A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. (September 2020) - Tao, Youshan; Winkler, Michael
Abstract: In a two-dimensional smoothly bounded domain, we consider the oncolytic virotherapy model given by u t = Δ u − ∇ ⋅ ( u ∇ v ) − ρ u z, v t = − ( u + w ) v, w t = D w Δ w − w + u z, z t = D z Δ z − z − u z + β w, with parameters D w > 0, D z > 0, β > 0 and ρ ≥ 0 . According to previous findings, a corresponding Neumann initial–boundary value problem possesses a globally defined classical solution whenever the prescribed initial data are suitably regular and satisfy appropriate positivity assumptions. In the present study it is shown that if β < 1, then any such solution is uniformly bounded. This complements a recent result which in the case ρ = 0 has asserted the existence of unbounded solutions whenever β > 1 .