Mathematical analysis and dynamic active subspaces for a long term model of HIV

Area of Science:

• Mathematical Biology
• Computational Biology
• Immunology

Background:

• A detailed model of HIV infection dynamics, involving numerous ordinary differential equations (ODEs), is computationally expensive to simulate.
• Understanding the long-term progression of HIV and its impact on T-cell counts is crucial for effective treatment strategies.

Purpose of the Study:

• To analyze a complex, long-term HIV infection model by identifying infection-free states and evaluating the stability of the disease equilibrium.
• To perform global sensitivity analysis on the model to understand how T-cell counts depend on various parameters.
• To develop computationally inexpensive methods for approximating T-cell count dynamics over time.

Main Methods:

• Analysis of steady states and local stability of the unique biologically-relevant equilibrium.
• Application of active subspace methods for global sensitivity analysis of T-cell count with respect to model parameters.
• Construction of dynamic active subspaces and reduced-order models for global-in-time approximation.

Main Results:

• Identification of all infection-free steady states and characterization of the unique biologically-relevant equilibrium's stability.
• Sensitivity analysis revealed key parameters influencing T-cell count dynamics.
• Development of reduced-order models enabling efficient computation of T-cell count approximations.

Conclusions:

• The developed methods significantly reduce the computational cost associated with simulating the long-term HIV infection model.
• This work provides a framework for efficient analysis and prediction of T-cell count trajectories in HIV infection.
• The findings facilitate a deeper understanding of HIV dynamics and parameter influence on disease progression.