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

Table 2

We take 𝑟=0.01,  𝐶=1,  𝑁=100,  𝐸₀=(500,0,0), and 𝑎=(√𝑟−𝑘(1−𝑛_rt)𝐶)²/𝜇₁, and we get the following.

(a)  

Line	𝑛rt	𝑛𝑝	𝑘(1−𝑛rt)𝐶	1−𝑎	𝑅0	𝐸^∗1	𝐸^∗2
1	0.1	0.05	0.00002	0.5454	1.6016	(194.9317, 30.9602, 1911.7950)	not exist
2	0.5	0.25	0.00001	0.5340	1.0607	(444.4444, 21.3511, 1040.8668)	not exist
3	0.5425	0.27125	0.00001	0.5326	1.0001	(499.8953, 19.2137, 910.1286)	not exist
4	0.5426	0.2713	0.00001	0.5326	1.0000	(500.0390, 0.000003, 0.0002)	(500.0389, 19.2082, 909.8039)
5	0.55	0.275	0.00001	0.5323	0.9893	(510.8556, 0.0009, 0.0444)	(510.8557, 18.7911, 885.5296)
6	0.6	0.3	0.000009	0.5305	0.9165	(595.2381, 0.0104, 0.4716)	(595.2381, 15.5354, 706.8618)
7	0.7	0.35	0.000007	0.5265	0.7649	(854.7009, 0.1186, 5.0099)	(854.7009, 5.4462, 230.1012)
8	0.7252	0.3626	0.000007	0.5254	0.7249	(951.5244, 0.8287, 34.3354)	(951.5245, 1.0116, 41.9104)
9	0.7253	0.3627	0.000007	0.5253	0.7247	Not exist	Not exist
10	0.8	0.4	0.000005	0.5217	0.6000	Not exist	Not exist
11	0.82	0.41	0.000005	0.5206	0.5644	Not exist	Not exist
12	0.8446	0.4223	0.000004	0.5191	0.5190	Not exist	Not exist
13	0.85	0.425	0.000004	0.5188	0.5087	Not exist	Not exist

(b)  

Line	𝐷(𝜆)	𝐴+𝐵	𝐶+𝐷	𝐸+𝐹	(𝐴+𝐵)(𝐶+𝐷)	Stability
1	−1.7882	2.7113	0.1317	0.0258	0.3570	(ii)
2	−0.5611	2.6825	0.0550	0.0078	0.1477	(ii)
3	−0.4497	2.6800	0.0484	0.0062	0.1297	(ii)
4	0.0165, −0.4495	2.6800, 2.6800	0.0484, 0.0484	−0.000001, 0.0062	0.1297, 0.1297	Unsuited (ii)
5	0.0346, −0.4305	2.6796, 2.6796	0.0473, 0.0473	−0.0003, 0.0060	0.1267, 0.1267	Unsuited (ii)
6	0.1125, −0.3054	2.6768, 2.6768	0.0399, 0.0399	−0.0014, 0.0042	0.1068, 0.1068	Unsuited (ii)
7	0.0681, −0.0707	2.6717, 2.6717	0.0263, 0.0263	−0.0008, 0.0010	0.0703, 0.0703	Unsuited (ii)
8	0.0060, 0.0015	2.6705, 2.6705	0.0232, 0.0232	−0.00003, 0.00003	0.0618, 0.0618	Unsuited (i)