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Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection.

Arafa A, Rida S, Khalil M - Nonlinear Biomed Phys (2012)

Bottom Line: In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells.We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model.Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of mathematics, Faculty of Science, South Valley University, Qena, Egypt. anaszi2@yahoo.com.

ABSTRACT
In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

No MeSH data available.


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The concentration of the infected CD4+ T cells at N = 1600 in the 1st case. Gray solid line (α = 1), Dotted line (α = 0.99), Black solid line (α = 0.95).
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Figure 7: The concentration of the infected CD4+ T cells at N = 1600 in the 1st case. Gray solid line (α = 1), Dotted line (α = 0.99), Black solid line (α = 0.95).

Mentions: We will solve the system (5) by using (GEM). Consider that α1 = α2 = α3 = α. We used the following data set: s = 10, b = 0.2, k = 0.000024, d = 0.01, δ = 0.16, c = 3.4, N varies. For this set of data R0 = 3.13 when N = 1000 (Figures 1, 2, 3, 4, 5, 6) and R0 = 5.01 when N = 1600 (Figures 7, 8, 9, 10, 11, 12). The initial conditions in the first case study are T(0) = 1000, I(0) = 0, V(0) = 0.001 while in the second case are T(0) = 1000, I(0) = 10, V(0) = 10. In the two cases the system goes to infected steady state.


Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection.

Arafa A, Rida S, Khalil M - Nonlinear Biomed Phys (2012)

The concentration of the infected CD4+ T cells at N = 1600 in the 1st case. Gray solid line (α = 1), Dotted line (α = 0.99), Black solid line (α = 0.95).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3275462&req=5

Figure 7: The concentration of the infected CD4+ T cells at N = 1600 in the 1st case. Gray solid line (α = 1), Dotted line (α = 0.99), Black solid line (α = 0.95).
Mentions: We will solve the system (5) by using (GEM). Consider that α1 = α2 = α3 = α. We used the following data set: s = 10, b = 0.2, k = 0.000024, d = 0.01, δ = 0.16, c = 3.4, N varies. For this set of data R0 = 3.13 when N = 1000 (Figures 1, 2, 3, 4, 5, 6) and R0 = 5.01 when N = 1600 (Figures 7, 8, 9, 10, 11, 12). The initial conditions in the first case study are T(0) = 1000, I(0) = 0, V(0) = 0.001 while in the second case are T(0) = 1000, I(0) = 10, V(0) = 10. In the two cases the system goes to infected steady state.

Bottom Line: In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells.We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model.Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of mathematics, Faculty of Science, South Valley University, Qena, Egypt. anaszi2@yahoo.com.

ABSTRACT
In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

No MeSH data available.


Related in: MedlinePlus