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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