University of Alberta

Hyperbolic transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria or animals. The most known example is the Goldstein-Kac model (1974) and its connection to the telegraph equation. To the...

Humans have been discussing the benefits and drawbacks of democratic vs. authoritarian governance for millennia, with perhaps the earliest and most famous discussion favoring enlightened authoritarian rule contained in Plato's 'Republic'. The...

In this talk, I will introduce two SIS reaction-diffusion epidemic models with cognition, and the cognitive diffusion either takes a Fokker-Planck type diffusion obtained by Chapman's diffusion law (called random diffusion) or follows Fick's...

In this talk, I will introduce an SIS patch endemic model with cognitive dispersal. When $\mathcal{R}_0>1$, I give a sufficient condition for the uniqueness of endemic equilibrium. At the unique endemic equilibrium, I prove that the disease...

Malignant gliomas are highly invasive brain tumors. Recent attention has focused on their capacity for network-driven invasion, whereby mitotic events can be followed by the migration of nuclei along long thin cellular protrusions, termed tumour...

The data association problem is the difficult part of the multi-object tracking problem. The problem is to: (i) classify measurements (e.g., position, shape, etc) as true positives or false positives, ( ii) classify tracked objects as observed (i.e...

The Game of Cycles, introduced in my book Mathematics for Human Flourishing, is played on a connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a...

The nonlinear incidence mechanism is a more general disease transmission mechanism to fit the data in clinical observations or laboratory experiments. In a heterogeneous environment, how to describe the cognitive dispersal of individuals is also an...

Habitat loss is a key component driving decreases in biodiversity and the extinction of species worldwide. Of particular concern is human-driven habitat loss, primarily through agriculture, resource extraction, and urbanization. In this talk, I will...

Transient dynamics are referred to as those dynamics that happen on ecologically relevant timescales, in which classical modelling techniques often fail to capture. Due to the ever-changing environments and ecosystems, increased interest has been...