  We consider the Neumann problem for a coupled chemotaxis-haptotaxis model of
cancer invasion with/without kinetic source in a 2D bounded and smooth domain.
For a large class of cell kinetic sources including zero source and
sub-logistic sources, we detect an explicit condition involving the chemotactic
strength, the asymptotic "damping" rate, and the initial mass of cells to
ensure uniform-in-time boundedness for the corresponding Neumann problem. Our
finding significantly improves existing 2D global existence and boundedness in
related chemotaxis-/haptotaxis systems.
