Uncertainty quantification for the random HIV dynamical model driven by drug adherence

Area of Science:

• Mathematical Biology
• Pharmacokinetics
• Immunology

Background:

• High variability in CD4+ T cell counts and viral loads in HIV patients complicates treatment efficacy assessment.
• Poor drug adherence is a potential driver of this variability and treatment uncertainty.

Purpose of the Study:

• To develop a dynamical HIV model incorporating pharmacokinetics and drug adherence as a random variable.
• To quantify the relationship between drug adherence and therapeutic outcomes in HIV treatment.
• To enhance the design of individualized antiretroviral therapy strategies.

Main Methods:

• Developed a dynamical HIV model coupled with pharmacokinetic principles.
• Employed adaptive generalized polynomial chaos for stochastic solution approximation.
• Validated model accuracy using Monte Carlo sampling and clinical patient data.

Main Results:

• The model accurately depicts HIV dynamics, fitting clinical data from four patients.
• Sensitivity analyses (Sobol index) reveal drug effect randomness significantly impacts CD4+ T cells and viral loads.
• Time-dependent probability density functions were calculated theoretically and numerically.

Conclusions:

• Drug adherence significantly influences HIV treatment efficacy, impacting CD4+ T cells and viral loads.
• The developed model provides a framework for interpreting clinical data fluctuations.
• This research contributes to designing optimal, individual-based antiretroviral strategies.