Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy - Tao, Youshan; Winkler, Michael (Journal of Differential Equations, 2020)
This work studies a haptotaxis system proposed as a model for oncolytic virotherapy, accounting for interaction between uninfected cancer cells, infected cancer cells, extracellular matrix (ECM) and oncolytic virus. In addition to random movement, both uninfected and infected tumor cells migrate haptotactically toward higher ECM densities; moreover, besides degrading the non-diffusible ECM upon contact the two cancer cell populations are subject to an infection-induced transition mechanism driven by virus particles which are released by infected cancer cells, and which assault the uninfected part of the tumor. The main results assert global classical solvability in an associated initial-boundary value problem posed in one- or two-dimensional domains with any given suitably regular initial data. This is achieved by discovering a quasi-Lyapunov functional structure that allows to appropriately cope with the presence of nonlinear zero-order interaction terms which apparently form the most significant additional mathematical challenge of the considered system in comparison to previously studied haptotaxis models.