I am interested in mathematical modelling of various biological phenomena with partial differential equations (PDEs). In particular, my main interest lies in the spatial patterns of biological organisms and their dependence on a heterogeneous environment or setting. Recently, I started working on the spatial spread of glioblastoma, a malignant type of brain cancer, and its therapy.
Nonlocal population model
Nonlocal perception and memory play crucial roles in movement models of species, including animals and cell-cell adhesion. I am interested in the effect of nonlocal perception and memory on the spatial pattern.
H. Shen, X. Fu, K.-H. Choi and H. Wang*, From aggregation to oscillations in a delayed nonlocal cell migration model, (preprint)
K.-H. Choi* and T. Hillen, The lingering phenomenon and pattern formation in a nonlocal population model with cognitive map, Eur. Jour. Appl. Math., Accepted (2026), (preprint)
TX. Wang+, K.-H. Choi+, and H. Wang*, Derivations of animal movement models with accumulated memory, J. Math. Biol. 92, 54 (2026) (DOI)
Chemotaxis model
Bacteria dispersal in a heterogeneous environment is different from random dispersal. In the framework of heterogeneous diffusion, we study chemotaxis models with density-suppressed motility and their spatial pattern.
K.-H. Choi, Y.-J. Kim, and M.-G. Lee*, Dweller-wanderer interaction for chemotaxis phenomena, SIAM J. Appl. Math. 85, 5, 2167-2189 (2025) (preprint) (DOI)
K.-H. Choi* and Y.-J. Kim, Chemotactic cell aggregation viewed as instability and phase separation, Nonlinear Anal.: Real World Appl. 80, 104147, (2024) (preprint) (DOI)
Brain Cancer: Glioblastomas
Glioblastomas are incurable primary brain tumors that depend on neural-like cellular processes, tumor microtubes (TM), to invade the brain.
A. Shyntar, K.-H. Choi, A. Swan, and T. Hillen*, The role of tumor microtubes for the growth of glioma: a mathematical modelling approach, submitted to Brain Res. Bull.
Cyanobacteria
I am also interested in various ecological phenomena such as cyanobacteria,
J. Serpico, K.-H. Choi, B. A. Zambrano-Luna, TX. Wang, and H. Wang*, Decoding the spatial spread of cyanobacterial blooms in an epilimnion, J. Math. Biol. 91, 44 (2025) (DOI)