Ryan Thiessen: Mathematical Analysis of Go-or-Grow Type Systems in Cancer Modelling

Please note this event occurred in the past.
October 28, 2025 4:00 pm - 5:00 pm ET
Seminars,
Applied Mathematics and Computation Seminar
LGRT 1681
Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not simultaneously. The reaction-diffusion ODE formulation of these models has a wide range of applications in biology and medicine, chiefly among those used to model the spread of brain cancer. The analysis of go-or-grow models has inspired new mathematics, particularly in connection to the Fisher-Kolmogorov-Petrovsky-Piskounov (FKPP) equation and the areas of travelling waves and steady-state solutions.  


In this talk, we focus on two special types of solutions of the go-or-grow models: travelling wave solutions and steady-state solutions in bounded domains with hostile boundaries. For travelling waves, we provide an existence and non-existence result for a general class of cooperative go-or-grow models and a particular non-cooperative glioma model. For the cooperative go-or-grow models, we show formal convergence of travelling wave solutions of the go-or-grow models to travelling wave solutions of an FKPP-type equation with nonlinear diffusion.

For steady-state solutions in bounded domains, we extend the constant rate critical domain results by Hadeler-Lewis's by changing from constant diffusion to a uniformly elliptic operator and constant transition rates to nonlinear functions of the two populations. The degenerate nature of the equation of the sedentary compartment requires us to use Young-measure valued weak solutions, which we call alright solutions. We show, under certain conditions, that the domain size determines whether a nontrivial, alright steady-state solution exists or not.