Assessment of a non-traditional operator split algorithm for simulation of reactive transport. - Matthew J. Simpson; Kerry A. Landman; T. Prabhakar Clement (Math. Comput. Simul., 2005)

Diffusive and Chemotactic Cellular Migration: Smooth and Discontinuous Traveling Wave Solutions. - Kerry A. Landman; Matthew J. Simpson; J. L. Slater; Donald F. Newgreen (SIAM J. Appl. Math., 2005)

Characterizing and minimizing the operator split error for Fisher's equation. - Matthew J. Simpson; Kerry A. Landman (Appl. Math. Lett., 2006)

Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems. - Matthew J. Simpson; Kerry A. Landman (J. Comput. Phys., 2007)

Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms. - Matthew J. Simpson; Kerry A. Landman (Math. Comput. Simul., 2008)

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. - Katrina K. Treloar; Matthew J. Simpson; Parvathi Haridas; Kerry J. Manton; David I. Leavesley; Donald L. S. McElwain; Ruth E. Baker (BMC Syst. Biol., 2013)

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model. - Stuart T. Johnston; Esha Shah; Lisa Chopin; D. L. Sean McElwain; Matthew J. Simpson (BMC Syst. Biol., 2015)

Quantifying the roles of random motility and directed motility using advection-diffusion theory for a 3T3 fibroblast cell migration assay stimulated with an electric field. - Matthew J. Simpson; Kai-Yin Lo; Yung-Shin Sun (BMC Syst. Biol., 2017)

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. - Minling Zheng; Fawang Liu; Qingxia Liu; Kevin Burrage; Matthew J. Simpson (J. Comput. Phys., 2017)

Three-dimensional experiments and individual based simulations show that cell proliferation drives melanoma nest formation in human skin tissue. - Parvathi Haridas; Alexander P. Browning; Jacqui A. McGovern; D. L. Sean McElwain; Matthew J. Simpson (BMC Syst. Biol., 2018)

Multilevel rejection sampling for approximate Bayesian computation. - David J. Warne; Ruth E. Baker; Matthew J. Simpson (Comput. Stat. Data Anal., 2018)

Biologically-informed neural networks guide mechanistic modeling from sparse experimental data. - John H. Lagergren; John T. Nardini; Ruth E. Baker; Matthew J. Simpson; Kevin B. Flores (PLoS Comput. Biol., 2020)

Exact sharp-fronted travelling wave solutions of the Fisher-KPP equation. - Scott W. McCue; Maud El-Hachem; Matthew J. Simpson (Appl. Math. Lett., 2021)

Travelling waves in a free boundary mechanobiological model of an epithelial tissue. - Ryan J. Murphy; Pascal R. Buenzli; Ruth E. Baker; Matthew J. Simpson (Appl. Math. Lett., 2021)

Exact time-dependent solutions of a Fisher-KPP-like equation obtained with nonclassical symmetry analysis. - Scott W. McCue; Bronwyn H. Bradshaw-Hajek; Matthew J. Simpson (Appl. Math. Lett., 2022)

Approximate analytical solution for transient heat and mass transfer across an irregular interface. - Elliot J. Carr; Dylan J. Oliver; Matthew J. Simpson (Commun. Nonlinear Sci. Numer. Simul., 2022)

Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes. - David J. Warne; Thomas P. Prescott; Ruth E. Baker; Matthew J. Simpson (J. Comput. Phys., 2022)

Rapid Bayesian Inference for Expensive Stochastic Models. - David J. Warne; Ruth E. Baker; Matthew J. Simpson (J. Comput. Graph. Stat., 2022)

Efficient inference and identifiability analysis for differential equation models with random parameters. - Alexander P. Browning; Christopher C. Drovandi; Ian W. Turner; Adrianne L. Jenner; Matthew J. Simpson (PLoS Comput. Biol., 2022)

Computationally efficient mechanism discovery for cell invasion with uncertainty quantification. - Daniel J. Vandenheuvel; Christopher C. Drovandi; Matthew J. Simpson (PLoS Comput. Biol., 2022)

Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. - Matthew J. Simpson; Oliver J. Maclaren (PLoS Comput. Biol., 2023)

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates. - Alexander P. Browning; Matthew J. Simpson (PLoS Comput. Biol., 2023)

Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability. - Ryan J. Murphy; Gency Gunasingh; Nikolas K. Haass; Matthew J. Simpson (PLoS Comput. Biol., 2023)

Generalised likelihood profiles for models with intractable likelihoods. - David J. Warne; Oliver J. Maclaren; Elliot J. Carr; Matthew J. Simpson; Christopher C. Drovandi (Stat. Comput., 2024)

A generalised sigmoid population growth model with energy dependence: Application to quantify the tipping point for Antarctic shallow seabed algae. - Elise Mills; Graeme F. Clark; Matthew J. Simpson; Mark E. Baird; Matthew P. Adams (Environ. Model. Softw., 2025)