Efficient resolution of metastatic tumor growth models by reformulation into integral equations

The McKendrick/Von Foerster equation is a transport equation with a non-local boundary condition that appearsfrequently in structured population models. A variant of this equation with a size structure has beenproposed 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 bereformulated into an integral equation counterpart, a Volterra equation of convolution type, for which a rich numerical andanalytical theory exists. Furthermore, we will point out the potential of this reformulation by addressing questions coming up inthe modelling of metastatic tumour growth. We will show how this approach permits to reduce the computational costof the numerical resolution and to prove structural identifiability.