Page 110 - IJOCTA-15-2

Collocation method with flood-based metaheuristic optimizer for optimal control ...

10 6 10 6
Without optimal control With twofold optimal control u ,u *
*
11 1 2
10
10
8
9
S 8 S 6
7
4
6
2
5
0 100 200 300 400 500 0 100 200 300 400 500
Time (days) Time (days)
(a 1 ) Susceptible people under no control. (a 2 ) Susceptible people under optimal control.
7 7
10 10
3.6
2.9
3.4
2.8
*
3.2 With twofold optimal control u ,u *
1 2
V 2.7 Without optimal control V
3
2.6 2.8
2.6
2.5
0 100 200 300 400 500 0 100 200 300 400 500
Time (days) Time (days)
(b 1 ) Vaccinated people under no control. (b 2 ) Vaccinated people under optimal control.
4
10
*
Without optimal control With twofold optimal control u ,u *
8 5000 1 2
4000
6
3000
I c I c
4
2000
2 1000
0
0 100 200 300 400 500 0 100 200 300 400 500
Time (days) Time (days)
(c 1 ) Infected population with common strain (c 2 ) Infected population with common strain
under no control. under optimal control.
*
2500 Without optimal control 150 With twofold optimal control u ,u *
1 2
2000
100
1500
I v I v
1000
50
500
0
0 100 200 300 400 500 0 100 200 300 400 500
Time (days) Time (days)
(d 1 ) Infected population with amplified strain (d 2 ) Infected population with amplified strain
under no control. under optimal control.
10 6 10 5
9.5
2.5
9.48
Without optimal control 9.46
2
R R
9.44
9.42
1.5
9.4
*
With twofold optimal control u ,u *
1 9.38 1 2
0 100 200 300 400 500 0 100 200 300 400 500
Time (days) Time (days)
(e 1 ) Recovered people under no control. (e 2 ) Recovered people under optimal control.
∗
∗
Figure 4. Effects of twofold optimal control u , u on various population groups over the time period [0, 500]
1 2

305