Efficient Resolution of Metastatic Tumour Growth Models by Reformulation into Integral Equations

The McKendrick/Von Foerster equation is a transport equation with a non-local boundary condition that appears frequently in structured population models. A variant of this equation with a size structure has been proposed as a metastatic growth model by Iwata et al. Here we will show how a family of metastatic models with 1D or 2D structuring variables, based on the Iwata model, can be reformulated into an integral equation counterpart, a Volterra equation of convolution type, for which a rich numerical and analytical theory exists. Furthermore, we will point out the potential of this reformulation by addressing questions coming up in the modelling of metastatic tumour growth. We will show how this approach permits to reduce the computational cost of the numerical resolution and to prove structural identifiability