Review of Statistical Methods for Within-Host HIV Dynamics in AIDS Studies
Highly active antiretroviral therapies (HAARTs) are currently the most effective treatment regime for HIV patients regarding suppressing HIV viral load. HIV dynamic study, in which ordinary differential equations (ODEs) play a vital quantitative role, facilitates understanding of HIV infection pathogenesis. ODEs have been widely adopted in modeling dynamic systems. By considering the dynamic changes and interactions among multiple biological components, ODE models can capture the essential behavior of dynamic immune systems such as nonlinearity and delay. HAART utilizes at least three different ARV drugs, including nucleoside or nucleotide reverse transcriptase inhibitor, non-nucleoside reverse transcriptase inhibitor, and a protease inhibitor (PI). Although HAART has been extremely effective in suppressing the plasma viral load below the detection limit in most HIV-1-infected patients, the therapy often fails to eradicate virus primarily due to the emergence of drug-resistant mutants. Theoretical identifiability and practical identifiability can be examined by structure identifiability analysis and Monte Carlo simulations.