Viral Infection Model With Advection–Diffusion, Immune Responses, and Distributed Delays

ABSTRACT A virus dynamics model is studied. In the formulation of the model, we take into account reaction–advection–diffusion, logistic growth terms, and a general nonlinear infection rate functional response. Three distributed delays include the case of state‐selective delay and are motivated by natural time delay in infection of susceptible host cells and immune responses (production of antibodies and CTL immune cells). We propose to consider the model on two spatial domains. The existence of a finite‐dimensional global attractor and a persistence property are discussed. The persistence result differs essentially from that of the model on one spatial domain. The last has a clear biological background.