Non-local multiscale approach for the impact of go or grow hypothesis on tumour-viruses interactions.

We propose and study computationally a novel non-local multiscale moving boundary mathematical model for tumour and oncolytic virus (OV) interactions when we consider the hypothesis for cancer dynamics. This spatio-temporal model focuses on two cancer cell phenotypes that can be infected with the OV or remain uninfected, and which can either move in response to the extracellular-matrix (ECM) density or proliferate. The interactions between cancer cells, those among cancer cells and ECM, and those among cells and OV occur at the macroscale. At the micro-scale, we focus on the interactions between cells and matrix degrading enzymes (MDEs) that impact the movement of tumour boundary. With the help of this multiscale model we explore the impact on tumour invasion patterns of two different assumptions that we consider in regard to cell-cell and cell-matrix interactions. In particular we investigate model dynamics when we assume that cancer cell fluxes are the result of local advection in response to the density of extracellular matrix (ECM), or of non-local advection in response to cell-ECM adhesion. We also investigate the role of the transition rates between mainly-moving and mainly-growing cancer cell sub-populations, as well as the role of virus infection rate and virus replication rate on the overall tumour dynamics.