Theoretical Analysis and Simulation of Acute and Chronic Phase HIV-1 Dynamics

Abstract

Aims: The dynamics of HIV-1 induced AIDS is attributed to several biological variables, which characterize the stage, virulence and morbidity of the disease. The aim of this research is to use a necessary and sufficient subset of these immunological variables to construct a clinically plausible mathematical model of the patho-physiological dynamics of HIV-1 induced AIDS during the acute and chronic phases. This model incorporates the interactions between uninfected CD4+ T cells, HIV-1 infected CD4+ T cells, HIV-1 virions in the blood plasma, and specific cytotoxic CD8+ T cells. The major objective is to derive mathematical criteria depicting conditions under which the HIV-1 virions can be maintained definitely at the subclinical viral blood plasma level such that the HIV-1 seropositive person does not develop full-blown AIDS. Study Design: The model is based on contemporary published patho-physiological data on acute and clinical chronic phase HIV-1 induced AIDS. These data are meticulously condensed into a clinically plausible four-compartmental mathematical model that incorporates the dynamics and interactions between non-HIV-1 infected CD4+ T lymphocytes. HIV-1 infected lymphocytes, free HIV-1 virions in the blood plasma, and HIV-1 specific cytotoxic CD8+ T lymphocytes. The relevant stoichiometric interaction rate constants, apoptotic rate constants, rate constants for viral recruitment from latent reservoirs, and other relevant parameters are clearly exhibited in the mathematical model. The role of CD4+ T cell-induced syncytia is explicitly incorporated into the HIV-1 virion dynamical equation. Place and Duration of Study: This research was done at Fayetteville State University, North Carolina USA and is sponsored by the FSU Mini-Grant Award and the HBCU Graduate STEM Grant. The research was conducted during the Spring of 2012. Methodology: The deterministic nonlinear HIV-1 AIDS patho-physio-dynamical equations are analyzed using the techniques of dynamical system theory, principles of linearized stability, Hartman-Grobman theory and other relevant mathematical techniques. The clinically desirable equilibrium states are and their local existence and global stability are analyzed. Investigative computer simulations are performed illustrating some physiological outcomes. Results: Mathematical criteria are derived under which the clinically desired outcomes can occur. These criteria are presented in terms of theorems. Investigative computer simulations are presented which elucidate a number of physiological scenarios of primary HIV-1 infection, involving the annihilation and persistence of HIV-1 in the absence of AIDS Pharmacotherapy. Conclusion: This research has demonstrated the existence of plausible criteria under which an HIV-1 sero-positive person can be maintained at an asymptomatic chronic state indefinitely. Some of the criteria are configured in terms of clinically measurable and biological quantifiable parameters which have been verified by the computer simulations.