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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 207 0 "" }{TEXT 200 0 "" }{TEXT 
200 33 "Modello SIR a popolazione chiusa\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 210 9 "Equazioni" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "e
qSIR := diff(S(t),t) + mybeta* S(t)*Y(t) = 0, diff(Y(t),t) - mybeta* S
(t)*Y(t)+mygamma*Y(t)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/,&-I%diff
G%*protectedG6$-I\"SG6\"6#I\"tGF+F-\"\"\"*(I'mybetaGF+F.F)F.-I\"YGF+F,
F.F.\"\"!/,(-F&6$F1F-F.F/!\"\"*&I(mygammaGF+F.F1F.F.F3" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 210 19 "Condizioni iniziali" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 28 "ini := S(0) = 100, Y(0) = 1;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$/-I\"SG6\"6#\"\"!\"$+\"/-I\"YGF&F'\"\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 210 20 "Valore dei parametri" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "mygamma := 1; mybeta := 0.1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "
$\"\"\"!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 20 "Risoluzione nume
rica" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "solSIR := dsolve(\{
eqSIR,ini\},\{S(t),Y(t)\},type = numeric);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "f*6#I(x_rkf45G6\"6)I$resGF%I%dataGF%I%varsGF%I)solnprocGF
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F'-F*6#/Faq7$Ffr-I#opGF:6#FfsYQKinitial~values~must~be~specified~in~a~
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e' la soluzione?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "solSIR(
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{EXCHG {PARA 0 "" 0 "" {TEXT 210 31 "ora vogliamo vederne un grafico" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 210 30 "gli infetti Y in funzione di t" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "odeplot(solSIR,[t,Y(t)],0..1
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{TEXT 211 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 81 "aggiungendo l'o
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%>T!#=$\"2yVp<T&zrB!#=7$$\"1\\')=wG%*=T!#=$\"2DtCkX,cD#!#=7$$\"1i5alv[
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#=$\"2&[5_#\\__V\"!#=7$$\"2&pN59WF:T!#>$\"2mlCO]R\\O\"!#=7$$\"20)\\)*H
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\"13MW1%)[9T!#=$\"2f+*3AA+u6!#=7$$\"1[9hr;D9T!#=$\"1HZhkt[;6!#<7$$\"1o
hD[l-9T!#=$\"2xMaeW!zh5!#=7$$\"0yzoY7Q6%!#<$\"2Zjb,bt(45!#=7$$\"1'e&Q%
))3O6%!#=$\"1-'ofI^Ig*!#=7$$\"1o#oSG:M6%!#=$\"1`7Tm+gK\"*!#=7$$\"11bLu
6B8T!#=$\"1)H&po0>&o)!#=7$$\"1F)=94cI6%!#=$\"1`U@m()pf#)!#=7$$\"0\\%>%
f*)G6%!#<$\"1j]&pKb]&y!#=-%&COLORG6&%$RGBG$\"#5!\"\"$\"\"!!\"\"$\"\"!!
\"\"-%+AXESLABELSG6'Q\"S6\"Q\"Y6\"-%%FONTG6%%!G%!G\"#5%+HORIZONTALG%+H
ORIZONTALG-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%.UNCONSTRAINEDG" 1 2 2
 1 10 1 2 6 0 4 2 1.0 45.0 45.0 0 0 "Curve 1" }}{TEXT 211 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 208 0 "" }{TEXT 200 0 "" }{TEXT 200 32 "M
odello SIR a popolazione aperta" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 
12 "Le equazioni" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "eqSIRo
pen := diff(S(t),t) +mu*(S(t)-N) + mybeta* S(t)*Y(t) = 0, diff(Y(t),t)
 - mybeta* S(t)*Y(t)+mygamma*Y(t)+mu*Y(t)=0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%*eqSIRopenG6$/,(-%%diffG6$-%\"SG6#%\"tG%\"tG\"\"\"*&%
#muG\"\"\",&-%\"SG6#%\"tG\"\"\"%\"NG!\"\"\"\"\"\"\"\"*($\"\"\"!\"\"\"
\"\"-%\"SG6#%\"tG\"\"\"-%\"YG6#%\"tG\"\"\"\"\"\"\"\"!/,*-%%diffG6$-%\"
YG6#%\"tG%\"tG\"\"\"*($\"\"\"!\"\"\"\"\"-%\"SG6#%\"tG\"\"\"-%\"YG6#%\"
tG\"\"\"!\"\"-%\"YG6#%\"tG\"\"\"*&%#muG\"\"\"-%\"YG6#%\"tG\"\"\"\"\"\"
\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 62 "Aggiungiamo i parametri
 in piu' rispetto al modello precedente" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "mu := 0.01; N := 1000;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#muG$\"\"\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"%+5
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 24 "Risolviamo numericamente" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "solSIRopen := dsolve(\{eqSI
Ropen,ini\},\{S(t),Y(t)\},type = numeric);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%+solSIRopenGf*6#%(rkf45_xG6'%\"iG%(rkf45_sG%)outpoint
G%#r1G%#r2G6#%aoCopyright~(c)~1993~by~the~University~of~Waterloo.~All~
rights~reserved.G6\"C&>%)outpointG-%&evalfG6#%(rkf45_xG@$52-%$absG6#,$
%)outpointG!\"\"-%$absG6#,&&%,loc_controlG6#\"\"#\"\"\"%)outpointG!\"
\"4-%'memberG6$&%,loc_controlG6#\"\"'<*!\"#!\"\"\"\"\"\"\"#$\"\"\"\"\"
!$\"\"#\"\"!$!\"\"\"\"!$!\"#\"\"!C%>%,loc_controlG-%%copyG6#=6\"6#;\"
\"\"\"#LE\\[lB\"\"\"\"\"#\"\"#$\"\"!\"\"!\"\"$$\"\"!\"\"!\"\"%$\"\"\"!
\")\"\"&$\"\"\"!\")\"\"'\"\"\"\"\"($\"\"\"!\"*\"\")\"&++$\"\"*\"%+5\"#
5\"\"!\"#6\"\"!\"#7\"\"!\"#8\"\"!\"#9\"\"!\"#:\"\"!\"#;\"\"!\"#<\"\"!
\"#=\"\"!\"#>\"\"!\"#?$\"$+\"\"\"!\"#@$\"\"\"\"\"!\"#A\"\"!\"#B\"\"!\"
#C\"\"!\"#D\"\"!\"#E\"\"!\"#F\"\"!\"#G\"\"!\"#H\"\"!\"#I\"\"!\"#J\"\"!
\"#K\"\"!\"#L\"\"!>%'loc_y0G-%%copyG6#=6\"6#;\"\"\"\"\"#E\\[l#\"\"\"$
\"$+\"\"\"!\"\"#$\"\"\"\"\"!>%'loc_y1G-%%copyG6#=6\"6#;\"\"\"\"\"#E\\[
l!@$0-%$absG6#,$%)outpointG!\"\"\"\"!C$>&%,loc_controlG6#\"\"$%)outpoi
ntG@%1%'DigitsG-%'evalhfG6#%'DigitsGC$>%(rkf45_sG-%*traperrorG6#-%'eva
lhfG6#-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG-%$varG6#%,loc_control
G-%$varG6#%'loc_y0G-%$varG6#%'loc_y1G-%$varG6#%'loc_F1G-%$varG6#%'loc_
F2G-%$varG6#%'loc_F3G-%$varG6#%'loc_F4G-%$varG6#%'loc_F5G-%$varG6#%)lo
c_workG@$/%(rkf45_sG%*lasterrorGC%>%#r1G-%+searchtextG6$.%'evalhfG-%(c
onvertG6$-%#opG6$\"\"\"7#%(rkf45_sG%%nameG>%#r2G-%+searchtextG6$.%)har
dwareG-%(convertG6$-%#opG6$\"\"\"7#%(rkf45_sG%%nameG@%50%#r1G\"\"!0%#r
2G\"\"!-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG%,loc_controlG%'loc_y
0G%'loc_y1G%'loc_F1G%'loc_F2G%'loc_F3G%'loc_F4G%'loc_F5G%)loc_workG-%&
ERRORG6#%(rkf45_sG-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG%,loc_cont
rolG%'loc_y0G%'loc_y1G%'loc_F1G%'loc_F2G%'loc_F3G%'loc_F4G%'loc_F5G%)l
oc_workG7$/%\"tG%(rkf45_xG-%$seqG6$/&%$ordG6#,&%\"iG\"\"\"\"\"\"\"\"\"
&%'loc_y0G6#%\"iG/%\"iG;\"\"\"\"\"#6\"6%%,loc_controlG%'loc_y0G%'loc_y
1G6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "odeplot(solSIRopen
,[S(t),Y(t)],0..10);" }}{PARA 13 "" 1 "" {TEXT 211 0 "" }{GLPLOT2D 400
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yjIH8'*!#9$\"2D6#[89*)>h!#;7$$\"1zu1?B2yr!#9$\"18J+T^n;H!#97$$\"2:FDDl
H')z#!#:$\"1hSs#QMe\\'!#97$$\"1,x7lqw/w!#:$\"13LYG]ros!#97$$\"2Q.]8A0(
[H!#;$\"1\"3v[-a\"3l!#97$$\"2jC>5zc80#!#;$\"1jfBdjheb!#97$$\"2CoiI^XA+
#!#;$\"1`^wN:76Z!#97$$\"28mO%RHl\">#!#;$\"17*Q#GDJ+S!#97$$\"1[i.h;AuC!
#:$\"1K%o\\qXNT$!#97$$\"1;2df/v3G!#:$\"1=#o$p[NJH!#97$$\"1\"3klCe3=$!#
:$\"28'3q2E`ND!#:7$$\"1>ls\\Zx$e$!#:$\"2ya4:7\"f5A!#:7$$\"1W='>QvG,%!#
:$\"2DhTF\"*QP%>!#:7$$\"1[Zz$*Q&RY%!#:$\"1@a>S:`C<!#97$$\"1lg;E.lK\\!#
:$\"2Q%4na^[W:!#:7$$\"1%>S+ozUT&!#:$\"2n#[ryks'R\"!#:7$$\"1)HVIb9Q!f!#
:$\"2H&>a(H%pv7!#:7$$\"1Gd&3mKfR'!#:$\"2j5&[l2*o<\"!#:7$$\"1HK())o%4&)
o!#:$\"2\"RSP:jn'4\"!#:7$$\"1lnT<*QcO(!#:$\"2UW,$[75K5!#:7$$\"1K`R8!))
=$y!#:$\"1/)3+!en2)*!#:7$$\"1V673sEy#)!#:$\"1x*\\wobrS*!#:7$$\"1zrJ?WV
*p)!#:$\"1>V+mFI.\"*!#:7$$\"1l)oCYA/4*!#:$\"0Bzg=WE)))!#97$$\"00k%\\<z
Y%*!#9$\"18\\x4huL()!#:7$$\"1w(ez9*yk(*!#:$\"1V!)R%>*oY')!#:7$$\"2OY*z
70:/5!#:$\"1l^loJk7')!#:7$$\"1Og\"ox,v-\"!#9$\"13SZbC`B')!#:7$$\"2)o#
\\7#4XY5!#:$\"1%Qk3(*)yr')!#:7$$\"2t-\\=)Q.h5!#:$\"1w?(H<!>]()!#:7$$\"
2zl:_$eSr5!#:$\"1>`mp(z<&))!#:7$$\"22:A0(e$y2\"!#:$\"1b*e!H_')p*)!#:7$
$\"2#**HJgWp!3\"!#:$\"1m(=>)43)4*!#:7$$\"2&RV!*oUV!3\"!#:$\"0#=e'>+0B*
!#97$$\"2:*yV`dcx5!#:$\"1xEB1Hxh$*!#:7$$\"2)ftZa(HE2\"!#:$\"1^>Q6dE([*
!#:7$$\"2y!pJo'ph1\"!#:$\"1EpBU$zJg*!#:7$$\"2X3URv0(e5!#:$\"1J9=e^i1(*
!#:7$$\"2tEk!yOr]5!#:$\"1cINh#\\cz*!#:7$$\"2r%[Am'3E/\"!#:$\"1@aAb;?p)
*!#:7$$\"2m0HbyNZ.\"!#:$\"0_v_&f0F**!#97$$\"1P#=06mt-\"!#9$\"1RA_.6pp*
*!#:7$$\"2A'pGVzp?5!#:$\"1QRoC'\\\")***!#:7$$\"1(zuk#>'[,\"!#9$\"2aX&z
B()Q,5!#:7$$\"1FX0#zG*45!#9$\"2aNELni=+\"!#:7$$\"2ENMcd=f+\"!#:$\"2'QP
<$eA9+\"!#:7$$\"2^GGWK5G+\"!#:$\"1)3Va^c-+\"!#97$$\"2#[R)3d^0+\"!#:$\"
0b[A4fa)**!#97$$\"1eq<N3n!***!#:$\"1.bO+(*ek**!#:-%&COLORG6&%$RGBG$\"#
5!\"\"$\"\"!!\"\"$\"\"!!\"\"-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%.UNC
ONSTRAINEDG" 1 2 2 1 10 1 2 6 0 4 2 1.0 45.0 45.0 0 0 "Curve 1" }}
{TEXT 211 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 85 "la soluzione te
nde all'equilibrio con poche oscillazioni. Lo rivediamo guardando Y(t)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "odeplot(solSIRopen,[t,Y
(t)],0..10);" }}{PARA 13 "" 1 "" {TEXT 211 0 "" }{GLPLOT2D 400 300 300
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1%Qk3(*)yr')!#:7$$\"+))*[C7'!\"*$\"1w?(H<!>]()!#:7$$\"+@1`Ej!\"*$\"1>`
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210 42 "Dobbiamo riassegnare (credo!) l'equazione:" }}}{EXCHG {PARA 0 
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[*)!#;7$$\"$)=!\"\"$\"29U[;`#[m5!#<7$$\"$*=!\"\"$\"2P^h,v_HH\"!#<7$$\"
$!>!\"\"$\"1^#3ai<\\e\"!#;7$$\"$\">!\"\"$\"1M*[v$4P\\>!#;7$$\"$#>!\"\"
$\"2Qs8!4!fIQ#!#<7$$\"$$>!\"\"$\"1,?-x5gjG!#;7$$\"$%>!\"\"$\"1<5V&fE?M
$!#;7$$\"$&>!\"\"$\"1&[#*Rq:Xu$!#;7$$\"$'>!\"\"$\"1hhta!y1*R!#;7$$\"$(
>!\"\"$\"2lk$oC;0DS!#<7$$\"$)>!\"\"$\"1iwL.(fK%Q!#;7$$\"$*>!\"\"$\"1Kg
BTn3$\\$!#;7$$\"$+#!\"\"$\"1.G9c'o-0$!#;-%*THICKNESSG6#\"\"$-%&STYLEG6
#%%LINEG-%%VIEWG6$;$\"\"!!\"\"$\"$+#!\"\";$\"\"!!\"\"$\"#5!\"\"-%+AXES
LABELSG6'Q\"t6\"Q\"Y6\"-%%FONTG6%%0Times~New~RomanG%&ROMANG\"#;%+HORIZ
ONTALG%+HORIZONTALG-%&COLORG6&%$RGBG$\"#5!\"\"$\"\"!!\"\"$\"\"!!\"\"-%
%FONTG6#%0Times~New~RomanG-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%.UNCON
STRAINEDG" 1 2 2 1 10 1 2 6 0 4 2 1.0 45.0 45.0 0 0 "Curve 1" "Curve 2
" }}{TEXT 211 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 115 "tramite \"
view\" abbiamo assegnato gli assi (questo e' particolarmente utile qua
ndo si vogliono sovrapporre grafici)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT
 209 0 "" }{TEXT 200 0 "" }{TEXT 200 34 "Modello SEIRS a popolazione a
perta" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "eqSEIR := diff(S(
t),t) +mu*(S(t)-N) + mybeta* S(t)*Y(t) -mydelta*(N-S(t)-E(t)-Y(t))= 0,
 diff(E(t),t) - mybeta* S(t)*Y(t)+nu*E(t)+mu*E(t),diff(Y(t),t) -nu*E(t
)+mygamma*Y(t)+mu*Y(t)=0;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 38 "Ass
egnamo un valore ai nuovi parametri" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "mydelta := 0.1; nu := 26;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 210 45 "Creiamo delle nuove condizioni  iniziali (3d)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "ini3 := S(0) = 100, E(0) =0.
5, Y(0) = 0.2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "solSEIR :
= dsolve(\{eqSEIR,ini3\},\{S(t),E(t),Y(t)\},type = numeric);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "odeplot(solSEIR,[S(t),Y(t)],
0..10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 101 "se uno confronta que
sto grafico con il precedente, vede che le oscillazioni sono molto piu
' marcate!." }}{PARA 0 "" 0 "" {TEXT 210 23 "Proviamo a sovrapporli." 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 118 "Usiamo DEplot (piu' bello). I
l trucco essenziale e' di assegnare DEplot (o altre istruzioni grafich
e) a una variabile:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "pl1:
=DEplot(\{eqSIRopen\},\{S(t),Y(t)\},t=0..20,[[S(0)=100,Y(0)=1]],stepsi
ze=.1,\n" }{MPLTEXT 1 0 60 "method=rkf45,arrows=none,linecolour=red,vi
ew=[0..130,0..5]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 183 "Ho termin
ato l'istruzione con \":\" se avessi terminato con \";\" l'output sare
bbe stato una sfilza di istruzioni incomprensibili. Per vedere il graf
ico creato, basta farsi mostrare \"pl1\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "pl1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 40 "Adesso c
ostruiamo una soluzione del SEIR" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 102 "pl2:=DEplot(\{eqSEIR\},\{S(t),E(t),Y(t)\},t=0..20,[[S(0)=100
,E(0)=0.8,Y(0)=0.2]],scene=[S,Y],stepsize=.1,\n" }{MPLTEXT 1 0 33 "met
hod=rkf45,view=[0..130,0..5]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 
64 "usando l'istruzione \"display\" si mostrano i grafici sovrapposti:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(pl1,pl2);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 210 190 "La differenza fra i due modelli \+
e' che non solo SEIRS ha il periodo di incubazione, ma ha anche i rimo
ssi che ridiventano suscettibili. Per eliminare quest'ultimo effetto, \+
poniamo delta = 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "myde
lta := 0; eqSEIR := diff(S(t),t) +mu*(S(t)-N) + mybeta* S(t)*Y(t) -myd
elta*(N-S(t)-E(t)-Y(t))= 0, diff(E(t),t) - mybeta* S(t)*Y(t)+nu*E(t)+m
u*E(t),diff(Y(t),t) -nu*E(t)+mygamma*Y(t)+mu*Y(t)=0;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 102 "pl3:=DEplot(\{eqSEIR\},\{S(t),E(t),Y(t)
\},t=0..20,[[S(0)=100,E(0)=0.8,Y(0)=0.2]],scene=[S,Y],stepsize=.1,\n" 
}{MPLTEXT 1 0 33 "method=rkf45,view=[0..120,0..2]):" }}}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 77 "pl1:=DEplot(\{eqSIRopen\},\{S(t),Y(t)\},t=
0..20,[[S(0)=100,Y(0)=1]],stepsize=.1,\n" }{MPLTEXT 1 0 60 "method=rkf
45,arrows=none,linecolour=red,view=[0..120,0..2]):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 18 "display (pl1,pl3);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT 210 61 "la temporaneita' dell'immunita' era la differenza pri
ncipale!" }}{PARA 0 "" 0 "" {TEXT 210 28 "Guardiamo ora le curve Y(t):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "pl1:=DEplot(\{eqSIRopen
\},\{S(t),Y(t)\},t=0..20,[[S(0)=100,Y(0)=1]],scene=[t,Y],stepsize=.1,
\n" }{MPLTEXT 1 0 61 "method=rkf45,arrows=none,linecolour=red,view=[0.
.20,0..1.5]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "pl3:=DEpl
ot(\{eqSEIR\},\{S(t),E(t),Y(t)\},t=0..20,[[S(0)=100,E(0)=0.8,Y(0)=0.2]
],scene=[t,Y],stepsize=.1,\n" }{MPLTEXT 1 0 34 "method=rkf45,view=[0..
20,0..1.5]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(pl1
,pl3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 128 "le oscillazioni nel S
EIR sono piu' smorzate (ma puo' dipendere dalle condizioni iniziali) e
 di periodo sensibilmente piu' lungo." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2
 33 1 1 }