Blow-up Prevention by Logistic Damping in a Chemotaxis-May-Nowak Model for Virus Infection

In this paper, we study the no-flux boundary initial-boundary problem for a three-component reaction-diffusion system originating from the classical May-Nowak model for viral infection {[ u_t=Δ u-χ∇· (u∇ v)+κ -u-uw-μ u^α,; v_t=Δ v-v+uw,; w_t=Δ w-w+v ]. in a smoothly bounded domain Ω⊂ℝ^n , n≥ 1 . It is shown that for any κ >0 , μ >0 and sufficiently regular nonnegative initial data (u_0,v_0,w_0) , the system possesses a unique nonnegative global bounded classical solution provided α >n+2/2. Moreover, we show the large time behavior of the solution with respect to the size of κ . More precisely, we prove that