Effects of Diffusion and Delays on the Dynamics of an HIV Infection Model

This paper investigates the effects of diffusion and two time delays on the dynamics of an HIV infection model in one-dimensional domain. The Galerkin method is employed to derived theoretical equations. A condition is established for identifying exact Hopf bifurcation points, followed by an in-depth discussion on stability analysis maps. Bifurcation maps are constructed to illustrate the system dynamics under three distinct delay scenarios, highlighting the stable and unstable areas. When the delay parameter τi>0, there are two distinct stability areas, whereas in the absence of delay, only one stable region exists. The findings indicate that the time delays and the diffusion rate significantly influence the stability regions of the system. Bifurcation maps are presented to illustrate selected examples of 3D periodic oscillations to validate all theoretical outputs shown in this paper.