A modeling approach to the impact of HIV mutations on the immune system

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

a long-term model of HIV infection dynamics [8] 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.

Dynamical models of biomarkers and clinical progression for personalized medicine: the HIV context

Mechanistic models, based on ordinary differential equation systems, can exhibit very good predictive abilities that will be useful to build treatment monitoring strategies. In this review, we present the potential and the limitations of such models for guiding treatment (monitoring and optimizing) in HIV-infected patients. In the context of antiretroviral therapy, several biological processes should be considered in addition to the interaction between viruses and the host immune system: the mechanisms of action of the drugs, their pharmacokinetics and pharmacodynamics, as well as the viral and host characteristics. Another important aspect to take into account is clinical progression, although its implementation in such modelling approaches is not easy. Finally, the control theory and the use of intrinsic properties of mechanistic models make them very relevant for dynamic treatment adaptation. Their implementation would nevertheless require their evaluation through clinical trials.

Modelling and control of HIV dynamics

Various models of HIV infection and evolution have been considered in the literature. This paper considers a variant of the Wodarz and Nowak mathematical model, adding "aggressiveness" as a new state variable in order to quantify the strength of the virus and its response to drugs. Although the model proposed is relatively simple, simulation results suggest that it may be useful in predicting the impact of the effectiveness of therapy on HIV dynamics.