Skip to content
Research Article Open access CC BY 4.0

Generalized Theoretical Criteria for Annihilation of HIV-1 Virions during HAART

Frank Nani, Mingxian Jin

Journal of Advances in Mathematics and Computer Science · pp. 262–299 · Published 30 Oct 2014

10.9734/BJMCS/2015/11394

Abstract

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.

HIV-1 patho-physiodynamics mathematical modeling HAART therapy AIDS cure criteria Michaelis-Menten kinetics

References (23)

  1. 1 The Theory of Matrices
  2. 2 Decay characteristics of HIV-1-infected compartments during combination therapy [DOI]
  3. 3 Anti-viral Drug Treatment: Dynamics of Resistance in Free Virus and Infected Cell Populations [DOI]
  4. 4 Specific therapy regimes could lead to long-term immunological control of HIV [DOI]
  5. 5 Modeling Latently Infected Cell Activation: Viral and Latent Reservoir Persistence, and Viral Blips in HIV-infected Patients on Potent Therapy [DOI]
  6. 6 New Concepts in the Immunopathogenesis of HIV Infection [DOI]
  7. 7 HIV-1 specific CD8+ T cells with an effector phenotype and control of viral replication [DOI]
  8. 8 Viral and Latent Reservoir Persistence in HIV-1–Infected Patients on Therapy [DOI]
  9. 9 Reservoirs of Human Immunodeficiency Virus Type 1: The Main Obstacles to Viral Eradication [DOI]
  10. 10 Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method [DOI]
  11. 11 Dynamics of HIV Infection Model with Therapy and Cure Rate
  12. 12 Sustained and Targeted Delivery of an Anti-HIV Agent Using Elastic Liposomal Formulation: Mechanism of Action [DOI]
  13. 13 Low-level HIV-1 replication and the dynamics of the resting CD4+T cell reservoir for HIV-1 in the setting of HAART [DOI]
  14. 14 Mutation and control of the human immunodeficiency virus [DOI]
  15. 15 Some state space models of HIV pathogenesis under treatment by anti-viral drugs in HIV-infected individuals [DOI]
  16. 16 Predicting differential responses to structured treatment interruptions during HAART [DOI]
  17. 17 An Antigenic Threshold for Maintaining Human Immunodeficiency Virus Type 1-specific Cytotoxic T Lymphocytes [DOI]
  18. 18 Short and long period optimization of drug doses in the treatment of AIDS [DOI]
  19. 19 T cell syncytia induced by HIV release T cell chemoattractants: demonstration with a newly developed single cell chemotaxis chamber [DOI]
  20. 20 Reconstitution of thymic function in HIV-1 patients treated with highly active antiretroviral therapy [DOI]
  21. 21 The Effects of Protease Inhibitors on the Spread of HIV and the Development of Drug-Resistant HIV Strains: A Simulation Study [DOI]
  22. 22 Antiretroviral therapy in previously untreated adults infected with the human immunodeficiency virus type I: established and potential determinants of virological outcome.
  23. 23 Theoretical Analysis and Simulation of Acute and Chronic Phase HIV-1 Dynamics [DOI]

Cited by 2

Analysis of Dynamics of HIV-1 Associated Kaposi Sarcoma during HAART and ACI

Frank Nani, Mingxian Jin · Journal of Advances in Mathematics and Computer Science · 2016

Showing 1 of 2 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

2

Page views

0

PDF downloads

0

Outbound clicks

2

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.