Aims: This paper is an elaborate and quantitative attempt to construct medically applicable mathematical models and derive criteria for efficacious Highly Active Anti-Retroviral Therapy (HAART) protocol for an AIDS patient. The patho-physiological dynamics of Human Immuno-deficiency Virus type 1 (HIV-1) induced AIDS during HAART is modeled by 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). The major objective of this research is to construct an elaborate mathematical model that depicts patho-physiodynamics of HIV-1 virions during HAART. The derived therapeutic criteria are expressed in terms of clinically measurable physiological parameters. Investigative computer simulations which describe certain aspects of HIV-1 dynamics during HAART are also presented in the paper.
Study Design: The mathematical model is constructed based on contemporary research data condensed from the clinical literature on HAART of AIDS. A system of coupled non-linear deterministic differential equations are used to characterize the patho-physiodynamics of HAART during the post chronic phase. 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. A syncytium term with stoichiometric coefficient is introduced into the model to account for the formation of large multinucleated gp120 bearing CD4+ T cells that are observed in some AIDS patients. By assigning a zero value to the stoichiometric coefficient, the role of syncytium is abrogated.
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 dynamics of HIV-1 AIDS equations are analyzed using the techniques of dynamical system theory, principles of linearized stability, non-linear system theory, and other relevant mathematical techniques. The clinically desirable equilibrium states, their local existence, and global stability are analyzed. Investigative computer simulations are performed illustrating some physiological outcomes.
Results: The therapeutic outcomes are presented in the form of theoretical criteria which are obtained from mathematical analysis of the model equations. In particular, the critical parameters which govern the dynamics of HIV-1 virions during HAART are clearly identified. Some clinical implications of HAART are elucidated in the computer simulations using hypothetical physiological parametric configurations.
Conclusion: This research has demonstrated the existence of plausible criteria under which HIV-1 virions can be annihilated using HAART. The latent HIV-1 virion reservoirs are implicated in unsuccessful scenarios of HAART. It has also been demonstrated that the rate constants associated with activation of lymphocytes by cytokine interleukin-2 (IL-2) play a significant role in determining the efficacious outcomes of HAART.
Nani, Frank and Jin, Mingxian, "Generalized Theoretical Criteria for Annihilation of HIV-1 Virions during HAART" (2014). Math and Computer Science Working Papers. Paper 23.