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Full-Text Articles in Life Sciences
Generalized Theoretical Criteria For Annihilation Of Hiv-1 Virions During Haart, Frank Nani, Mingxian Jin
Generalized Theoretical Criteria For Annihilation Of Hiv-1 Virions During Haart, Frank Nani, Mingxian Jin
Math and Computer Science Faculty Working Papers
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 …
Theoretical Analysis And Simulation Of Acute And Chronic Phase Hiv-1 Dynamics, Frank Nani, Mingxian Jin
Theoretical Analysis And Simulation Of Acute And Chronic Phase Hiv-1 Dynamics, Frank Nani, Mingxian Jin
Math and Computer Science Faculty Working Papers
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 …
Numerical Algorithms For Solving A Generalized Cancer Chemotherapy Problem, Frank Nani, Mingxian Jin
Numerical Algorithms For Solving A Generalized Cancer Chemotherapy Problem, Frank Nani, Mingxian Jin
Math and Computer Science Faculty Working Papers
In this paper, two elaborate numerical algorithms are presented for solving the Nani- Oguztoreli functional differential equations associated with cell-cycle specific cancer chemotherapy. The generalized cell-cycle specific cancer chemotherapy model of Nani- Oguztoreli contains discrete time delays which represent the times that the cancer cells spend in each cell-cycle phase. The model also takes into account that inter-cell cycle phase transition rate constants, recruitment of resting cells from the GO phase, and effect of chemotherapy drug on cells in each phase. The algorithms utilize a modified version of the Method of Steps algorithms. The constructed numerical schemes can be implemented …