Mathematical Analysis and Dynamic Active Subspaces for a Long term model of HIV

TL;DR

This paper analyzes a complex HIV long-term model using stability analysis and active subspace methods, creating reduced order models for efficient long-term predictions of T-cell counts.

Contribution

It introduces dynamic active subspaces and reduced order models to efficiently analyze and simulate a detailed HIV infection model.

Findings

Identified all infection-free steady states and analyzed stability.

Performed global sensitivity analysis of T-cell count to parameters.

Developed reduced order models enabling inexpensive long-term simulations.

Abstract

Recently, a long-term model of HIV infection dynamics was developed to describe the entire time course of the disease. It consists of a large system of ODEs with many parameters, and is expensive to simulate. In the current paper, this model is analyzed by determining all infection-free steady states and studying the local stability properties of the unique biologically-relevant equilibrium. Active subspace methods are then used to perform a global sensitivity analysis and study the dependence of an infected individual's T-cell count on the parameter space. Building on these results, a global-in-time approximation of the T-cell count is created by constructing dynamic active subspaces and reduced order models are generated, thereby allowing for inexpensive computation.