Asymptotic behavior of a doubly haptotactic cross-diffusion model for oncolytic virotherapy

Abstract

This paper considers a model for oncolytic virotherapy given by the doubly haptotactic cross-diffusion systemwith positive parameters D u , D w , D z , ξ u , ξ w , δ z , ρ, α u , α w , µ u , β. When posed under noflux boundary conditions in a smoothly bounded domain Ω ⊂ R 2 , 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). Based on the suitable quasi-Lyapunov functional, it is shown that when the virus replication rate β < 1, the global classical solution (u, v, w, z) is uniformly bounded and exponentially stabilizes to the constant equilibrium (1, 0, 0, 0) in the topology (L ∞ (Ω)) 4 as t → ∞.

Dampening effects on global boundedness in a quartic haptotactic model with fusogenic oncolytic virus and syncytia

“…For the boundedness, our result shows that logistic source is not the weakest damping effect in two-dimensional domain which extends Theorem 1.1 in [30], Theorem 1.1 in [15] and Theorem 1.1 in [31]. But we also need to note that not all sub-logistic sources are included in Theorem 1.1.…”

“…When n ≤ 3, Tao obtained the global weak solution with ξ z = 0 in convex domain [24]. For more results, we can refer to [19,[31][32][33] and references therein. However, in experiments and in clinical trials it has been observed that some types of oncolytic viruses lead to better anti-tumor results than others [11,13,17].…”