Global existence for a go-or-grow multiscale model for tumor invasion with therapy

Abstract

We investigate a PDE–ODE system describing cancer cell invasion in a tissue network. The model is an extension of the multiscale setting in [G. Meral, C. Stinner and C. Surulescu, On a multiscale model involving cell contractivity and its effects on tumor invasion, Discrete Contin. Dynam. Syst. Ser. B 20 (2015) 189–213] and [C. Stinner, C. Surulescu and M. Winkler, Global weak solutions in a PDE–ODE system modeling multiscale cancer cell invasion, SIAM J. Math. Anal. 46 (2014) 1969–2007], by considering two subpopulations of tumor cells interacting mutually and with the surrounding tissue. According to the go-or-grow hypothesis, these subpopulations consist of moving and proliferating cells, respectively. The mathematical setting also accommodates the effects of some therapy approaches. We prove the global existence of weak solutions to this model and perform numerical simulations to illustrate its behavior for different therapy strategies.