id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6347	Abbas, Nadeem; Shatanawi, Wasfi; Zanib, Syeda Alishwa	Mathematical Modeling of SARS-CoV-2 Epidemics Using Fractional Calculus and Optimal Interventions	2025	34	.pdf	application/pdf	11487	576	64	For the optimal control (a∗2, a ∗ 2, a ∗ 3) and corresponding state solution (S,E,U,Q, P,H,C, F, V,R) that minimize J over U of the corresponding system of equation (2.4) having the adjoint variable ξ1, ...., ξ10 such that, dξ1 dt = (ξ1 − ξ2)ϕE + (ξ1 − ξ9)a1 − aξ1, (3.62) dξ2 dt = (ξ1 − ξ2)ϕS + (ξ9 − ξ2)γV + (ξ2 − ξ3)λ1U − (ξ2 − ξ4)λ2Q+ ξ2(µ+ d1)−X1, (3.63) dξ3 dt = (ξ2 − ξ3)λ1E + (ξ3 − ξ10)α1 + (ξ3 − ξ5)α2 + ξ3(µ+ d2)−X2, (3.64) dξ4 dt = (ξ2 − ξ4)λ2E + (ξ4 − ξ5)b1 + (ξ4 − ξ1)b2 + (ξ4 − ξ9)b3 + ξ4(µ+ d3)−X3, (3.65) dξ5 dt = (ξ5 − ξ6)φ1 + (ξ5 − ξ7)φ2 + (ξ5 − ξ8)φ3 + ξ5(µ+ d4)−X4, (3.66) dξ6 dt = (ξ6 − ξ10)a2 + (ξ6 − ξ7)m2 + (ξ6 − ξ8)m3 + ξ6(µ+ d5)−X5, (3.67) dξ7 dt = (ξ7 − ξ6)η + ξ7(µ+ d6)−X6, (3.68) dξ8 dt = (ξ8 − ξ10)a3 + (ξ8 − ξ6)σ2 + ξ8(µ+ d7)−X7, (3.69) dξ9 dt = (ξ9 − ξ2)γE + ξ9(µ)− ξ9a, (3.70) dξ10 dt = ξ10 (µ+ τ)− ξ1τ. (3.71) ξi(T ) = 0, for i = 1, 2, 3....10 having conditions, a∗1 = max{0,min(1,(ξ1 − ξ9)S 2Y1 )}, a∗2 = max{0,min(1, (ξ6 − ξ10)H 2Y2 )}, a∗3 = max{0,min(1, (ξ8 − ξ10)F 2Y3 )}, (3.72) N. Abbas, W. Shatanawi, S. A. Zanib / Eur. =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 10 15 20 25 30 Qu ar an tin ed (Q ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Cl in ica lly P os iti ve (P ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Ho sp ita liz ed (H ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 1.5 1.6 1.7 1.8 1.9 2.0 As ym pt om at ic (F ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.70 0.75 0.80 0.85 0.90 0.95 1.00 IC U (C ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 Va cc in at ed (V ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Re co ve re d (R ) =0.1 =0.3 =0.5 =0.7 =0.9 Figure 9: Dynamic convergence of conformable fractional model solutions to classical solutions as ς → 1. Shading represents solution variance across ς ∈	cache/ejpam-6347.pdf	txt/ejpam-6347.txt