Asymptotic behaviour in a doubly haptotactic cross-diffusion model for oncolytic virotherapy

This paper considers a model for oncolytic virotherapy given by the doubly haptotactic cross-diffusion system with positive parameters,. When posed under no-flux boundary conditions in a smoothly bounded domain, and along with initial conditions involving suitably regular data, the global existence of classical solution to this system was asserted in Tao and Winkler (2020, J. Differ. Equ. 268, 4973-4997). Based on the suitable quasi-Lyapunov functional, it is shown that when the virus replication rate <![CDATA[$\beta, the global classical solution is uniformly bounded and exponentially stabilizes to the constant equilibrium in the topology as.