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Theory and Modern Applications

Table 4 Sensitivity of \(I_{v}^{*}\) corresponding to all parameters:

From: Dynamical features of pine wilt disease through stability, sensitivity and optimal control

Parameters

Initial value

Final value

Change

Percentage change

Initial value of \(I_{v}^{*}\)

Final value of \(I_{v}^{*}\)

Change

Percentage change

\(C_{5}/ 42.85714286\)

\(C_{9}*C_{10}\)

α

0.06

0.3

0.24

400

36.95

30.47

−6.48

−17.53721245

9.333333

−163.681

β

0.4

2

1.6

400

17.69

30.47

12.78

72.24420577

9.333333

674.2793

κ

0.06

0.4

0.34

566.6666667

30.57

31.16

0.59

1.929996729

13.22222

25.51885

γ

0.002

0.07

0.068

3400

12.25

51.08

38.83

316.9795918

79.33333

25,147.05

\(\beta _{1}\)

0.001

0.2

0.199

19,900

26.16

57.58

31.42

120.1070336

464.3333

55,769.7

\(\mu _{v}\)

0.2

0.9

0.7

350

125.1

9.77

−115.33

−92.1902478

8.166667

−752.887

\(\lambda _{h}\)

21

30

9

42.85714286

28.27

32.78

4.51

15.95330739

1

15.95331

ψ

2

12

10

500

16.18

30.47

14.29

88.31891224

11.66667

1030.387

ϕ

0.01

0.1

0.09

900

38.07

30.47

−7.6

−19.96322564

21

−419.228

θ

0.0001

0.001

0.0009

900

12.65

30.47

17.82

140.8695652

21

2958.261

\(\mu _{h}\)

0.06

0.6

0.54

900

30.95

26.52

−4.43

−14.31340872

21

−300.582

ρ

0.01

0.5

0.49

4900

30.01

32.35

2.34

7.797400866

114.3333

891.5028

\(\lambda _{v}\)

10

32

22

220

8.336

32.93

24.594

295.0335893

5.133333

1514.506

δ

0.3

0.9

0.6

200

30.47

17.31

−13.16

−43.19002297

4.666667

−201.553