Publications

Preprints

  1. T.A. Tambyah, R.J Murphy, P.R. Buenzli, M.J. Simpson (2020). A free boundary mechanobiological model of epithelial tissues.
  2. A. Surendran, M.J. Plank, M.J. Simpson (2020). Population dynamics with spatial structure and an Allee effect.
  3. D.G. Wilson, F.G. Woodhouse, M.J. Simpson, R.E. Baker (2020). Reconceptualising transport in crowded and complex environments.
  4. J. Lagergren, J.T. Nardini, R.E. Baker, M.J. Simpson, K.B. Flores (2020). Biologically-informed neural networks guide mechanistic modeling from sparse experimental data.
  5. E. Gavagnin, S.T. Vittadello, G. Gunasingh, N.K. Haass, M.J. Simpson, T. Rogers, C.A. Yates (2020). Synchronised oscillations in growing cell populations are explained by demographic noise.
  6. A.P Browning, J.A. Sharp, T. Mapder, C.M. Baker, K. Burrage, M.J. Simpson (2020). Persistence is an optimal hedging strategy for bacteria in volatile environments.
  7. D.J. Warne, R.E. Baker, M.J. Simpson (2020). Rapid Bayesian inference for expensive stochastic models.
  8. N.T. Fadai, S.T. Johnston, M.J. Simpson (2020). Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics.

Publications

  1. R.J Murphy, P.R. Buenzli, R.E. Baker, M.J. Simpson (2020). Travelling waves in a free boundary mechanobiological model of an epithelial tissue. Applied Mathematics Letters.
  2. E.J. Carr, J.M. Ryan, M.J. Simpson (2020). Diffusion in heterogeneous discs and spheres: new closed-form expressions for exit times and homogenization formulae. The Journal of Chemical Physics.
  3. R.J. Murphy, P.R. Buenzli, R.E. Baker, M.J. Simpson (2020). Mechanical cell competition in heterogeneous epithelial tissues. Bulletin of Mathematical Biology.
  4. S.T. Vittadello, S.W. McCue, G. Gunasingh, N.K. Haass, M.J. Simpson (2020). A novel mathematical model of heterogeneous cell proliferation. Journal of Mathematical Biology.
  5. Y. Li, P. van Heijster, R. Marangell, M.J. Simpson (2020). Travelling wave solutions in a negative nonlinear diffusion-reaction model. Journal of Mathematical Biology.
  6. P.R. Buenzli, M. Lanaro, C.S. Wong, M.P. McLaughlin, M.C. Allenby, M.A. Woodruff, M.J. Simpson (2020). Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size. Acta Biomaterialia.
  7. A. Surendran, M.J. Plank, M.J. Simpson (2020). Small-scale spatial structure affects predator-prey dynamics and coexistence. Theoretical Ecology.
  8. M.J. Simpson (2020). Critical length for the spreading-vanishing dichotomy in higher dimensions. ANZIAM Journal.
  9. M.J. Plank, M.J. Simpson, R.N. Binny (2020). Small-scale spatial structure influences large-scale invasion rates. Theoretical Ecology.
  10. M. El-Hachem, S.W. McCue, M.J. Simpson (2020). A sharp-front moving boundary model for malignant invasion. Physica D: Nonlinear Phenomena. 412, 132639.
  11. N.T. Fadai, M.J. Simpson (2020). Population dynamics with threshold effects gives rise to a diverse family of Allee effects. Bulletin of Mathematical Biology. 82, 74.
  12. S.T. Johnston, M.J. Simpson, E.J. Crampin (2020). Predicting population extinction in lattice-based birth-death-movement models. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 476: 20200089.
  13. A.P. Browning, W. Jin, M.J. Plank, M.J. Simpson (2020). Identifying density-dependent interactions in cell populations. Journal of the Royal Society Interface. 17: 20200143.
  14. D.J. Warne, R.E. Baker, M.J. Simpson (2020). A practical guide to pseudo-marginal methods for computational inference in systems biology. Journal of Theoretical Biology. 496, 110255.
  15. J.A. Sharp, A.P. Browning, T. Mapder, C.M. Baker, K. Burrage, M.J. Simpson (2020). Designing combination therapies using multiple optimal controls. Journal of Theoretical Biology. 497, 110277.
  16. S.T. Vittadello, S.W. McCue, G. Gunasingh, N.K. Haass, M.J. Simpson (2020). Examining go-or-grow using fluorescent cell-cycle indicators and cell cycle-inhibiting drugs. Biophysical Journal. 118, 1243-1247. Selected for the cover of Biophysical Journal.
  17. W. Jin, K-Y. Lo, Y-S. Sun, Y-H. Ting, M.J. Simpson (2020). Quantifying the role of different surface coatings in experimental models of wound healing. Chemical Engineering Science. 220, 115609. Selected for the cover of Chemical Engineering Science
  18. M.J. Simpson, R.E. Baker, S.T. Vittadello, O.J. Maclaren (2020). Parameter identifiability analysis for spatiotemporal models of cell invasion. Journal of the Royal Society Interface. 17, 20200055.
  19. N.T. Fadai, M.J. Simpson (2020). New travelling wave solutions of the Porous-Fisher model with a moving boundary. Journal of Physics A: Mathematical and Theoretical. 53, 095601.
  20. N.T. Fadai, R.E. Baker, M.J. Simpson (2019). Accurate and efficient discretisations for stochastic models providing near agent-based spatial resolution at low computational cost. Journal of the Royal Society Interface. 16, 20190421.
  21. A. Surendran, M.J. Plank, M.J. Simpson (2019). Spatial structure arising from chase-escape interactions with crowding. Scientific Reports. 9, 14988.
  22. O.M. Matsiaka, R.E. Baker, M.J. Simpson (2019). Continuum descriptions of spatial spreading for heterogeneous cell populations: theory and experiment. Journal of Theoretical Biology. 482, 109997.
  23. R.E. Baker, A. Parker, M.J. Simpson (2019). A free boundary model of epithelial dynamics. Journal of Theoretical Biology. 481: 61 - 74.
  24. M. El-Hachem, S.W. McCue, W. Jin, Y. Du, M.J. Simpson (2019). Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 475: 20190378.
  25. S.T. Vittadello, S.W. McCue, G. Gunasingh, N.K. Haass, M.J. Simpson (2019). Mathematical models incorporating a multi-stage cell cycle replicate normally-hidden inherent synchronisation in cell proliferation. Journal of the Royal Society Interface. 16: 20190382.
  26. A.P. Browning, F.G. Woodhouse, M.J. Simpson (2019). Reversible signal transmission in an active mechanical metamaterial. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 475, 20190146.
  27. R.J. Murphy, P. Buenzli, R.E. Baker, M.J. Simpson (2019). An individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 475, 20180838. Selected for the cover of Proceedings A.
  28. S.W. McCue, W. Jin, T.J. Moroney, K-Y Lo, S-E Chou, M.J. Simpson (2019). Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology. Physica D: Nonlinear Phenomena. 398, 130-140.
  29. O.M. Matsiaka, R.E. Baker, E.T. Shah, M.J. Simpson (2019). Mechanistic and experimental models of cell migration reveal the importance of intercellular interactions in cell invasion. Biomedical Physics & Engineering Express. 5, 045009.
  30. D.J. Warne, R.E. Baker, M.J. Simpson (2019). Using experimental data and information criteria to guide model selection for reaction-diffusion problems in mathematical biology. Bulletin of Mathematical Biology. 81, 1760-1804.
  31. J.A. Sharp, A.P. Browning, T. Mapder, K. Burrage, M.J. Simpson (2019). Optimal control of acute myeloid leukaemia. Journal of Theoretical Biology. 470, 30-42
  32. D.J. Warne, R.E. Baker, M.J. Simpson (2019). Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art. Journal of the Royal Society Interface. 16, 20180943.
  33. A.P. Browning, P. Haridas, M.J. Simpson (2019). A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin. Bulletin of Mathematical Biology. 81, 676-698. Selected for the 2021 Lee A Segel Prize for the best student paper.
  34. M.J. Simpson (2019). Mathematical models of cell invasion track spatial position and progression through the cell cycle. SIAM News. 52, 1-2.
  35. E.J. Carr, M.J. Simpson (2019). New homogenization approaches for stochastic transport through heterogeneous media. Journal of Chemical Physics. 150, 044104.
  36. S. McInerney, E.J. Carr, M.J. Simpson (2019). Parameterising continuum models of heat transfer in heterogeneous living skin using experimental data. International Journal of Heat and Mass Transfer. 128, 964-975.
  37. W. Jin, X. Liang, A. Brooks, K. Futrega, X. Liu, M.R. Doran, M.J. Simpson, M.S. Roberts, H. Wang (2018). Modelling of the SDF-1/CXCR4 regulated in vivo homing of therapeutic mesenchymal stem/stromal cells in mice. PeerJ. 6, e6072
  38. H. Yang, R.M. Villani, H. Wang, M.J. Simpson, M.S. Roberts, M. Tang, X. Liang (2018). The role of cellular reactive oxygen species in cancer chemotherapy. Journal of Experimental & Clinical Cancer Research. 37, 266.
  39. A. Surendran, M.J. Plank, M.J. Simpson (2018). Spatial moment description of birth-death-movement processes incorporating the effects of crowding and obstacles. Bulletin of Mathematical Biology. 80, 2828-2855.
  40. Z. Welsh, M.J. Simpson, Md I.H. Khan, M.A. Karim (2018). Multiscale modelling of food drying: State of the art. Comprehensive Reviews in Food Science and Food Safety. 17, 1293-1308.
  41. A. Parker, M.J. Simpson, R.E. Baker (2018). The impact of experimental design choices on parameter inference for models of growing cell colonies. Royal Society Open Science. 5, 180384.
  42. M.J. Simpson, W. Jin, S.T. Vittadello, T.A. Tambyah, J.M. Ryan, G. Gunasingh, N.K. Haass, S.W. McCue (2018). Stochastic models of cell invasion with fluorescent cell cycle indicators. Physica A: Statistical Mechanics and its Applications. 510, 375-386.
  43. P. Haridas, A.P. Browning, J.A. McGovern, D.L.S. McElwain, M.J. Simpson (2018). Three-dimensional experiments and individual based simulations show that cell proliferation drives melanoma nest formation in human skin tissue. BMC Systems Biology. 12, 34.
  44. O.M. Matsiaka, C.J. Penington, R.E. Baker, M.J. Simpson (2018). Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics. Bulletin of Mathematical Biology. 80, 738-757.
  45. D.J. Warne, R.E. Baker, M.J. Simpson (2018). Multilevel rejection sampling for approximate Bayesian computation. Computational Statistics & Data Analysis. 124, 71–86.
  46. W. Jin, S.W. McCue, M.J. Simpson (2018). Extended logistic growth model for heterogeneous populations Journal of Theoretical Biology. 445, 51-61.
  47. S.T. Vittadello, S.W. McCue, G. Gunasingh, N.K. Haass, M.J. Simpson (2018). Mathematical models for cell migration with real-time cell cycle dynamics. Biophysical Journal. 114, 1241 – 1253.
  48. E.J Carr, M.J. Simpson (2018). Rapid calculation of maximum particle lifetime for diffusion in complex geometries. Journal of Chemical Physics. 148, 094113.
  49. M.J. Simpson (2018). Calculating groundwater response times for flow in heterogeneous porous media. Groundwater. 56, 337-342.
  50. W. Jin, K-Y. Lo, S-E Chou, S.W. McCue, M.J. Simpson (2018). The role of initial geometry in experimental models of wound closing. Chemical Engineering Science. 179, 221-226. Selected for the cover of Chemical Engineering Science.
  51. E.J. Carr, M.J. Simpson (2018). Accurate and efficient calculation of response times for groundwater flow. Journal of Hydrology. 558, 470–481.
  52. A.P. Browning, S.W. McCue, R.N. Binny, M.J. Plank, E.T. Shah, M.J. Simpson (2018). Inferring parameters for a lattice-free model of cell migration and proliferation using experimental data. Journal of Theoretical Biology. 437, 251-260.
  53. D.J. Warne, R.E. Baker, M.J. Simpson (2017). Optimal quantification of contact inhibition in cell populations . Biophysical Journal (Biophysical Letter). 113, 1920-1924.
  54. M.J. Simpson, M.J. Plank (2017). Simplified calculation of diffusivity for a lattice-based random walk with a single obstacle. Results in Physics. 7, 3346-3348.
  55. M.J. Simpson, S. McInerney, E.J. Carr, L. Cuttle (2017). Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments. Scientific Reports. 7, 10925
  56. P. Haridas, J.A. McGovern, D.L.S. McElwain, M.J. Simpson (2017). Quantitative comparison of the spreading and invasion of radial growth phase and metastatic melanoma cells in a three-dimensional human skin equivalent model. PeerJ. 5, e3754.
  57. W. Jin, C.J. Penington, S.W. McCue, M.J. Simpson (2017). A computational modelling framework to quantify the effects of passaging cell lines. PLOS ONE. 12, e0181941.
  58. A.P. Browning, S.W. McCue, M.J. Simpson (2017). A Bayesian computational approach to explore the optimal duration of a cell proliferation assay. Bulletin of Mathematical Biology. 79, 1888-1906.
  59. P. Haridas, C.J. Penington, J.A. McGovern, D.L.S. McElwain, M.J. Simpson (2017). Quantifying rates of cell migration and cell proliferation in co-culture barrier assays reveals how skin and melanoma cells interact during melanoma spreading and invasion. Journal of Theoretical Biology. 423, 13-25.
  60. O.M. Matsiaka, C.J. Penington, R.E. Baker, M.J. Simpson (2017). Continuum approximations for lattice-free multi-species models of collective cell migration. Journal of Theoretical Biology. 422, 1-11.
  61. W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, P.K. Maini, M.J. Simpson (2017). Logistic proliferation of cells in scratch assays is delayed. Bulletin of Mathematical Biology. 79, 1028-1050.
  62. M. Zheng, F. Liu, Q. Liu, K. Burrage, M.J. Simpson (2017). A novel numerical approximation of the time fractional reaction-diffusion equation with a moving boundary. Journal of Computational Physics. 338, 493-510.
  63. M.J. Simpson, K-Y. Lo, Y-S. Sun (2017). 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. BMC Systems Biology. 11, 39.
  64. S.T. Johnston, R.E. Baker, M.J. Simpson (2017). A new and accurate continuum description of moving fronts. New Journal of Physics. 19, 033010.
  65. S.T. Johnston, R.E. Baker, D.L.S. McElwain, M.J. Simpson (2017). Co-operation, competition and crowding: a discrete framework linking Allee kinetics, nonlinear diffusion, shocks and sharp-fronted travelling waves. Scientific Reports. 7, 42134.
  66. M.J. Simpson (2017). Critical time scales for morphogen gradient formation: Concentration or gradient criteria. International Journal of Heat and Mass Transfer. 106, 570-572.
  67. F. Jazaei, M.J. Simpson, T.P. Clement (2017). Understanding time scales of diffusive fluxes and the implication for steady state and steady shape conditions. Geophysical Research Letters. 44, 174-180.
  68. W. Jin, C.J. Penington, S.W. McCue, M.J. Simpson (2016). Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions. Physical Biology. 13, 056003.
  69. A.J. Ellery, R.E. Baker, M.J. Simpson (2016). An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice. Fast Track Letter, Physical Biology. 13, 05LT02.
  70. P.R. Taylor, R.E. Baker, M.J. Simpson, C.A. Yates (2016). Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches. Journal of the Royal Society Interface. 13, 2016336.
  71. C.J. Penington, R.E. Baker, M.J. Simpson (2016). Exits in order: how crowding affects particle lifetimes. The Journal of Chemical Physics. 144, 244107.
  72. C.J. Andrews, L. Cuttle, M.J. Simpson (2016). Quantifying the role of burn temperature, burn duration and skin thickness in an in vivo animal skin model of heat conduction. International Journal of Heat and Mass Transfer. 101, 542-549.
  73. A.J. Ellery, R.E. Baker, M.J. Simpson (2016). Distinguishing between short-time non-Fickian diffusion, and long-time Fickian diffusion for a random walk on a crowded lattice. Communication, The Journal of Chemical Physics. 144, 171104.
  74. S.T. Johnston, R.E. Baker, M.J. Simpson (2016). Filling the gaps: A robust description of adhesive birth-death-movement processes. Physical Review E. 93, 042413.
  75. S.T. Johnston, J.V. Ross, B.J. Binder, D.L.S. McElwain, P. Haridas, M.J. Simpson (2016). Quantifying the effect of experimental design choices for in vitro scratch assays. Journal of Theoretical Biology. 400, 19-31.
  76. P. Haridas, J.A. McGovern, A.S. Kashyap, D.L.S. McElwain, M.J. Simpson (2016). Standard melanoma-associated markers do not identify the MM127 metastatic melanoma cell line. Scientific Reports. 6, 24569.
  77. R.N. Binny, P. Haridas, A. James, R. Law, M.J. Simpson, M.J. Plank (2016). Spatial structure arising from neighbour-dependent bias in collective cell movement. PeerJ. 4, e1689.
  78. B.J. Binder, M.J. Simpson (2016). Cell density and cell size dynamics during in vitro tissue growth experiments: Implications for mathematical models of collective cell behaviour. Applied Mathematical Modelling. 40, 3438-3446.
  79. A.J. Ellery, R.E. Baker, S.W. McCue, M.J. Simpson (2016). Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes. Physica A: Statistical Mechanics and its Applications. 449, 74-84.
  80. W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, L.K. Chopin, M.J. Simpson (2016). Reproducibility of scratch assays is affected by the initial degree of confluence: experiments, modelling and model selection. Journal of Theoretical Biology. 390, 136-145.
  81. F. Jazaei, M.J. Simpson , T.P. Clement (2016). Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests. Journal of Hydrology. 532: 1-8.
  82. C. Irons, M.J. Plank, M.J. Simpson (2016). Lattice-free models of directed cell motility. Physica A: Statistical Mechanics and its Applications. 442, 110-121.
  83. A.J. Ellery, R.E. Baker, M.J. Simpson (2015). Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes. Physical Biology. 12: 066010.
  84. P.R. Taylor, C.A. Yates, M.J. Simpson, R.E. Baker (2015). Reconciling transport models across scales: the role of volume exclusion. Rapid Communication, Physical Review E. 92, 040701(R).
  85. M.J. Simpson, J.A. Sharp, L.C. Morrow, R.E. Baker (2015). Exact solutions of coupled multispecies linear reaction-diffusion equations on a uniformly growing domain. PLOS ONE. 10, e0138894.
  86. M.J. Simpson, R.E. Baker (2015). Exact calculations of survival probability for diffusion on growing lines, disks and spheres: the role of dimension. The Journal of Chemical Physics. 143, 094109.
  87. S.T. Johnston, E.T. Shah, L.K. Chopin, D.L.S. McElwain, M.J. Simpson (2015). Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM assay data using the Fisher-Kolmogorov model. BMC Systems Biology. 9, 38.
  88. M.J. Simpson, L.C. Morrow (2015). Analytical model of reactive transport processes with spatially variable coefficients. Royal Society Open Science. 2, 140348.
  89. M.J. Simpson, R.E. Baker (2015). Spatial moment techniques for modelling biological processes. Bulletin of Mathematical Biology. 77, 581-585.
  90. D.C. Markham, M.J. Simpson, R.E. Baker (2015). Choosing an appropriate modelling framework for analysing multispecies co-culture experiments. Bulletin of Mathematical Biology. 77, 713-734.
  91. M.J. Simpson, J.A. Sharp, R.E. Baker (2015). Survival probability for a diffusive process on a growing domain. Physical Review E. 91, 042701.
  92. B.N. Vo, C.C. Drovandi, A.N. Pettitt, M.J. Simpson (2015). Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation. Mathematical Biosciences. 263, 133-142.
  93. M.J. Simpson (2015). Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: Criteria for successful colonization. PLOS ONE. 10, e0117949.
  94. S.T. Johnston, M.J. Simpson, R.E. Baker (2015). Modelling the movement of interacting cell populations: A moment dynamics approach. Journal of Theoretical Biology. 370, 81-92.
  95. B.J Binder, M.J. Simpson (2015). Spectral analysis of pair-correlation bandwidth: Application to cell biology images. Royal Society Open Science. 2, 140494.
  96. M.J. Simpson, S.W. McCue (2015). ANZIAM 2015. Gazette of the Australian Mathematical Society. 42, 23-25.
  97. F. Jazaei, M.J. Simpson, T.P. Clement (2014). An analytical framework for quantifying aquifer response time scales associated with transient boundary conditions. Journal of Hydrology. 519, 1642-1648.
  98. S.T Johnston, M.J. Simpson, D.L.S. McElwain, B.J. Binder, J.V. Ross (2014). Interpreting scratch assays using pair density dynamics and approximate Bayesian computation. Royal Society Open Biology. 4, 140097.
  99. K.K. Treloar, M.J. Simpson, B.J. Binder, D.L.S McElwain, R.E. Baker (2014). Assessing the role of spatial correlations during collective cell spreading. Scientific Reports. 4, 5713.
  100. S.T. Johnston, M.J. Simpson, D.L.S McElwain (2014). How much information can be obtained from tracking the position of the leading edge in a scratch assay? Journal of the Royal Society Interface. 11, 20140325.
  101. K.K. Treloar, M.J. Simpson, D.L.S McElwain, R.E Baker (2014). Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geomentry? Journal of Theoretical Biology. 356, 71-84.
  102. H.M. Young, A.J. Bergner, M.J. Simpson, S.J. McKeown, M.M. Hao, C.R. Anderson, H. Enomoto (2014). Colonizing while migrating: How do individual enteric neural crest cells behave? BMC Biology. 12, 23.
  103. M.J. Simpson , A.J. Ellery (2014). Exact series solutions of reactive transport models with general initial conditions. Journal of Hydrology. 513, 7-12.
  104. D.J.G. Agnew, J.E.F. Green, T.M. Brown, M.J. Simpson, B.J. Binder (2014). Distinguishing between mechanisms of cell aggregation using pair-correlation functions. Journal of Theoretical Biology. 352, 16-23.
  105. D.C. Markham, M.J. Simpson, P.K. Maini, E.A. Gaffney, R.E. Baker (2014). Comparing methods for modelling spreading cell fronts. Journal of Theoretical Biology. 353, 95-103.
  106. A.J. Ellery, M.J. Simpson, S.W. McCue, R.E. Baker (2014). Characterizing transport through a crowded environment with different obstacle sizes. The Journal of Chemical Physics. 140, 054108.
  107. M.J. Simpson, P. Haridas, D.L.S. McElwain (2014). Do pioneer cells exist? PLOS ONE. 9, e85488.
  108. M.J. Simpson, J.A Sharp, R.E. Baker (2014). Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes. Physica A: Statistical Mechanics and its Applications. 395, 236-246.
  109. K.K. Treloar, M.J. Simpson, P. Haridas, K.J. Manton, D.I. Leavesley, D.L.S. McElwain, R.E. Baker (2013). Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. BMC Systems Biology. 7, 137.
  110. S.T. Johnston, M.J. Simpson, M.J. Plank (2013). Lattice-free descriptions of collective motion with crowding and adhesion. Physical Review E. 88, 062720.
  111. A.J. Ellery, M.J. Simpson, S.W. McCue, R.E. Baker (2013). A simplified approach for calculating the moments of action for linear reaction-diffusion equations. Physical Review E. 88, 054102.
  112. D.C. Markham, M.J. Simpson, P.K. Maini, E.A. Gaffney, R.E. Baker (2013). Incorporating spatial correlations into multi-species mean-field models. Physical Review E. 88, 052713.
  113. M.J. Simpson, F. Jazaei, T.P. Clement (2013). How long does it take for aquifer recharge or aquifer discharge processes to reach steady state? Journal of Hydrology. 501, 241-248.
  114. L.G. Bowden, M.J. Simpson, R.E. Baker (2013). Design and interpretation of cell trajectory assays. Journal of the Royal Society Interface. 10, 20130630.
  115. M.J. Plank, M.J. Simpson (2013). Lattice-free models of cell invasion: discrete simulations and travelling waves. Bulletin of Mathematical Biology. 75, 2150-2166.
  116. B.J. Binder, M.J. Simpson (2013). Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions. Physical Review E. 88, 022705.
  117. A.J. Ellery, M.J. Simpson, S.W. McCue (2013). Comment on Local accumulation times for source, diffusion and degradation models in two and three dimensions. The Journal of Chemical Physics. 139, 017101.
  118. D.C. Markham, M.J. Simpson, R.E. Baker (2013). Simplified method for including spatial correlations in mean-field approximations. Physical Review E. 87, 062702.
  119. K.K. Treloar, M.J. Simpson (2013). Sensitivity of edge detection methods for quantifying cell migration assays. PLOS ONE. 8, e67389.
  120. M.J. Simpson, B.H. Foy, S.W. McCue (2013). Travelling waves for a velocity-jump model of cell migration and proliferation. Mathematical Biosciences. 244, 98-106.
  121. M.J. Simpson, B.J. Binder, P. Haridas, B.K. Wood, K.K. Treloar, D.L.S. McElwain, R.E. Baker (2013). Experimental and modelling investigations of monolayer development with clustering. Bulletin of Mathematical Biology. 75, 871-889.
  122. M.J. Simpson, K.K. Treloar, B.J. Binder, P. Haridas, K.J. Manton, D.I. Leavesley, D.L.S. McElwain, R.E. Baker (2013). Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. Journal of the Royal Society Interface. 10, 20130007.
  123. K.K. Treloar, M.J. Simpson, S.W. McCue (2013). Velocity-jump processes with proliferation. Journal of Physics A: Mathematical and Theoretical. 46, 015003. Highlighted by IOP Insights.
  124. M.J. Simpson, A.J. Ellery, S.W. McCue, R.E. Baker (2013). Critical timescales and time intervals for coupled linear processes. ANZIAM Journal. 54, 127-142.
  125. A.J. Ellery, M.J. Simpson, S.W. McCue, R.E. Baker (2012). Moments of action provide insight into critical times for advection-diffusion-reaction processes. Physical Review E. 86, 031136.
  126. M.J. Simpson, G.N. Mercer (2012). Infectious disease modelling. ANZIAM Journal. 54, 1-2.
  127. B.J. Binder, J.V. Ross, M.J. Simpson (2012). A hybrid model for studying spatial aspects of infectious diseases. ANZIAM Journal. 54, 37-49.
  128. S.T. Johnston, M.J. Simpson, R.E. Baker (2012). Mean-field descriptions of collective migration with strong adhesion. Physical Review E. 85, 051922.
  129. M.J. Plank, M.J. Simpson (2012). Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. Journal of the Royal Society Interface. 9, 2983-2996.
  130. A.J. Ellery, M.J. Simpson, S.W. McCue, R.E. Baker (2012). Critical timescales for advection–diffusion–reaction processes. Physical Review E. 85, 041135.
  131. R.E. Baker, M.J. Simpson (2012). Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation and travelling waves. Physica A: Statistical Mechanics and its Applications. 391, 3729-3750.
  132. M.J. Simpson, A.J. Ellery (2012). An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell. Applied Mathematical Modelling. 36, 3329-3334.
  133. K.K. Treloar, M.J. Simpson, S.W. McCue (2011). Velocity-jump models with crowding effects. Physical Review E. 84, 061920.
  134. S.W. Chang, T.P. Clement, M.J. Simpson, K-K. Lee (2011). Does sea-level rise have an impact on saltwater intrusion? Advances in Water Resources. 34, 1283-1291.
  135. M.J. Simpson, R.E. Baker (2011). Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena. Physical Review E. 83, 051922.
  136. A.J. Ellery, M.J. Simpson (2011). An analytical method to solve a general class of nonlinear reactive transport models. Chemical Engineering Journal. 169, 313-318.
  137. M.J. Simpson, R.E. Baker, S.W. McCue (2011). Models of collective cell spreading with variable cell aspect ratio: A motivation for degenerate diffusion models. Physical Review E. 83, 021901.
  138. M.J. Simpson, C. Towne, D.L.S. McElwain, Z. Upton (2010). Migration of breast cancer cells: Understanding the roles of volume exclusion and cell-to-cell adhesion. Physical Review E. 82, 041901.
  139. R.E. Baker, M.J. Simpson (2010). Correcting mean-field approximations for birth-death-movement processes. Physical Review E. 82, 041905.
  140. M.J. Simpson, K.A. Landman, B.D. Hughes (2010). Cell invasion with proliferation mechanisms motivated by time-lapse data. Physica A: Statistical Mechanics and its Applications. 389, 3779-3790.
  141. A.E. Fernando, K.A. Landman, M.J. Simpson (2010). Nonlinear diffusion and exclusion processes. Physical Review E. 81, 011903.
  142. M.J. Simpson, K.A. Landman, B.D. Hughes, A.E. Fernando (2010). A model for mesoscale patterns in motile populations. Physica A: Statistical Mechanics and its Applications. 389, 1412-1424.
  143. M.J. Simpson, B.D. Hughes, K.A. Landman (2009). Diffusing populations: Ghosts or Folks? Australasian Journal of Engineering Education. 15, 59-68.
  144. M.J. Simpson, K.A. Landman, B.D. Hughes (2009). Pathlines in exclusion processes. Physical Review E. 79, 031920.
  145. M.J. Simpson (2009). Depth-averaging errors in reactive transport modelling. Water Resources Research. 45, W02505.
  146. M.J. Simpson, K.A. Landman, B.D. Hughes (2009). Distinguishing between directed and undirected cell motility within an invading cell population. Bulletin of Mathematical Biology. 71, 781-799.
  147. M.J. Simpson, K.A. Landman, B.D. Hughes (2009). Multi-species simple exclusion processes. Physica A: Statistical Mechanics and its Applications. 388, 399-406.
  148. B.J. Binder, K.A. Landman, M.J. Simpson, M. Mariani, D.F. Newgreen (2008). Modeling proliferative tissue growth: a general approach and an avian case study. Physical Review E. 78, 031912.
  149. K.A. Landman, M.J. Simpson, G.J. Pettet (2008). Tactically-driven nonmonotone travelling waves. Physica D: Nonlinear Phenomena. 237, 678-691.
  150. M.J. Simpson, K.A. Landman (2008). Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms. Mathematics and Computers in Simulation. 77, 9-21.
  151. M.J. Simpson (2008). Discussion of Direct and split operator approaches with ELLAM for reactive transport equations. AIChE Journal. 54, 588-588.
  152. M.J. Simpson, A. Merrifield, K.A. Landman, B.D. Hughes (2007). Simulating invasion with cellular automata: connecting cell-scale and population-scale properties. Physical Review E. 76, 021918.
  153. M.J. Simpson, K.A. Landman (2007). Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems. Journal of Computational Physics. 225, 6-12.
  154. M.J. Simpson, K.A. Landman (2007). Analysis of split operator methods applied to reactive transport with Monod kinetics. Advances in Water Resources. 30, 2026-2033.
  155. M.J. Simpson, K.A. Landman, K. Bhaganagarapu (2007). Coalescence of interacting cell populations. Journal of Theoretical Biology. 247, 525-543.
  156. K.A. Landman, M.J. Simpson, D.F. Newgreen (2007). Mathematical and experimental insight into the development of the enteric nervous system and Hirschsprung's Disease. Development, Growth and Differentiation. 49, 277-286.
  157. M.J. Simpson, D.C. Zhang, M. Mariani, K.A. Landman, D.F. Newgreen (2007). Cell proliferation drives neural crest cell invasion of the intestine. Developmental Biology. 302, 553-568. Selected for the cover of Developmental Biology.
  158. M.J. Simpson (2007). Reply to comment on Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal. 15, 431-432.
  159. M.J. Simpson, K.A. Landman, B.D. Hughes, D.F. Newgreen (2006). Looking inside an invasion wave of cells using continuum models: Proliferation is the key. Journal of Theoretical Biology. 243, 343-360.
  160. M.J. Simpson, K.A. Landman, D.F. Newgreen (2006). Chemotactic and diffusive migration on a non-uniformly growing domain: Numerical algorithm development and applications. Journal of Computational and Applied Mathematics. 192, 282-300.
  161. M.J. Simpson, K.A. Landman (2006). Characterizing and minimizing the operator split error for Fisher's equation. Applied Mathematics Letters. 19, 604-612.
  162. M.J. Simpson, T.P. Clement, F.E. Yeomans (2006). Erratum, Analytical model for computing residence times near a pumping well. Groundwater. 44, 509-510.
  163. M.J. Simpson, K.A. Landman, T.P. Clement (2005). Assessment of a non-traditional operator split algorithm for simulation of reactive transport. Mathematics and Computers in Simulation. 70, 44-60.
  164. M.J. Simpson (2005). Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal. 13, 889-894.
  165. K.A. Landman, M.J. Simpson, J.L. Slater, D.F. Newgreen (2005). Diffusive and chemotactic cellular migration: smooth and discontinuous travelling wave solutions. SIAM Journal on Applied Mathematics. 65, 1420-1442.
  166. M.J. Simpson (2004). SEAWAT-2000: Variable-density flow processes and integrated MT3DMS transport processes. Groundwater. 42, 642-645.
  167. M.J. Simpson, T.P. Clement (2004). Improving the worthiness of the Henry problem as a benchmark for density-dependent ground water flow problems. Water Resources Research. 40, W01504.
  168. M.J. Simpson, T.P. Clement, F.E. Yeomans (2003). Analytical model for computing residence times near a pumping well. Groundwater. 41, 351-354.
  169. M.J. Simpson, T.P. Clement, T.A. Gallop (2003). Laboratory and numerical investigation of flow and transport near a seepage-face boundary. Groundwater. 41, 690-700.
  170. M.J. Simpson, T.P. Clement (2003). A theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models. Advances in Water Resources. 26, 17-31.
  171. M.J. Simpson, T.P. Clement (2003). Comparison of finite difference and finite element solutions to the variably saturated flow equation. Journal of Hydrology. 270, 49-64.