{VERSION 4 0 "APPLE_PPC_MAC" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 
0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Modello SIR con mortalita'" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 27 "schema generale del modello" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 247 "eqSIRmor:=diff(S(t),t)=b(N(t))*(S(t)+(1-csi)
*Y(t)+N(t)-S(t)-Y(t))-muu(N(t))*S(t)-c(N(t))*S(t)*Y(t)/(N(t)),diff(Y(t
),t)=c(N(t))*S(t)*Y(t)/(N(t))-muu(N(t))*Y(t)-alfa*Y(t)-gama*Y(t),diff(
N(t),t)= b(N(t))*(N(t)-csi*Y(t)) - muu(N(t))*N(t) - alfa*Y(t); " }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "ora definiamo le funzioni che si u
sano." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Fertilita' costante:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "b := N -> b0;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 91 "Mortalita' che cresce linearmente (K e' l
a capacita' portante dove fertilita' = mortalita')" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "muu := N -> muu0+(b0-muu0)*N/K;" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "tas
so di contatto in genere cresce come N^a (a=0, non dipende da N; a=1, \+
il caso \"classico\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "c \+
:= N -> betta*N^a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eqSIRm
or;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "c(N);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "c(N(t));" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 29 "diamo dei valori ai parametri" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 84 "K := 500; alfa :=20; b0:= 0.02; muu0 := 0.01; csi :
=0; a:=0.5; betta := 10;gama:=50;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
19 "condizioni iniziali" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "
SIRmorini := S(0) = 450, Y(0) =1, N(0) = 460;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 66 "sol := dsolve(\{eqSIRmor,SIRmorini\},\{S(t),Y(t)
,N(t)\},type=numeric);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "so
l(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sol(20);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 395 "with(DEtools):DEplot(\{eqSI
Rmor\},[S(t),Y(t),N(t)],0..20,[[S(0)=450,Y(0)=1,N(0)=460]],scene=[t,S]
,stepsize=0.02,method=rkf45);\nwith(DEtools):DEplot(\{eqSIRmor\},[S(t)
,Y(t),N(t)],0..20,[[S(0)=450,Y(0)=1,N(0)=460]],scene=[t,N],stepsize=0.
02,method=rkf45);\nwith(DEtools):DEplot(\{eqSIRmor\},[S(t),Y(t),N(t)],
0..20,[[S(0)=450,Y(0)=1,N(0)=460]],scene=[S,Y],stepsize=0.02,method=rk
f45,view=[0..100,0..15]);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "S
i ha una grande epidemia, con crollo della popolazione, crollo degli i
nfetti e lenta risalita della popolazione." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Proviamo un'altra condizione in
iziale:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 323 "with(DEtools):D
Eplot(\{eqSIRmor\},[S(t),Y(t),N(t)],0..20,[[S(0)=135.21216644618448,Y(
0)=0.00001,N(0)=361.850270654633562]],scene=[t,S],stepsize=0.02,method
=rkf45);\nwith(DEtools):DEplot(\{eqSIRmor\},[S(t),Y(t),N(t)],0..20,[[S
(0)=135.21216644618448,Y(0)=0.00001,N(0)=361.850270654633562]],scene=[
t,N],stepsize=0.02,method=rkf45);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
60 "il grafico di N e S sono piu' sensati. Guardiamo anche Y(t):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 147 "DEplot(\{eqSIRmor\},[S(t),Y
(t),N(t)],0..20,[[S(0)=135.21216644618448,Y(0)=0.00001,N(0)=361.850270
654633562]],scene=[t,Y],stepsize=0.02,method=rkf45);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 158 "Si vedono delle violente epidemie ogni alcuni \+
anni. La violenza delle epidemie decresce, perche' in realta' si ha co
nvergenza (molto lenta!!) a un equilibrio." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 147 "DEplot(\{eqSIRmor\},[S(t),Y(t),N(t)],0..50,[[S(0)=
135.21216644618448,Y(0)=0.00001,N(0)=361.850270654633562]],scene=[t,Y]
,stepsize=0.05,method=rkf45);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "
per allungare la simulazione fino a t=50, ho dovuto allungare la steps
ize" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "31" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }