2021/11/16 by Yifu Wang, Chi Xu, Wang, Yifu +1
Mathematics · Biochemistry, Genetics and Molecular Biology · Medicine · #Mathematical Biology Tumor Growth #Evolution and Genetic Dynamics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2111.08378
This paper considers a model for oncolytic virotherapy given by the doubly haptotactic cross-diffusion system \ut=DuΔu-ξu∇⋅(u∇ v)+μu u(1-u)-ρuz, vt=- (αu u+αw w)v,
wt=DwΔw-ξw∇⋅(w∇ v)- w+ρuz,
zt=DzΔz-δz z- ρuz+βw,. with positive parameters Du,Dw,Dz,ξu,ξw,δz,ρ, αu,αw,μu,β. When posed under no-flux boundary conditions in a smoothly bounded domain Ω⊂ ℝ2, 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→ ∞.