Dynamics of a diffusive delayed viral infection model in a heterogeneous environment
Salih Djilali, Soufiane Bentout, Anwar Zeb
Abstract
This paper investigates the asymptotic analysis of spatially heterogeneous viral transmission, incorporating cell‐to‐cell transmission, virus nonlocal dispersal, and intracellular delay. Due to the noncompactness of the semiflow, we used the Kuratowski measure of noncompactness to demonstrate the existence of a global compact attractor. This noncompactness issue generates difficulties in calculating the basic reproduction number , which is the principal eigenvalue of the next‐generation operator. The threshold role of this number is determined, where we derived two different cases: (i) the global stability of the virus‐free steady state, which is globally stable for by the Lyapunov direct method, and (ii) the global stability of the virus steady state for . Indeed, the second case is demonstrated through several steps that include uniform persistence, the existence of a virus steady state, and the global stability of the virus steady state. The results are supported by different graphical representations with proper biological justifications.