driven Instability in a Reaction-Diffusion System on an Annular Domain | International Journal of Bifurcation and Chaos | 2025 | link |
| Quantifying the organization and dynamics of M. smegmatis morphology from Long-Term Time-Lapse Atomic Force Microscopy | openRxiv | 2025 | link |
| A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions | Journal of Theoretical Biology | 2024 | link |
| Understanding the dual effects of linear cross-diffusion and geometry on reaction–diffusion systems for pattern formation | Chaos, Solitons and Fractals | 2024 | link |
| VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D | Numerical Algorithms | 2024 | link |
| Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection | Nonlinear Dynamics | 2024 | link |
| A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains | Nonlinear Analysis: Real World Applications | 2024 | link |
| The Sussex COVID-19 modelling cell: the methods and successes of a collaboration between public health teams in local authorities, NHS hospital trusts, NHS commissioners, and universities | The Lancet | 2023 | link |
| Virtual element method for elliptic bulk-surface PDEs in three space dimensions | Numerical Methods for Partial Differential Equations | 2023 | link |
| COVID-19 transmission dynamics and the impact of vaccination: modelling, analysis and simulations | Royal Society Open Science | 2023 | link |
| A hospital demand and capacity intervention approach for COVID-19 | PLoS One | 2023 | link |
| Complex dynamics of a discrete-time seasonally forced SIR epidemic model | Mathematical Methods in the Applied Sciences | 2023 | link |
Awards and Recognitions #
- Royal Society Wolfson Research Merit Award (2016–2021): Recognizes Madzvamuse’s world-leading research in mathematical and computational biology, including modeling, analysis, numerical analysis, simulations, applications, and inference theory.
- Theodore von Kaman Fellowship (2013): Awarded by RWTH Aachen University for his significant contributions to mathematical biology.
- Tier-1 Canada Research Chair in Theoretical and Computational Biology (2022–present): Recognizes his leadership and excellence in the field.
- EPSRC Awards: Multiple grants supporting his research on spatial patterning and computational modeling.
- GCRF Award: For the UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences.
Media and Public Engagement #
Madzvamuse has actively engaged with the public and media through several platforms.
A Mathematician Like Me
Anotida Madzvamuse, a Professor of Mathematics at the University of British Columbia, specializes in applied mathematics with applications in cellular and developmental biology, cancer research, inflammation, and wound healing. His work focuses on creating mathematical models from data and observations that are amenable to rigorous analysis, often involving differential geometry, PDEs, and numerical methods. He emphasizes the predictive power of these models as tools for experimentalists, public health analysts, and other researchers, enabling exploration of scenarios that are experimentally inaccessible. Madzvamuse highlights the importance of resilience and perseverance in securing research funding and overcoming career obstacles, such as promotions and job acquisitions, which he attributes to systemic challenges tied to diversity. He advises early-career mathematicians to believe in their abilities, learn from failures, and persist in their efforts, as success often comes from continuous improvement and determination. His journey reflects a deep commitment to advancing mathematical biology and mentoring the next generation of researchers.
From rural Zimbabwe to international academia
Featured in Living Proof Podcast (Isaac Newton Institute).
Professor Anotida Madzvamuse, a mathematician and computational biologist at the University of Sussex, shares his extraordinary journey from a rural Zimbabwean village to international academia in this podcast interview. He recounts his early life in a resource-limited environment, where he developed resilience and a passion for mathematics, eventually excelling in school despite hardships. Madzvamuse’s career path includes studying in Cuba, earning advanced degrees at Oxford, and teaching in Zimbabwe before securing positions in the US and UK. His research focuses on mathematical and computational biology, particularly pattern formation in nature and single-cell migration, with applications in cancer biology, wound healing, and COVID-19 modeling. He emphasizes the importance of perseverance, mentorship, and learning from failures, while also highlighting initiatives like the Masamu Program and African Institute for Mathematical Sciences (AIMS), which support African mathematicians. His story underscores the transformative power of education, hard work, and global collaboration in overcoming systemic barriers.
The mathematics of cells walking through complex environments:
Known as the smallest biological entity, the cell, is fundamental to life, human or otherwise. Unlike humans, animals and many other living organisms, the cell has no legs, head nor tail, yet cells have a remarkable ability to polarise and exhibit the front and back, associated with human mobility, during migration in complex environments such as in blood, tissue or during disease, such as cancer or during the wound healing process. In this presentation, Prof Anotida Madzvamuse will demonstrate the crucial role of mathematics to help understand how cells walk through complex environments. He will also present current challenges where mathematics has a pivotal role to help lead future discoveries.
Models for growth development in cell motility and pattern formation:
Professor Anotida Madzvamuse discusses the integration of geometric partial differential equations (PDEs) with physics to model cell morphology, motility, and pattern formation, emphasizing the coupling of models for pattern formation and cell motility. He highlights the importance of deriving models driven by experimental observations and physical laws, aiming to create predictive models that can guide and validate experiments. Madzvamuse explores the challenges of coupling interior, surface, and extracellular dynamics, particularly in the context of cell migration and pattern formation on evolving domains. He presents mathematical frameworks, including reaction-diffusion systems with cross-diffusion and domain growth, to relax classical Turing instability conditions, allowing for more flexible and biologically relevant modeling. The talk also touches on viscoelastic models for cell motility, the role of actin concentrations, and the need for experimental validation to refine and calibrate these theoretical models.
Black Excellence in STEM Speaker Series at UBC:
Presented on “Unraveling the Mathematics of Single-Cell Dynamics,” sharing his research and experiences with a broad audience.
Demonstrations #
In this section, we highlight some of the computational models generated in Dr. Madzvamuse’s work and provided to us through his kindness.
Software & Mathematical Context:
- The visualizations below were rendered using ParaView, an open-source 3D scientific data analysis and visualization engine.
- The simulations model coupled reaction-diffusion systems, illustrating how spatial patterns, 3D spiral wave dynamics in excitable media, and traveling fronts evolve across 3D bulk volumes and 2D surface manifolds.
- For the mathematical foundations behind these models, see Dr. Madzvamuse’s papers on Rho-GEF-H1 spatio-temporal dynamics and cross-diffusion and geometry in pattern formation.
Spatiotemporal Dynamics in 3D Bulk Domains #
This visualization is a 3D scientific simulation of a spatio-temporal reaction-diffusion system (or wave/pattern propagation model) rendered in ParaView.
Key Elements of the Visualization #
- Geometry: A 3D solid sphere with a quarter-wedge cut out (a cross-sectional view) to allow inspection of internal volumetric dynamics alongside surface patterns.
- Variable (\(u\)): The field variable \(u\) is color-mapped on a scale ranging from \(0.2756\) (blue) to \(1.389\) (red/yellow).
- Temporal Dynamics: As time progresses from \(t = 0.09\) to \(t = 3.49\), spatial wavebands and localized concentration zones form, interfere, and evolve across both the exterior boundary and the internal bulk.
Physical Context #
In computational physics and applied mathematics, “spatiotemporal bulk” refers to the time-dependent evolution of a field within the interior volume of a 3D domain (as opposed to strictly on its boundary surface). Common applications of this specific pattern formation include:
- Turing Patterns & Reaction-Diffusion Models: Simulating chemical concentrations or biological morphogenesis (e.g., Gray-Scott or FitzHugh-Nagumo equations).
- Bulk-Surface Coupled Systems: PDEs where dynamic processes occurring in the interior 3D bulk interact continuously with dynamics restricted to the 2D surface boundary.
- Acoustic/Electromagnetic Cavity Waves: Standing wave modes and transient interference inside spherical geometries.
Scroll Wave & Spiral Dynamics in Bulk Domains #
This visualization shows a 3D scientific simulation of scroll wave dynamics and rotating spiral patterns in a volumetric bulk domain, rendered using ParaView.
Key Elements of the Visualization #
- Geometry: A 3D solid sphere with a quarter-wedge cut away to expose the interior slice and cross-sectional dynamics.
- Variable (\(u\)): The field variable \(u\) is mapped across a color scale ranging from \(0.1731\) (blue/cyan) to \(1.495\) (red/yellow).
- Spiral Wave Topography: As time progresses from \(t = 0.04\) to \(t = 2.44\), an initial disturbance on the internal face curls into self-sustaining, rotating spiral arms. The cross-cut reveals how these 2D spiral waves on the surface connect to 3D scroll waves extending into the interior bulk.
Physical Context #
While the previous simulation highlighted general spatio-temporal band/wave propagation, “spiral bulk” focuses on the formation and stability of rotating spiral patterns and scroll wave filaments in three dimensions:
- Excitable Media & Reaction-Diffusion: Common in non-linear models such as the Belousov-Zhabotinsky reaction or Barkley/FitzHugh-Nagumo models, where spiral tips act as re-entrant wave rotors.
- Cardiac Electrophysiology: Simulations of 3D ventricular tissue where scroll waves (3D generalizations of 2D spiral waves) can organize re-entrant electrical activity associated with ventricular tachycardia or fibrillation.
- Phase-Singularity & Filament Dynamics: The center of the rotating spiral on the slice represents a cross-section of a 1D filament around which the 3D scroll wave rotates within the bulk.
Surface-Bound Spiral Wave Dynamics #
This visualization demonstrates a 3D simulation focusing specifically on surface-bound spiral wave formation and surface PDE dynamics, rendered in ParaView.
Key Elements of the Visualization #
- Geometry: A 3D domain (sphere with a quarter-wedge cut away) revealing both the spherical surface boundary and the inner planar cuts.
- Variable (\(w\)): The field variable \(w\) is mapped across a narrow concentration gradient from \(0.6888\) (blue) to \(0.7368\) (red/yellow).
- Surface-Localized Wave Evolution: As time advances from \(t = 0.04\) to \(t = 2.44\), distinct, tightly localized spiral wave rotors form and remain pinned to specific boundary regions on the interior cut surfaces, displaying localized rotation without filling or propagating deep into the bulk volume.
Physical Context #
In reaction-diffusion systems, contrast between “bulk” and “surface” models highlights differences in dynamic dimensionality and boundary behavior:
- Surface PDEs (Partial Differential Equations on Manifolds): Modeling wave propagation restricted to curved surfaces or manifold boundaries (e.g., cell membranes, thin elastic shells, or boundary layer dynamics).
- Surface Reaction Kinetics: Represents recovery/inhibitor variables (often denoted by \(w\) or \(v\) in activator-inhibitor systems like FitzHugh-Nagumo or Thomas models) where active wave generation or chemical phase locking is restricted primarily to the surface geometry.
- Bulk-Surface Coupling Disconnect: Unlike full volumetric scroll waves that penetrate the interior bulk, surface spiral dynamics focus on stable localized phase singularities (spiral centers) operating strictly on two-dimensional manifolds embedded within a 3D geometry.
Traveling Wave Propagation in Bulk Domains #
This visualization demonstrates a 3D scientific simulation of directed traveling wave propagation through a volumetric bulk domain, rendered in ParaView.
Key Elements of the Visualization #
- Geometry: A 3D solid sphere with a quarter-wedge cut away to expose the interior radial slice and core dynamics.
- Variable (\(u\)): The field variable \(u\) is color-mapped on a scale ranging from \(0.1837\) (blue) to \(1.391\) (red/yellow).
- Translational Wave Dynamics: As the time advances from \(t = 0.04\) to \(t = 3.99\), a sharp concentration front originates on one side of the volume and sweeps directly across the domain as a coherent planar/planar-curved wavefront. Unlike the stationary rotors of spiral waves or complex interference patterns of general spatio-temporal dynamics, this pattern represents unidirectional wave transport across the entire interior bulk.
Physical Context #
In reaction-diffusion systems and continuum transport models, “traveling wave bulk” dynamics represent fundamental excitation fronts and transport phenomena:
- Unidirectional Excitation Waves: Models pulse propagation in excitable media (e.g., action potential propagation through 3D biological tissue or chemical front propagation in the Belousov-Zhabotinsky reaction) where the refractory period prevents back-propagation.
- Advection-Diffusion & Traveling Wave Solutions: PDE solutions where the spatial profile maintains a steady shape while translating at a constant velocity, described by \(u(x, t) = U(x - ct)\).
- Phase-Front Transitions: Simulating bulk phase transformations or thermal/chemical combustion fronts advancing through a dense 3D medium.
Surface-Bound Traveling Wave Propagation #
This visualization demonstrates a 3D scientific simulation of directed traveling wave propagation restricted to a surface variable/manifold, rendered in ParaView.
Key Elements of the Visualization #
- Geometry: A 3D domain (sphere with a quarter-wedge cut away) exposing both the exterior boundary and internal cross-sectional cuts.
- Variable (\(w\)): The field variable \(w\) is mapped across a narrow concentration gradient ranging from \(0.6865\) (blue) to \(0.7327\) (red/yellow).
- Surface-Bound Front Evolution: As time advances rapidly from \(t = 0.04\) to \(t = 0.44\), a sharp wavefront sweeps across the surface of the domain. Unlike the bulk variant where the excitation pulse fully occupies the 3D volume, this wave dynamics represents transport confined to boundary interfaces and cut planes.
Physical Context #
In coupled reaction-diffusion systems, surface traveling waves represent specific boundary-layer transport mechanisms:
- Advection & Front Dynamics on Manifolds: Models rapid signal propagation or state transitions that travel strictly along surface boundaries or biological membranes without diffusing deep into the surrounding bulk fluid or matrix.
- Coupled Inhibitor/Recovery Dynamics: In two-variable excitable media models (such as FitzHugh-Nagumo or Barkley models), \(w\) often acts as the slower recovery/inhibitor variable. A traveling surface front in \(w\) demonstrates how boundary-layer refractory states translate across space to regulate or suppress primary volumetric excitations.
- High-Speed Surface Transport: The brief duration of \(t = 0.44\text{ s}\) highlights a high phase velocity across the surface relative to bulk diffusion rates, typical of fast surface-catalyzed chemical reactions or membrane-bound wave propagation.
Research Profiles #
UBC Department of Mathematics Profile
ResearchGate Profile
ICIAM 2027 Biography
LinkedIn Profile
Google Scholar Profile
Loop Profile
References #
UBC News on CRC Appointment
Black Excellence in STEM Speaker Series
UBC Department of Mathematics Faculty Page
Sussex Profile
Newton Gateway