A Method of Directly Defining the inverse Mapping for a HIV infection of CD4+ T-cells model

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Minimum of the squared residual error E(h,A) for three different sets of μI and N for fixed parametric values T0 = 1000, I0 = 0, V0 = 0_001, r = 0_03, μT = 0_02, μb = 0_24, μV = 2_4, k1 = 2_4 × 10−5, k1'=2×10−5 k_1^{'} = 2 \times 10^{-5} , s = 10, Tmax = 1500_

μI	N	h	A	E[h,A]
0.26	500	−0.4295	0.4869	4.068 × 10−10
0.26	600	−0.4187	0.4731	5.682 × 10−10
0.1	500	−0.4311	0.4852	4.235 × 10−10

Numerical comparison for I(t)

t	MDDiM	OHAM	Runge-Kutta
0.0	0	0	0
0.2	3.1568 × 10−6	1.7626 × 10−7	3.1318 × 10−6
0.4	5.1445 × 10−6	2.9451 × 10−7	5.1352 × 10−6
0.6	6.5569 × 10−6	3.7344 × 10−7	6.5894 × 10−6
0.8	7.7445 × 10−6	4.2602 × 10−7	7.8026 × 10−6
1.0	8.8153 × 10−6	4.6108 × 10−7	8.9418 × 10−6

Numerical comparison for V (t)

t	MDDiM	OHAM	Runge-Kutta
0.0	0.01	0.01	0.01
0.2	6.4618 × 10−4	6.1744 × 10−4	5.5042 × 10−4
0.4	4.7805 × 10−4	3.8431 × 10−4	4.8189 × 10−4
0.6	4.0834 × 10−4	2.4258 × 10−4	4.0993 × 10−4
0.8	3.8591 × 10−4	1.5659 × 10−4	3.9044 × 10−4
1.0	3.9576 × 10−4	1.0406 × 10−4	4.0056 × 10−4

Variables and parameters for viral spread

Parameters and Variables	Meaning
DependentVariables
T	Uninfected CD+ T-cell population size
I	Infected CD+ T-cell density
V	Initial density of HIV RNA
Parameters and Constants
μT	Natural death rate of CD+ T-cell
μI	Blanket death rate of infected CD+ T-cel
μb	Lytic death rate for infected cells
μv	Death rate of free virus
k1	Rate CD+ T-cel become infected with virus
k1′ k_1'	Rate infected cells becomes active
r	Growth rate of CD+ T-cell population
N	Number of virions produced by infected CD+ T-cel
Tmax	Maximal population level of CD+ T-cel
s	Source term for uninfected CD+ T-cel
Derived quantities
T0	CD+ T-cel population for HIV-negative persons