#### Document Type

Article

#### Abstract

- Aims: To construct a clinically plausible mathematical model of the patho-physiological dynamics of HIV-1 induced AIDS during the acute and chronic phases which 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. In particular, the model describes quantitatively the time evolution of AIDS in the patient during the acute phase and the asymptomatic chronic clinical latency phase and elucidates the effect of latent HIV-1 reservoirs on the prognosis of AIDS. The major objective is to derive mathematical criteria depicting the necessary and sufficient conditions under which the HIV-1 virions can be maintained definitely at the subclinical viral blood plasma level such that the HIV-1 seriopositive 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.
- 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 done 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. 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: Mathematical modeling can be a useful technique in the derivation of prognostic criteria and quantitative analysis of AIDS during the acute and chronic phases.

#### Recommended Citation

Nani, Frank and Jin, Mingxian, "Mathematical Modeling and Simulation of 1 Acute and Chronic Phase HIV-1 Dynamics" (2012). *Math and Computer Science Working Papers.* Paper 17.

http://digitalcommons.uncfsu.edu/macsc_wp/17

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