In this paper, the patho-physiological dynamics of Human Immuno-deficiency Virus type 1( HIV-1) induced AIDS during Highly Active Anti Retroviral Therapy (HAART) is modeled using a system of non-linear deterministic differential equations. The physiologically relevant and clinically plausible equations depict the dynamics of uninfected CD4+ T cells (x1), HIV-1 infected CD4+ T cells (x2), HIV-1 virions in the blood plasma (x3), HIV-1 specific CD8+ T cells (x4), and the concentration of HAART drug molecules (x5). Criteria for the existence of therapeutic outcomes are presented. In particular, the necessary and sufficient conditions for the annihilation of HIV-1 virions, and HIV-1 infected helper T cells are clearly exhibited in terms of biological measureable model physiological parameters. Investigative computer simulations are presented elucidating the patho-physiodynamics of HIV-1 induced AIDS and various hypothetical patient parametric configurations. The mathematical analysis of the model equations and the computer simulations are performed with regard to HAART protocols with constant continuous intravenous and transdermal drug infusions.
Nani, Frank and Jin, Mingxian, "Generalized Necessary and Sufficient Conditions for Annihilation of HIV-1 Virions During HAART" (2012). Math and Computer Science Working Papers. Paper 18.