Detecting and Resetting Tipping Points to Create More HIV Post-Treatment Controllers with Bifurcation and Sensitivity Analysis

The existence of HIV post-treatment controllers (PTCs) offers hope for an HIV functional cure, and understanding the critical mechanisms determining PTC represents a key step toward this goal. Here, we have studied these mechanisms by analyzing an established mathematical model for HIV viral dynamics. In mathematical models, critical mechanisms are represented by parameters that affect the tipping points to induce qualitatively different dynamics, and in cases with multiple stability, the initial conditions of the system also play a role in determining the fate of the solution. As such, for the tipping points in parameter space, we developed and implemented a sensitivity analysis of the threshold conditions of the associated bifurcations to identify the critical mechanisms for this model. Our results suggest that the infected cell death rate and the saturation parameter for cytotoxic T lymphocyte proliferation significantly affect post-treatment control. For the case with multiple stability, in state space of initial conditions, we first investigated the saddle-type equilibrium point to identify its stable manifold, which delimits trapping regions associated to the high and low viral set points. The identified stable manifold serves as a guide for the loads of immune cells and HIV virus at the time of therapy termination to achieve post-treatment control.