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

Nani, Frank; Jin, Mingxian

doi:10.9734/bjmcs/2014/1815

Cited by 1 publication

(4 citation statements)

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“…In this HAART scenario, the plasma HIV-1 virions (x 3 ) completely overwhelmed the non-infected CD4 + T helper cells (x 1 ) and the HIV-1 specific CD8 + cytotoxic T cells (x 4 ). The HIV-1 infected CD4 + T cells (x 2 ) exhibit periodic dynamics and the prognosis for the hypothetical patient is unwholesome (see Nani and Jin [15,16]).…”

Section: Simulation Results For Hypothetical Aids Patient #4mentioning

confidence: 99%

“…The derivative of V along the solution curves of the model equations yields the result: C 2 3 33 2 3 23 1 3 13 3 2 23 2 2 22 1 2 12 3 1 13 2 1 (6.22) But it can be shown that (6.23) In particular, (cf. Nani and Jin [7,15,16]) (6.24) Similarly, (6.25) Using the specifications in (4.31), the matrix C has the form (6.26)…”

Section: Global Stability Ofmentioning

confidence: 99%

“…Mathematical models which incorporate the explicit computation of the cure rate of HIV-1 induced AIDS during HAART include models by [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…These processes lead to viral persistence after initial successful HAART [18]. Mathematical models which demonstrate persistence due to viral reservoirs have been constructed by Nani and Jin [15,16]. Other models which elegantly address the role of viral reservoirs in persistence include papers by Rong and Perelson in [19], Kim and Perelson in [20], and Sedaghat, Siliciano and Wilke in [21].…”

Section: Introductionmentioning

confidence: 99%

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

Nani

Jin

2015

BJMCS

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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 (x 1 ), HIV-1 infected CD4 + T cells (x 2 ), HIV-1 virions in the blood plasma (x 3 ), HIV-1 specific CD8 + T cells (x 4 ), and the concentration of HAART drug molecules (x 5 ). 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 263 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 virio...

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Section: Simulation Results For Hypothetical Aids Patient #4mentioning

confidence: 99%

Section: Global Stability Ofmentioning

confidence: 99%

“…Mathematical models which incorporate the explicit computation of the cure rate of HIV-1 induced AIDS during HAART include models by [15][16][17].…”

Section: Introductionmentioning

confidence: 99%