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Theory and Modern Applications

Table 4 Comparisons between the value of objective function \(J^{*}(\mathfrak{X},\mathfrak{U})\) with and without control cases and \(E(T_{f})+I(T_{f})\) when \(0 \leq u_{1}\leq 0.8\), \(0 \leq u_{2}\leq 0.5\), at different time delay d and different α with \(\Delta t=0.1\), \(T_{f}=100\) by using NSFDM

From: Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

d

α

\(J^{*}(\mathfrak{X},\mathfrak{U})\) with control

\(E(T_{f})+I(T_{f})\)

\(J^{*}(\mathfrak{X},\mathfrak{U})\) without control (i.e., \(u_{1}=u_{2}=0\))

0

1

43,256

389.4656

68,650

0.98

37,592

329.6513

59,318

0.90

21,107

165.8036

32,751

0.80

9867.9

66.7680

15,225

0.70

4376.3

24.9857

6859.5

1

1

44,507

403.6675

68,771

0.98

38,732

341.7494

59,450

0.90

21,901

172.1452

32,911

0.80

10,397

69.6851

15,401

0.70

4759.8

26.4368

7042.2

3

1

47,716

437.1639

69,281

0.98

41,612

370.0171

59,951

0.90

23,752

186.2351

33,360

0.80

11,465

75.5492

15,767

0.70

5390.6

28.9362

7320.8

5

1

52,063

478.2057

70,195

0.98

45,446

404.2531

60,795

0.90

26,022

202.3538

33,950

0.80

12,616

81.6707

16,120

0.70

5981.6

31.2947

7517.1

7

1

56,867

522.7261

71,011

0.98

49,617

440.9938

61,304

0.90

28,350

218.8961

34,564

0.80

13,721

87.6141

16,123

0.70

6521.5

33.4921

8195.7