Simulacion TP 2014_2 UNA

7/25/2019 Simulacion TP 2014_2 UNA

1/24

TRABAJO PRCTICO

ASIGNATURA: CD.ASIGNATURA:

SIMULACIN DE SISTEMAS 337NOMBRE DEL ESTUDIANTE:

CDULA DE IDENTIDAD:

CORREO ELECTRNICO:

TELFONO (S):

CENTRO LOCAL: CD. CENTRO

LOCAL:METROPOLITANO (SAN ANTONIO) 0104

CARRERA: CD. CARRERA:INGENIERA DE SISTEMAS 236

ASESOR: PROF.

FIRMA DEL ESTUDIANTE:_____________________________

LAPSO: 2014-2

UNIVERSIDAD NACIONAL AIERTAAREA DE INGENIERACARRERA DE INGENIERA DE SISTEMAS


2/24

T!" #$ %&'$'#&

2 OBJETI*O 4 RUNGE +UTTA...........................................,

2.1 G% %&'/$# %&' "&/ "&$/ #$ /3"%' 5 " 53$/3"%' 60 #7/ ......................................................................8

2.2 G% 5 " /$'# /3"%' 60 #7/ %&' %3!& #$!"$ $' +9 2x 107 ................................................................10

2., *$%%' #$ "/ /3"%&'$/ /3"%' #$ %&'&/

/3";'$&/ $' $" $35& ...............................................................12

3 OBJETI*O < MONTECARLO.........................................1=

4 CONCLUSIONES........................................................20

5 BIBLIOGRAFIA..........................................................21

1

2


3/24

2 OBJETI*O 4 RUNGE +UTTA

E! "! #$%&'$ *+'!+, ' &' -'#+'& *, /' #,*,!+'$ "! #$%&,'

, "!' ,!,,' -$!+'$*'. L$* ,*#$!*'%&,* ,& -$!+$&,#,$&-$ 5",,! ,+,!' &' -'!+' , /'%+'!+,* 5",#$%'%&,,!+, ,*+'! !,-+'$* '& -'%$ , 60 '*.

P'' ,*+, -'*$ *, #",, "+&8' "!' ,-"'-! ,,!-'&,&'+9',!+, ,&,,!+'& #'' #,,- ,& !:,$ , !9"$* ,&' #$%&'-! !,-+'$* ,! "! +,#$ '$. S"#!'*, 5", +$$*&$* !9"$* , &' #$%&'-! ;(+) *, ,!$+' '& !:,$ , !9"$* 9"&!,'%&,* ,! ,&

+,#$ + = * -$! =(+) '& !:,$ , &$* !,-+'$* *, *"#$!,'8$!'%&,,!+, 5", &' '#,8 -$! 5", ,& !:,$ , &$*!,-+'$* -'%' ,* #$#$-$!'& '& #$"-+$ , >(+) = =(+)#$5", &' '#,8 ,#,!, ,& !:,$ , !9"$* !,-+'$* =,& !:,$ , !9"$* 9"&!,'%&,* 5", ,>*+,! ,! ,*, +,#$.S &' #$%&'-! ,* &$ *";-,!+,,!+, !",$*' #'' *"#$!, 5",>(+) = =(+) *$! 9''%&,* -$!+!"'* #$,$* ,>#,*' ,& #$%&,'-$$?

dy

dt( t)=kx(t)y (t) ,

$!, @ ,* "!' -$!*+'!+, = >(+) =(+) B ,* &' #$%&'-! +$+'&.

S"#$!,!$ 5", B100.000 =(0) B 1000 @ B 2 > 106 = 5", ,&+,#$ *, , ,! '* ,!-",!+, "!' '#$>'-! '& !:,$ ,!9"$* !,-+'$* '& -'%$ , 60 '*.

'*!$*, ,! &' *+"'-! '!+,$ 5", ,*-%, "! -'*$ ,#$#''-! , "!' ,!,,' -$!+'$*' ,'&-, &$ *",!+,?

C$!*+"=' "! $,&$ #$%&'-$!'& ' +'9* , ,-"'-$!,* ,,*+'$ 5", ,#,*,!+, &' *+"'-! #&'!+,''.

'' "*$ ,& +$$ , R"!, "++' , -"'+$ $,! =*"&, ,& -$#$+',!+$ , &' *+"'-! #&'!+,'' #$ "!#,$$ , 30 '*.

S"&, = '!'&-, -$ *, -$#$+' ,& $,&$ '& 9'' '&:!#',+$ '& 5", #",' *, *,!*%&,.

3


4/24

O%+,!' &'* ;-'* 5", ,*-%'! &' *+"'-! #&'!+,''. P,*,!+, ,& '!&** = &'* -$!-&"*$!,* , &$* ,*"&+'$*

$%+,!$*.

SOLUCION:

MODELO POBLACIONAL

C"'&5", #,*$!' *'%, 5", &'* #,* = &$* ,*'$* *, #$#''!#',!+, ,*#,-'&,!+, ,! &"',* -,'$* -$$ &'*$;-!'*. N",9'* !9,*+'-$!,* #",,! '-&'' ,>'-+',!+,-$ ,!,,',* -$!+'$*'* -$$ &$* ,*'$* &' !",!8'= &' +$* ,!' *, #",,! #$#'' ,!+$ "!' -$"!' #$#,*$!'* 5", /'! ,*+'$ ,! -$!+'-+$ -$! $+'* #,*$!'*

,!,'*. D, ,*+, $$ *,' =(+) ,& !:,$ , #,*$!'* 5", /'!-$!+'$ &' ,!,,' = *,' >(+) ,& !:,$ , #,*$!'* 5", !$/'! -$!+'$ &' ,!,,' = *$! *"*-,#+%&,* '& -$!+'$. S*"#$!,$* 5", +$$* &$* !9"$* +,!,! &' *' #$%'%&', -$!+''*, = ,>*+, "! &+, , !9"$* !,-+'$*. E*+,&+, ,* &' #$%&'-! +$+'& 5", ,*!',$* -$$ H !$*,!$ "!' 9''%&, 5", ,#,!' ,& +,#$ #'' ,*+, -'*$ ,!#'+-"&'.

D$!, @ ,* &' -$!*+'!+, , -$!+'$.

E!+$!-,* * *, !+$"-, $ '*",!$ "!' #$%'%&' -$$-$!*+'!+, , 5", "!$ !,-+, ' $+$.

P$-,,$* #,$ ' ,9'&"' &' ,-"'-! ,,!-'& ''?

C$! &' -$!-! !-'&? =(0) B1.000 = &' -$!*+'!+, @ B 2> 106

dy

dt

( t)=kx(t)y (t)= yydtdy

*)000.100(*10*2 6 =

S $%*,9'$* &' ,-"'-! 9,$* "!' ,-"'-! ,,!-'%&, ,9''%&,* *,#''%&,* #'' ,*$&9, #$-,,$* ' ,'&8' &$*#'*$* *",!+,*?

4


5/24

P/& 1 '& *,#'' &'* 9''%&,* &' ,-"'-! ,,!-'& !$* 5",', &' $'?

dtyy

dy 610*2)000.100(

= BJ

= dtyydy 610*2

)000.100(

P/& 2L",$ +$'$* &' !+,'& yy

dy

)000.100( = &' ,*$&9,$*#$ ,*-$#$*-! ,! '--$!,* #'-'&,*?

yy

yBAy

y

B

y

A

yy )000.100(

)000.100(

000.100)000.100(

1

+

=+

=

D, $!, *, ,*#,' 5",? 1 B A= (100.000 K =)

P/& ,P'' ,+,!' &$* 9'&$,* , A = ,*$&9,$*?

S = B 0 ,!+$!-,*? 1 B 100.000 #$ &$ +'!+$? 000.1001

=B

S = B 100.000 ,!+$!-,*? 1 B 100.000A , $!,? 000.1001

=A

C$!*,-",!+,,!+,

= yydy )000.100(

( )yLnyLny

dy

y

dy=+

000.100()(

000.100

1

000.100

1

000.100000.100

1

A& ,*$&9, !$* 5",' &' ,-"'-! , ,*+' '!,'?

( ) CtyLnyLn += 610*2000.100()(000.100

1

D$!, C ,* &' -$!*+'!+, , !+,'-!.

P/& 4D,*#,


6/24

A& +$' ,& '!+&$'+$ *, +'!*$'?

tCt eCey

y 2,01

2,0 1

000.100==

+

P/& =#'' $%+,!, ,& 9'&$ HC , &' -$!*+'!+, , !+,'-!"*',$* ,& 9'&$ !-'& , &' -$!-! '' =(0)B 1.000 &",$

*"*++"$* = $%+,!,$*?

99

1

000.1000.100

000.11

0*2,0

1 ==

CeC

P/& 6 #'' $%+,!, &' *$&"-! #'+-"&' , &' ,-"'-!,,!-'& ,*#,


7/24

Q ,* *"',!+, :+& #'' -'*$* ,! &$* 5", &' *$&"-! !$ #",,/'&&'*, #$ &$* +$$* -$!9,!-$!'&,* (-$$ *,#''-! ,9''%&,*). '= 9''-$!,* ,! ,& +$$ , R"!,"++' , -"'+$$,! #,$ ,& * "+&8'$ ,* ,& +$$ ,! ,& -"'& *, ,&, "!+''$ , #'*$ ?= "! !:,$ >$ , +,'-$!,* '.

P'' !",*+$ -'*$ ,*$&9, !"-',!+, "!' ,-"'-!,,!-'& , $,! "!$ -$! *" ,*#,-+9' -$!-! !-'&"*'!$ ,& +$$ , R"!, K "++' , -"'+$ $,! *, #$-,,

, &' *",!+, '!,'? L' ,-"'-! ' *"&'),( ytf

dt

dy=

-$! &'

-$!-! !-'& ( ) 00 yty =

E!+$!-,* ,& +$$ R4 #'' ,*+, #$%&,' ,*+ '$ #$ &'

*",!+, ,-"'-!?

D$!,?

A* ,& *",!+, 9'&$ ( Yn+1 ) ,* ,+,!'$ #$ ,& #,*,!+,9'&$ ( Yn ) * ,& #$"-+$ ,& +''$ ,& !+,9'&$ (/) #$ "!'#,!,!+, ,*+''. L' #,!,!+, ,* "! #$,$ #$!,'$ ,#,!,!+,* $!, K1 ,* &' #,!,!+, '& #!-#$ ,& !+,9'&$

K2 ,* &' #,!,!+, ,! ,& #"!+$ ,$ ,& !+,9'&$ "*'!$ K1

#'' ,+,!' ,& 9'&$ , HQ,! ,& #"!+$ xn+h

2"*'!$ ,&

+$$ , E"&,. K3 ,* $+' 9,8 &' #,!,!+, ,& #"!+$ ,$#,$ '/$' "*'!$ K2 #'' ,+,!' ,& 9'&$ , HQ K4 ,*&' #,!,!+, '& ;!'& ,& !+,9'&$ -$! ,& 9'&$ , HQ ,+,!'$#$ K3 .

7


8/24

P$,'!$ &'* -"'+$ #,!,!+,* *, &, '*!' '=$ #,*$ ' &'*#,!,!+,* ,! ,& #"!+$ ,$?

S,!$ H/ ,& #'*$ -$,*#$!,!+, #'' -$!*," &' *$&"-!

!"-' ,! !",*+$ -'*$ ,& 9'&$ , / B 1.

L",$ ,,-+"'$* = -''$* +$'* &'* ,-"'-$!,* = $"&'*

*",!+,* ,! E>-,& #'' 5", !$* ",*+, &' ;-' 5", *,

$%+,! , &' *"&'-! , '-",$ ' &$* '+$* $%+,!$*?

L' ,-"'-! ,,!-'& ' ,*$&9, ,*?

( )yydt

dy= 000.10010*2 6

-$! &' -$!-! !-'&? =(0) B1.000.

E& +1 5",$ ,;!$ #$? K1=hf(x i ; y i)

( ) ( ) 261 000002,02,0000.10010*2;* nnnnnn yyyyytfhK ===

E& +2 5",$ ,;!$ #$? K2=f(x i+

1

2 h; y i+1

2 k1h)

))2/((*)))2/((000.100(10*2;* 11116

2221 kykyytfhK nn

Khn ++=++=

E& +, 5",$ ,;!$ #$? K3=f(x i+1

2h ; yi+

1

2k2h)

))2/((*)))2/((000.100(10*2;* 21216

2232 kykyytfhK nn

Khn ++=++=

E& +4 5",$ ,;!$ #$? K4=f(xi+h ; y i+k3h)

( ) )(*))(000.100(10*2;* 31316

34 kykykyhtfhK nnn ++=++=

E*+'* ,-"'-$!,* &'* "+&8'$* ,! E>-,& = -$!*,"$* &' *$&"-!!"-' , &' ,-"'-! #&'!+,'' -$! &' -$!-! !-'& ''.


9/24

2.1 G';-' -$!*,"' -$! &$* 9'&$,* , *"&'-! #''&' #,' *"&'-! 60 '*.

N:,$ , I!9"$* I!,-+'$* ,! 60 '*

+ Q

F"' 1

T'%&' -$! &$* '+$* , &' #,' *"&'-!?

@ +1 +2 +, +4 '%' E&

0 1000.00000 1.00000 217.3440 21.2004 240.272 1000.00000 0.00000

1121.701

3 240.762264.2310

7 266.14022.6314

7121.704

1 0.002

2144.172

1 22.46320.342

4 323.723.001

0144.234

4 0.00623

3107.247

0 34.17643.063

7 32.34204430.241

4107.260

7 0.01126

421.71

7 430.0414471.06

0 474.727720.4144

421.62

3 0.0106

2672.3360

2 20.14446.273

73.0462.1726

2672.3631

0 0.0270

63244.741

7 627.01466.416

61.3276.331

03244.330

0 0.034

7

334.24

6 76.0176

2.33

31.7176

07.70

7

334.7

0 0.03

4764.60

0 07.16.2111

2 6.244010.4

24764.62

6 0.07307

7.741

10.4234

110.7

3611.2130

2123.044

07.460

4 0.0610

64.16

122.666

1403.03371

1412.3710

131.17

64.317 0.12611

11

34.3771

131.2762

167.67

1667.204

103.776

34.01 0.16130


10/24

12

1001.762

103.00020

14.4717

16.6741

210.26477

1001.0 0.202

13

1171.3747

2107.64736

226.7213

2277.406

2443.70063

1171.624 0.207

14

14244.3100

2443.0613

2614.731

2626.6264

204.304

14244.61613 0.3023

1

1666.114

0

204.212

1

26.13

31

27.720

1

313.623

12

1666.47

7 0.364716

1.737

313.0064

336.2266

330.47220

367.7202

1.167 0.420

17

23233.764

367.17

371.730

3760.2

341.3231

23234.40 0.420

1

26.64347

341.046

4114.60

4121.407

426.42

260.13 0.636

1

31106.4244

426.0661

443.364

4443.403

42.41636

31107.036 0.6120

20

34.43271

42.1307

4704.04

4707.011

40.7213

346.071 0.66600

21

40247.341

40.707

42.0327

43.24043

42.7171

4024.4110 0.706

22

4136.636

42.6642

4.6042

4.7760

4.62

4137.42121 0.731

23

0121.26032

4.70

46.214

46.324

447.204

0122.0030 0.7431

24

103.4222

447.1016

4.16670

46.1160

400.4127

104.1612 0.7363

2

.2377

400.00

463.171

46.162

46.3123

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26

64676.0760

46.2002

4424.6416

442.34

426.12

64677.20123 0.6363

27

6101.0622

4270.2701

40.04467

410.342

322.2302

6101.7423 0.6613

2

73201.063

323.411

3733.66740

3743.177

34.01100

73201.617 0.6127

2

763.61347

34.62221

331.132

3362.4724

3163.6023

763.1771 0.6624

30

02.1660

3164.40213

267.66304

20.1674

27.4773

02.712 0.16

31

326.46317

276.264

27.0074

2610.11133

242.31227

326.347 0.47170

32

73.760

2426.143

224.13233

2262.2463

201.26

74.14 0.4263

33

130.46767

202.1347

130.31

143.076

17.2213

130.110 0.3343

34

006.3462

17.02

1644.02

16.213

11.164

006.647 0.3431

3

171.624

11.621

131.06222

1401.167

121.07

171.631 0.302

36

3117.2242

121.023

1170.41

110.10

107.47727

3117.42 0.27140

37 423.6703 1076.143 0.2321 .2733 .322 423.62 0.233

27.171 .1

17.7126 2.2026

74.761

27.4104 0.21123

3

6101.6603 74.2122

67.230 66.36

621.7727

6101.7134 0.131

40

67.04 622.23240

63.1 6.31663

1.0410

67.67044 0.161

41

732.7647 1.43132

466.442 471.1437

42.7471

732.0601 0.14114

10


11/24

42

722.17073 426.077

3.23706 3.16002

31.3317

722.2330 0.122

43

20.722 31.61643

317.61 320.307

2.20

20.742 0.10614

44

2.11 2.7744

261.14 264.33333

23.3074

2.6346 0.0166

4

72.10

73 23.0373

21.2007

0 217.4003

1.632

0

72.

67 0.0746

00.47 16.122

176.471 17.7743

161.01770

00.61663 0.0674

47

17.62620 161.146

14.222 146.14

132.2161

17.6436 0.016

4

333.016 132.3322

11.26660 120.740

10.12

333.146 0.0477

4

43.30 10.606 7.6 .2313 .011

44.02640 0.0420

0

2.16 .0640 0.2623 1.1376 73.00072

2.17 0.03623

1

633.3321 73.06467 6.012 66.26 .4743

633.36302 0.0304

2

6.71 .000 3.4427 4.3661 4.0234

6.62340 0.02621

3

73.1621 4.064 44.2004 44.62 40.164

73.346 0.0222

4

7.43310 40.23212 36.22432 36.62364 32.3424

7.41 0.016

34.1014 32.6346 2.67746 30.000 26.046

34.2611 0.016

6

64.747 27.00444 24.3104 24.763 22.10060

64.047 0.0130

7

.27600 22.1202 1.121 20.13320 1.1017

.2741 0.01140

0.323 1.117 16.3022 16.47 14.236

0.3300 0.0063

2.712 14.3 13.363 13.040 12.1412

2.76003 0.0012

60

3.20244 12.1212 10.331 11.06 .426

3.202 0.0064

2.2 G';-' #'' &' *,"!' *"&'-! ' 60 '* -$!-'%$ , 9''%&, ,! B 2x 107

11


12/24

C$!+'3)$* #'' 60()'* -$! FB 2>10N7

+ Q

T'%&' -$! &$* '+$* , &' *,"!' *"&'-! 60 '* = -'%$, 9''%&, , &' -$!*+'!+, B 2>107

@ +1 +2 +, +4'%

' E&0 1000.00000 19.80000 19.99402 19.99592 20.19184 1000.00000 0.0000000

1 1019.99529 20.19183 20.38961 20.39154 20.59126 1019.99529 0.0000000

2 1040.38618 20.59124 20.79285 20.79482 20.99840 1040.38618 0.0000001

3 1061.18035 20.99839 21.20389 21.20590 21.41341 1061.18035 0.0000001

4 1082.38558 21.41340 21.62288 21.62492 21.83644 1082.38558 0.0000001

5 1104.00982 21.83643 22.04995 22.05204 22.26763 1104.00982 0.0000001

6 1126.06116 22.26762 22.48526 22.48738 22.70714 1126.06116 0.0000002

7 1148.54783 22.70712 22.92895 22.93112 23.15511 1148.54783 0.0000002

8 1171.47823 23.15509 23.38119 23.38340 23.61169 1171.47823 0.0000002

9 1194.86089 23.61168 23.84213 23.84437 24.07706 1194.86089 0.0000003

10 1218.70451 24.07704 24.31191 24.31421 24.55136 1218.70451 0.0000003

11 1243.01795 24.55134 24.79072 24.79305 25.03475 1243.01795 0.0000003

12 1267.81023 25.03474 25.27870 25.28108 25.52741 1267.81023 0.0000004

13 1293.09051 25.52739 25.77603 25.77845 26.02950 1293.09051 0.0000004

14 1318.86816 26.02948 26.28288 26.28534 26.54118 1318.86816 0.0000005

15 1345.15267 26.54117 26.79940 26.80191 27.06264 1345.15267 0.0000005

16 1371.95375 27.06262 27.32579 27.32835 27.59404 1371.95375 0.0000005

17 1399.28123 27.59403 27.86221 27.86481 28.13557 1399.28123 0.0000006

18 1427.14517 28.13555 28.40884 28.41149 28.68740 1427.14517 0.0000006

19 1455.55578 28.68739 28.96587 28.96857 29.24972 1455.55578 0.0000007

20 1484.52344 29.24971 29.53348 29.53623 29.82272 1484.52344 0.0000007

21 1514.05875 29.82270 30.11185 30.11466 30.40657 1514.05875 0.0000008

22 1544.17247 30.40656 30.70118 30.70404 31.00148 1544.17247 0.0000008

23 1574.87555 31.00146 31.30167 31.30457 31.60764 1574.87555 0.0000009

24 1606.17914 31.60762 31.91349 31.91645 32.22524 1606.17914 0.0000009

25 1638.09460 32.22522 32.53686 32.53988 32.85449 1638.09460 0.0000010

26 1670.63347 32.85447 33.17198 33.17505 33.49558 1670.63347 0.0000010

27 1703.80748 33.49556 33.81904 33.82217 34.14872 1703.80748 0.0000011

28 1737.62860 34.14870 34.47826 34.48144 34.81413 1737.62860 0.0000012

12


13/24

29 1772.10897 34.81411 35.14985 35.15308 35.49200 1772.10897 0.0000012

30 1807.26097 35.49198 35.83401 35.83730 36.18256 1807.26097 0.0000013

31 1843.09716 36.18254 36.53096 36.53432 36.88603 1843.09716 0.0000014

32 1879.63035 36.88600 37.24093 37.24435 37.60261 1879.63035 0.0000014

33 1916.87355 37.60259 37.96413 37.96760 38.33254 1916.87355 0.0000015

34 1954.83998 38.33252 38.70078 38.70432 39.07604 1954.83998 0.0000016

35 1993.54311 39.07602 39.45112 39.45472 39.83334 1993.54311 0.0000017

36 2032.99662 39.83332 40.21537 40.21904 40.60467 2032.99662 0.0000017

37 2073.21442 40.60464 40.99377 40.99750 41.39026 2073.21442 0.0000018

38 2114.21066 41.39024 41.78655 41.79034 42.19035 2114.21066 0.0000019

39 2155.99972 42.19033 42.59395 42.59781 43.00518 2155.99973 0.0000020

40 2198.59623 43.00516 43.41621 43.42014 43.83500 2198.59623 0.0000021

41 2242.01504 43.83497 44.25357 44.25757 44.68004 2242.01504 0.0000022

42 2286.27125 44.68002 45.10629 45.11035 45.54056 2286.27126 0.0000023

43 2331.38023 45.54054 45.97461 45.97874 46.41681 2331.38023 0.0000024

44 2377.35757 46.41679 46.85878 46.86298 47.30904 2377.35758 0.0000025

45 2424.21913 47.30901 47.75906 47.76334 48.21751 2424.21913 0.0000026

46 2471.98102 48.21748 48.67570 48.68006 49.14247 2471.98102 0.0000027

47 2520.65959 49.14245 49.60898 49.61340 50.08420 2520.65960 0.0000028

48 2570.27150 50.08417 50.55914 50.56364 51.04295 2570.27150 0.0000029

49 2620.83361 51.04292 51.52646 51.53104 52.01899 2620.83361 0.0000030

50 2672.36310 52.01896 52.51121 52.51587 53.01259 2672.36310 0.0000031

51 2724.87738 53.01256 53.51365 53.51839 54.02402 2724.87738 0.0000033

52 2778.39415 54.02399 54.53406 54.53888 55.05356 2778.39416 0.0000034

53 2832.93139 55.05353 55.57272 55.57761 56.10148 2832.93139 0.0000035

54 2888.50734 56.10145 56.62990 56.63488 57.16807 2888.50734 0.0000036

55 2945.14051 57.16804 57.70588 57.71094 58.25361 2945.14052 0.0000038

56 3002.84973 58.25357 58.80095 58.80610 59.35837 3002.84973 0.0000039

57 3061.65407 59.35834 59.91540 59.92062 60.48265 3061.65407 0.0000040

58 3121.57291 60.48261 61.04950 61.05481 61.62673 3121.57291 0.0000042

59 3182.62590 61.62670 62.20355 62.20894 62.79091 3182.62591 0.0000043

60 3244.83300 62.79087 63.37783 63.38332 63.97547 3244.83300 0.0000045

2.3 V,;-'-! , &'* *"&'-$!,* *"&'-! ,-$!+'$* *"&+!,$* ,! ,& +,#$

13


14/24

Contagiados simultaneos

ti funcion Yi

T'%&' -$! &$* 9'&$,* , &' *"&'-! , -$!+'$* *"&+!,$*

+ "!-! Q0 1000 1000.000000001 121.7041 121.7013332 144.2344 144.1721413 107.2607 107.2470334 21.623 21.7162 2672.3631 2672.336022316 3244.33 3244.74166337 334.7 334.246

4764.626 4764.6007 7.4604 7.741473310 64.317 64.1111 34.01 34.37712412 1001. 1001.7617713 1171.62 1171.37473314 14244.6161 14244.310601 1666.47 1666.11403316 1.166 1.7377017 23234.40 23233.76441 260.1 26.643467171 31107.037 31106.42442120 346.07 34.43271010

21 4024.411 40247.3413322 4137.4212 4136.63610623 0122.003 0121.2603240324 104.161 103.42222 .602 .2377426 64677.2012 64676.076003727 6101.7424 6101.06220742 73201.62 73201.06332 763.177 763.61347170

14


15/24

30 02.713 02.167631 326.34 326.463166232 74.1 73.76030733 130.11 130.467667034 006.6 006.34623343 171.63 171.62433

36 3117.4 3117.22416337 423.6 423.6702733 27.410 27.17073 6101.713 6101.660344240 67.6704 67.0442141 732.06 732.76461042 722.233 722.1707266743 20.74 20.7220344 2.63 2.10604 72.7 72.1072646 00.6166 00.4710247 17.644 17.6261734 333.1 333.01642

4 44.0264 43.30020 2.1 2.101 633.363 633.332177362 6.6234 6.713 73.3 73.1621364 7.42 7.4330620 34.261 34.10142446 64.0 64.7473467 .274 .2760037 0.33 0.3237666 2.76 2.71173660 3.203 3.202437261 0.2233 0.217234

62 .2426 .237740163 66.622 66.624120464 72.67 72.67240176 77.6277 77.624761266 1.624 1.6772667 .0023 .00030026 7.7206 7.7116 .463 .44432170 1.76 1.76737271 3.2606 3.260372 4.421 4.413104373 .423 .41617074 6.3012 6.30062114

7 6.717 6.71174076 7.206 7.20163277 7.7 7.66477 .33 .337707117 .633 .63021300 . .71631 .07 .0762 .232 .23067413 .36 .34606

1


16/24

4 .44 .431172 .01 .006446 .6644 .6643747 .723 .7221323 .771 .770220 .1 .103

0 .42 .412211 .766 .762602 . .033 .173 .1723404 .323 .322367 .44 .4416 .46 .476667 .62 .62103 .66 .6163 .71 .70700100 .76 .772

A';"// %&'%"/&'$/ #$ "&/ $/"#&/:

C$$ *, ,$*+ ,! &'* ;-'* = +'%&'* -$!+,!+9'* , &' '+'*"&'' '!+,$,!+, ,& +$$ !$* ,",*+' 5", ,& !:,$, !9"$* 9' ,! '",!+$ '& +'!*-" ,& +,#$.E! &' :&+' *"&'-! , &$* -$!+'$* *"&+!,$* #$,$*$%*,9' 5", '%'* ';-'* ,*+! *"#,#",*+'* &$ 5",,",*+' 5", E& +$$ , R"!, "++' ,* "! +$$%$!'$*$ #'' ,*$&9, ,*+, +#$ , *+"'-$!,* !"-'* #",*9,$* ,! &' +'%&' -$$ *, ,*+'%&8' ,! ,& +,#$ = ,& '",!+$ ,*,!$ '& #'*' , &$* 60 '* /'*+' &&,' ' &$* 100 '* = ,&'",!+$ ,* !*!;-'!+,.

3 OBJETI*O < MONTECARLO

E& $%,!$ , "! #'* *"',-'!$ ,*+ *,'!$ &'

-$!*+"--! , "!' ,#,*' &' -"'& *, "+&8'' #'' ,!,',!,' ,&-+-' = #'' ,& -$!+$& , "


17/24

E& !9,& ,& ,%'&*, '& ;!'& , "! ,* ,*+ '$ #$?S ,& '"' ,! &' ,#,*' ,>-,, &' -'#'-' >' ,& '"'*$%'!+, *, %$+' ' +'9* ,& 9,+,,$ 5", ,* , "


18/24

E+B E+1 A+K S+ $!, A+ -$,*#$!, '& '"' 5", &&,' ' &',#,*' = S+ '& '"' 5", *'&, , &' ,#,*' %,! *,' ,& '"' 5",*, 9,+, $ 5", *, *",&+' #'' ,!,' ,!,'.

E& #$-,,!+$ ,!,'& , *"&'-! #'' "! ,* -"'&5",' *,

#",, ,#,*,!+' #$ &$* *",!+,* #'*$*?

S, ,+,!' ,& '"' 5", &&,' ' &' ,#,*' A+ S, -'&-"&' ,& 9$&",! !-'& ,& ,%'&*, ','!$ ,&'"' 5", &&,'? E+ B E+1 A+ S ,& 9$&",! ,& ,%'&*, ,>-,, &' -'#'-' ,& *$*, -'&-"&' ,& '"' 5", *, 9,+, = ,& ,%'&*, 5",' ,! *"!9,& >$.

S E+J C'# V+B E+ C'#

E+B C'#

S, -'&-"&' &' ,'!' ,!*"'& #'' ,!,' ,!,' D+ S ,& !9,& ,& ,%'&*, ,* "'& $ *"#,$ ' &' ,'!' *,*'+*'-, +$' &' ,'!' = '& !9,& ,& ,%'&*, *, &, ,*+'&' ,'!'.

S E+ D+ DS+B D+

E+B E+ D+

S ,& !9,& ,& ,%'&*, ,* !,$ ' &' ,'!' *,*'+*'-, #'+, , &' ,'!' = '& !9,& ,& ,%'&*, *,/'-, "'& ' -,$.

S E+ D+ DS+ B E+

E+B 0

D$!, C'# ,#,*,!+' &' -'#'-' , &' ,#,*' V+ ,&9,+,!+$ ,! ,& ,* + = DS+ &' ,'!' *'+*,-/' ,! ,& ,* +.

P'' +,!' , ,*'$&&' ,& $,&$ *, ,5",, ,+,!'-$ *, ,!,' ,& '"' 5", &&,' '& ,%'&*, = &' ,'!' ,,!,'.

P'' -'&-"&' ,& '"' 5", &&,' '& ,%'&*, 5", ,* "! ,!,!$'&,'+$$ *, ,,-+:' ,'!+, &' '="' , &$* !:,$* '&,'+$$*.

1


19/24

P'' ,&&$ *, ,!,' "! !:,$ '&,'+$$ A1 ,! E>-,& = &",$ *,/'-, "!' -$,*#$!,!-' ,!+, -/$ !:,$ = &'* #$%'%&',*,*#,-+9'* , 5", &&,", -,+' -'!+' , '"' '& ,%'&*,. E*,- ,& !:,$ '&,'+$$ A1 -$! "! '!$ , 9''-! , 0 '"!$ ,%, ,#,*,!+' &'* ,,!+,* #$*%&',* , &&,' '"' '&

,%'&*, -$! &$* 9'&$,* , 0 1 2 = 3. E& '!$ , 9''-! ,-,$ ' "!$ ,%, 9*, ,! 100 #'+,* = '*!'*, 20 ' &'#$*%&' , 5", !$ &&,", '"' ,! ,& ,* 20 ' &' #$*%&', 5", &&,", "!' "!' 30 ' &' #$*%&' , 5", &&,",! $*"!',* = ;!'&,!+, 30 ' &' #$*%&' , 5", &&,",! +,*"!',* , '"'. L' +'%&' *",!+, #,*,!+' "!' #$*%&,'*!'-! ,& !:,$ '&,'+$$ A1 ' &'* ,,!+,* -'!+',* ,'"' 5", #",,! &&,' '& ,%'&*,.

Valores del Nmero Aleatorio A10.2 0.2 0.3 0.320 40 70 100

A1 < 20 20


20/24


21/24

I3$' 1

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del mes(Et)

0 4 4

1 4 0.328 33 1 1 4 0.131 13 1 1 3

2 3 0.368 37 1 0 4 0.448 45 1 1 3

3 3 0.806 81 3 2 4 0.827 83 2 2 2

4 2 0.374 37 1 0 3 0.036 4 1 1 2

5 2 0.283 28 1 0 3 0.368 37 1 1 26 2 0.418 42 2 0 4 0.610 61 2 2 2

7 2 0.111 11 0 0 2 0.941 94 2 2 0

8 0 0.976 98 3 0 3 0.458 46 1 1 2

9 2 0.327 33 1 0 3 0.411 41 1 1 2

10 2 0.390 39 1 0 3 0.902 90 2 2 1

11 1 0.152 15 0 0 1 0.328 33 1 1 0

12 0 0.251 25 1 0 1 0.772 77 2 1 0

21


22/24

13 0 0.592 59 2 0 2 0.084 8 1 1 1

14 1 0.819 82 3 0 4 0.981 98 2 2 2

15 2 0.865 87 3 1 4 0.969 97 2 2 2

16 2 0.144 14 0 0 2 0.102 10 1 1 1

17 1 0.975 98 3 0 4 0.670 67 2 2 2

18 2 0.628 63 2 0 4 0.304 30 1 1 3

19 3 0.883 88 3 2 4 0.537 54 2 2 2

20 2 0.319 32 1 0 3 0.022 2 1 1 2

21 2 0.832 83 3 1 4 0.899 90 2 2 2

22 2 0.570 57 2 0 4 0.432 43 1 1 3

23 3 0.012 1 0 0 3 0.580 58 2 2 1

24 1 0.541 54 2 0 3 0.585 59 2 2 1

25 1 0.432 43 2 0 3 0.969 97 2 2 1

26 1 0.412 41 2 0 3 0.736 74 2 2 1

27 1 0.133 13 0 0 1 0.451 45 1 1 0

28 0 0.633 63 2 0 2 0.868 87 2 2 0

29 0 0.317 32 1 0 1 0.945 95 2 1 0

30 0 0.570 57 2 0 2 0.729 73 2 2 0

Prom

edio

1+, 0-.&

1+0 0&// &/

0,0 1,

1,0 1,&

22


23/24

4 CONCLUSIONES

E! ,& $%, "! '=$ !:,$ , $#,'-$!,* = 5", ,! -''#'*$ +$' ,& #$,$ #$!,'$ , -"'+$ #,!,!+,*.

E! ,*+, $%


24/24

5 BIBLIOGRAFIA

U!9,*' N'-$!'& A%,+' (2006) I'$/%' #$ O5$%&'$/

II (,0). E&'%$'$ #$ G"+,,8 M. C''-'*./++#*?YY

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