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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 47 "MTH 455  A DISCRE
TE LINEAR AGE-STRUCTURED MODEL" }{TEXT -1 120 "\nJR 2/3/2005  age_stru
ctured_2.mws\nMore age groups (81) than the 4 in age_structured.mws\nS
ee Haberman, Section 35, p138." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 385 "# SET UP THE MATRIX A\nrestart:\nwith(LinearAlgebra):\nM:=80;\n
b:=Vector([seq(0,a=0..15),seq(.08,a=16..35),seq(0,a=36..80)]):   # bir
th rates\nd:=Vector([seq(0.01,a=0..65),seq(0.2,a=66..80)]): # death ra
tes\nA:=Matrix([seq([seq(0,col=0..M)],row=0..M)]):  #fill A with zeros
\nfor col from 0 to M-1 do\n   A[1,col+1]:=b[col+1];\n   A[col+2,col+1
]:=1-d[col+1];\nend do:\nA;\nconvert(b,list);\nnops(b);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"MG\"#!)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%'RTABLEG6+\"*s,qP\"%)anythingG%'MatrixG%,rectangularG%.Fortran_orderG
7\"\"\"#;\"\"\"\"#\")F-" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7]p\"\"!F$F
$F$F$F$F$F$F$F$F$F$F$F$F$F$$\"\")!\"#F%F%F%F%F%F%F%F%F%F%F%F%F%F%F%F%F
%F%F%F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F
$F$F$F$F$F$F$F$F$F$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 689 "# SOME USEFUL PROCEDURES\n
\n# NORMALIZE A VECTOR\nnormaliz:=proc(N)\n   local tot,i,Nlocal;\n   \+
Nlocal:=convert(N,list);\n   tot:=0;\n   for i from 1 to nops(Nlocal) \+
do tot:=tot+abs(N[i]); end do:\n   unassign('i'):\n   for i from 1 to \+
nops(Nlocal) do Nlocal[i]:=N[i]/tot; end do:\n#   for i from 1 to nops
(Nlocal) do Nlocal[i]:=N[i]/N[1]; end do:\n   return Vector(Nlocal);\n
end proc:\n\n# MAKE A HISTOGRAM OF A VECTOR\nmy_histogram:=proc(N,myti
tle,mycolor)\n   local Nlocal,n,i,r;\n   Nlocal:=convert(N,list);\n   \+
n:=nops(Nlocal);\n   for i from 0 to n-1 do\n     r[i]:=plottools[rect
angle]([i,N[i+1]],[i+1,0],color=mycolor);\n   end do:\n   return plots
[display](seq(r[i],i=0..n-1),title=mytitle);\nend proc:\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 539 "# ITERATE AND MAKE AN ANIMATED HIS
TOGRAM\nN:=Vector([2,seq(1,a=1..80)]);\nhisto[0]:=my_histogram(N,\"0\"
,magenta):\nsnapshot_interval:=5;  # ONLY MAKE A SNAPSHOT EVERY SO MAN
Y TIMESTEPS\ncount:=0:\nfor t from 1 to 120 do\n   N:= A . N;\n   if( \+
t mod snapshot_interval = 0 ) then\n      count:=count+1;\n      histo
[count]:=my_histogram(N,convert(t,string),magenta):\n   end if;\nend d
o: unassign('t'):\nplots[display]( seq( histo[0], c=0..10),\n         \+
       seq( histo[c], c=0..count ), \n                seq( histo[count
], c=0..10),insequence=true );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"NG-%'RTABLEG6*\"*7VlO\"%)anythingG&%'VectorG6#%'columnG%,rectangular
G%.Fortran_orderG7\"\"\"\";F1\"#\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%2snapshot_intervalG\"\"&" }}{PARA 13 "" 1 "" {GLPLOT2D 302 289 289 
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urve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve
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urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve
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urve 81" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 653 "# SAME EXPERIM
ENT, BUT THIS TIME NORMALIZE POPULATION \n# IN ORDER TO SEE BETTER WHA
T'S HAPPENING TO THE AGE-DISTRIBUTION\nN:=Vector([2,seq(1,a=1..80)]);
\nN:=normaliz(N);\nhisto[0]:=my_histogram(N,\"0\",magenta):\nsnapshot_
interval:=5;  # ONLY MAKE A SNAPSHOT EVERY SO MANY TIMESTEPS\ncount:=0
:\nfor t from 1 to 120 do\n   N:= A . N;\n   N:=normaliz(N);\n   if( t
 mod snapshot_interval = 0 ) then\n      count:=count+1;\n      histo[
count]:=my_histogram(N,convert(t,string),magenta):\n   end if;\nend do
: unassign('t'):\nplots[display]( seq( histo[0], c=0..10),\n          \+
      seq( histo[c], c=0..count ), \n                seq( histo[count]
, c=0..10),insequence=true );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"N
G-%'RTABLEG6*\"*7\">g8%)anythingG&%'VectorG6#%'columnG%,rectangularG%.
Fortran_orderG7\"\"\"\";F1\"#\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
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