- MATRIX Mathematical Research Institute (2024) Parameter identifiability in mathematical biology. MJ Simpson, RE Baker, OJ Maclaren.
- Australian Research Council Discovery Project (2023-2025) New mathematical approaches to learn the equations of life from noisy data. MJ Simpson, A Jenner, PR Buenzli and RR Baker.
- Australian Research Council Centre of Excellence (2023-2029) The ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. M Stumpf, J Flegg, M McConville, G Reid, H Shim, A Coster, M Wilkins, W Zhang, R Morris, T Beilharz, T Lithgow, M McDonald, L Nguyen, MJ Simpson, C Drovandi, R Nayak, R Araujo, J Wen, E Eyras, E Stone.
- QUT Edge Grant (2021). Mathematical models of cell migration in three-dimensional living tissues. MJ Simpson.
- Australian Research Council Discovery Project (2020-2022) Mathematical models of 4D spheroids: mathematical model development and parameterisation. MJ Simpson, N Haass and MJ Plank.
- USA Aerospace Research and Development Research Program (2017-2018). Cellular hedging. K Burrage and MJ Simpson.
- Royal Society International Exchanges Scheme (2017-2019) Single-file diffusion in networks. F Woodhouse and MJ Simpson.
- Banff International Research Station (2018) Mathematical and statistical challenges in bridging model development, parameter identification and model selection in the biological sciences. RE Baker, D Coombs and MJ Simpson.
- Australian Research Council Discovery Project (2017-2019) Mathematical models of cell migration in three-dimensional living tissues. MJ Simpson, RE Baker and MJ Plank.
- Australian Research Council Future Fellowship (2014-2018) New data-driven mathematical models of collective cell motion. MJ Simpson.
- Australian Research Council Discovery Project (2014-2016) A new hierarchy of mathematical models to quantify the role of ghrelin during cell invasion. MJ Simpson, SW McCue, A Herington, L Chopin and PK Maini.
- CRC for Wound Management Innovation Project Grant (2013-2015) Cell clustering in wound healing. MJ Simpson and DLS McElwain.
- Australian Research Council Discovery Project (2012-2014) Modelling cell invasion incorporating the epithelial to mesenchymal transition: Exploring therapies to control wound healing and cancer progression. MJ Simpson, DLS McElwain, DI Leavesley and RE Baker.
- Marsden Fund New Zealand (2012-2014) Cell invasion: Interactions across scales. MJ Plank, MJ Simpson and R Law.
- Royal Society International Exchanges Scheme (2012-2014) Multiscale models of cell motility for populations with variable cell shape. RE Baker and MJ Simpson.
- Australian Research Council Discovery (2006-2009) Multiscale modelling of cell migration in developmental biology. KA Landman, BD Hughes and MJ Simpson. Australian Postdoctoral fellowship to MJ Simpson.
- Australian Research Council Small Grant (2001-2001) Experimental and numerical investigation of unconfined flow systems with seepage face boundaries. TP Clement and Matthew Simpson.