Bistability of an HIV Model with Immune Impairment

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1108-1132, June 2024.
Abstract.The immune response is a crucial factor in controlling HIV infection. However, oxidative stress poses a significant challenge to the HIV-specific immune response, compromising the body’s ability to control viral replication. In this paper, we develop an HIV infection model to investigate the impact of immune impairment on virus dynamics. We derive the basic reproduction number ([math]) and threshold ([math]). Utilizing the antioxidant parameter as a bifurcation parameter, we establish that the system exhibits saddle-node bifurcation backward and forward bifurcations. Specifically, when [math], the virus will rebound if the antioxidant parameter falls below the post-treatment control threshold. Conversely, when the antioxidant parameter exceeds the elite control threshold, the virus remains under elite control. The region between the two thresholds represents a bistable interval. These results can explain why some HIV-infected patients experience rapid viral rebound after treatment cessation while others achieve post-treatment control for a longer time.