Presented by: 
Petrus van Heijster (QUT)
Mon 30 Mar, 2:00 pm - 2:45 pm
Hawken Building (50), room N202

We discuss the influence of Allee effects, or growth thresholds, on the existence of travelling wave solutions in a reaction-advection- diffusion-type model describing the invasion of malignant tumour cells. Using geometric singular perturbation theory and canard theory, the existence of travelling wave solutions with semi-compact support is shown. Moreover, the relationship between the speed of the travelling wave solution and the background state of the extracellular matrix is biphasic. In earlier work, the spread of cancer cells was modelled by logistic growth and this biphasic relationship, which is observed experimentally, was not present. Also, the logistic model supports unrealistic stable travelling wave solutions. Concluding that the Allee model is superior to the logistic model in qualitatively capturing biological realism. This is joint work with: Lotte Sewalt, Kristen Harley and Sanjeeva Balasuriya