Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4⁺ T-Cell Proliferation under Antiretroviral Therapy

Table 1

Parameters and values of model (4).

Parameter	Description	Value
𝑇	Uninfected CD4^+ T-cell population size	1000 mm^−3
𝐼	Infected CD4^+ T-cell density	0
𝑉𝐼	Free infectious virus particles	10^−3 mm^−3
𝑉NI	Noninfectious virus particles	10^−3 mm^−3
𝑇0	CD4^+ T-cell population for HIV-negative persons	1000 mm^−3
𝜇1	Natural death rate of CD4^+ T-cell	0.02 day^−1
𝜇2	Blanket death rate of infected CD4^+ T-cell	0.26 day^−1
𝜇3	Death rate of free virus	2.4 day^−1
𝑘	Rate of CD4^+ T-cell becoming infected with virus	2.4×10^−5 mm^3 day^−1
𝑘^′	Rate of infected cells becoming active	2×10^−5 mm^3 day^−1
𝑠	Source term for uninfected CD4^+ T-cell	10 day^−1 mm^−3
𝑁	Number of virions produced by infected CD4^+ T-cell	Varies
𝑟	The maximal proliferation rate (𝑟<𝜇1)	Varies
𝐶	The half saturation constant of the proliferation process	Varies
𝑛rt	The effectiveness of RTIs (𝑛rt = 0 means the therapy is totally ineffective, while 𝑛rt = 1 indicates the therapy is 100% effective and the cell-to-cell infection is completely stopped)	Varies
𝑛𝑝	The effectiveness of PIs (𝑛𝑝 = 1 meaning the therapy with PIs is 100% effective and no newly infectious virus particles will be produced [42])	Varies
𝑟𝑇𝑉𝐼𝐶+𝑉𝐼	The stimulation of T-cell to proliferate in the presence of virus [43]	Varies