Global boundedness and finite time blow-up of solutions for a quasilinear chemotaxis-May–Nowak model

In this paper, we introduce the nonlinear diffusion term [Formula: see text] into the chemotaxis-May–Nowak model to investigate the effects of [Formula: see text] and chemotaxis on the global existence, boundedness, and finite time blow-up of solutions. Here, [Formula: see text] generalizes the prototype [Formula: see text] with [Formula: see text]. For the parabolic-elliptic-parabolic case, if [Formula: see text] when [Formula: see text] and [Formula: see text] when [Formula: see text], then all solutions exist globally and remain bounded, whereas if [Formula: see text] and [Formula: see text], finite time blow-up occurs when [Formula: see text] is a ball and the initial data are radially symmetric. For the fully parabolic case, if [Formula: see text], then all solutions exist globally and remain bounded.