Staff profile

I completed my PhD in Applied Mathematics at Dublin City University in 2018. I was then a postdoctoral researcher in the Mathematics Department at Brandeis University with Prof. Jonathan Touboul. Subsequently, I joined the High Meadows Environmental Institute and Prof. Simon Levin’s lab at Princeton University. In August 2023, I joined the Department of Mathematical Sciences in the Applied Mathematics Group.

In my doctoral work, I studied qualitative properties of nonlinear differential systems with memory and subject to random noise. In my postdoctoral work, I expanded my research interests to include applications of techniques from dynamical systems and stochastic analysis to problems in ecology (savanna-forest modelling), developmental biology (cell fate dynamics in the brain), and epidemiology (malaria immune dynamics).

Currently, I'm working on mathematical problems related to understanding the movement of forest-savanna boundaries, within-host malaria dynamics, and coexistence in microbial ecosystems.

Teaching

I lecture the Michaelmas term of the 4H/Masters-level course "Advanced Mathematical Biology" at Durham. More details on courses I've taught and my teaching philosophy are available on my teaching page. 

I’m always open to discussing potential summer research opportunities with motivated students, and my students have been supported by London Mathematical Society and Biophysical Sciences Institute Bursaries in the past. Please get in touch with me if you are interested in a summer project on topics related to my research.

• Mathematical biology, dynamical systems, (nonlocal) PDEs, stochastic processes, mathematical modelling.

Journal Article

• Spatial Dynamics with Heterogeneity
  
  Patterson, D. D., Staver, A. C., Levin, S. A., & Touboul, J. D. (2023). Spatial Dynamics with Heterogeneity. SIAM Journal on Applied Mathematics, 84(3), S225-S248. https://doi.org/10.1137/22m1509850
• Revealing Physical Mechanisms of Spatial Pattern Formation and Switching in Ecosystems via Nonequilibrium Landscape and Flux
  
  Su, J., Wu, W., Patterson, D. D., Levin, S. A., & Wang, J. (2025). Revealing Physical Mechanisms of Spatial Pattern Formation and Switching in Ecosystems via Nonequilibrium Landscape and Flux. Advanced Science. Advance online publication. https://doi.org/10.1002/advs.202501776
• Mathematical modeling of malaria vaccination with seasonality and immune feedback
  
  Qu, Z., Patterson, D., Zhao, L., Ponce, J., Edholm, C. J., Prosper Feldman, O. F., & Childs, L. M. (2025). Mathematical modeling of malaria vaccination with seasonality and immune feedback. PLOS Computational Biology, 21(5), Article e1012988. https://doi.org/10.1371/journal.pcbi.1012988
• Pattern Formation in Mesic Savannas
  
  Patterson, D., Levin, S., Staver, A. C., & Touboul, J. (2024). Pattern Formation in Mesic Savannas. Bulletin of Mathematical Biology, 86(1). https://doi.org/10.1007/s11538-023-01231-7
• Modeling Immunity to Malaria with an Age-Structured PDE Framework
  
  Qu, Z., Patterson, D., Childs, L. M., Edholm, C. J., Ponce, J., Prosper, O., & Zhao, L. (2023). Modeling Immunity to Malaria with an Age-Structured PDE Framework. SIAM Journal on Applied Mathematics, 83(3), 1098-1125. https://doi.org/10.1137/21m1464427
• Non-equilibrium early-warning signals for critical transitions in ecological systems
  
  Xu, L., Patterson, D., Levin, S. A., & Wang, J. (2023). Non-equilibrium early-warning signals for critical transitions in ecological systems. Proceedings of the National Academy of Sciences, 120(5), Article e2218663120. https://doi.org/10.1073/pnas.2218663120
• COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex
  
  Feng, J., Hsu, W.-H., Patterson, D., Tseng, C.-S., Hsing, H.-W., Zhuang, Z.-H., Huang, Y.-T., Faedo, A., Rubenstein, J. L., Touboul, J., & Chou, S.-J. (2021). COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex. Science Advances, 7(27), Article eabf6808. https://doi.org/10.1126/sciadv.abf6808
• Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach
  
  Xu, L., Patterson, D., Staver, A. C., Levin, S. A., & Wang, J. (2021). Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach. Proceedings of the National Academy of Sciences, 118(24), Article e2103779118. https://doi.org/10.1073/pnas.2103779118
• Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications
  
  Patterson, D. D., Levin, S. A., Staver, C., & Touboul, J. D. (2020). Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications. SIAM Journal on Applied Dynamical Systems, 19(4), 2682-2719. https://doi.org/10.1137/19m1298329