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

Table 5

We take 𝐶=10,  𝑛_rt=0.5,  𝑛_𝑝=0.25,  𝑟=0.01,  𝐸₀=(500,0,0), and 𝑎=(√𝑟−𝑘(1−𝑛_rt)𝐶)²/𝜇₁, and we get the following.

(a)  

Line	𝑁	𝑘(1−𝑛rt)𝐶	1−𝑎	𝑅0	𝐸^∗1	𝐸^∗2
26	10	0.00001	0.5340	0.3354	Not exist	Not exist
27	30	0.00001	0.5340	0.5809	Not exist	Not exist
28	40	0.00001	0.5340	0.6708	Not exist	Not exist
29	47	0.00001	0.5340	0.7271	Not exist	Not exist
30	48	0.00001	0.5340	0.7348	(925.9259, 0.6491, 15.1879)	(925.9259, 2.1572, 50.4788)
31	60	0.00001	0.5340	0.8216	(740.7407, 0.0641, 1.8756)	(740.7407, 9.8732, 288.7910)
32	88	0.00001	0.5340	0.9950	(505.0505, 0.0005, 0.0204)	(505.0505, 19.0127, 815.6462)
33	89	0.00001	0.5340	1.0006	(499.3758, 19.2318, 834.4192)	Not exist
34	100	0.00001	0.5340	1.0607	(444.4444, 21.3511, 1040.8668)	Not exist
35	200	0.00001	0.5340	1.5000	(222.2222, 29.9116, 2916.3810)	Not exist
36	600	0.00001	0.5340	2.5981	(74.0741, 35.6123, 10416.5867)	Not exist
37	1000	0.00001	0.5340	3.3541	(44.4444, 36.7520, 17916.6202)	Not exist
38	10000	0.00001	0.5340	10.6066	(4.4444, 38.2906, 186666.6622)	Not exist
39	20000	0.00001	0.5340	15.0000	(2.2222, 38.3761, 374166.6644)	Not exist

(b)  

Line	𝐷(𝜆)	𝐴+𝐵	𝐶+𝐷	𝐸+𝐹	(𝐴+𝐵)(𝐶+𝐷)	Stability
30	0.1109, 0.0417	2.6742, 2.6723	0.0328, 0.0278	−0.0014, −0.0005	0.0878, 0.0743	Unsuited, unsuited
31	0.0747, −0.1399	2.6784, 2.6738	0.0443, 0.0319	−0.0008, 0.0020	0.1185, 0.0853	Unsuited (i)
32	0.0173, −0.4352	2.6800, 2.6799	0.0483, 0.0482	−0.00001, 0.0060	0.1296, 0.1291	Unsuited (i)
33	−0.4454	2.6801	0.0487	0.0062	0.1307	(ii)
34	−0.5570	2.6826	0.0553	0.0077	0.1483	(ii)
35	−1.5273	2.7050	0.1150	0.0218	0.3110	(ii)
36	−4.7830	2.7950	0.3543	0.0780	0.9903	(ii)
37	−7.1387	2.8850	0.5937	0.1342	1.7129	(ii)
38	30.8901	4.9100	5.9802	1.3978	29.3628	(i)
39	482.3545	7.1600	11.9652	11.9652	85.6708	(i)