{VERSION 5 0 "IBM INTEL NT" "5.0" }
{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 }{PSTYLE "Title
" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }
3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" 
-1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 
2 0 1 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 10 "AIDS Model" }}{PARA 19 "
" 0 "" {TEXT -1 15 "file:  aids.mws" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 111 "The model is based on the work in Anderson and May, and report
ed in Murray.  Extensions are based on the papers" }}{PARA 0 "" 0 "" 
{TEXT -1 44 "by Castillo-Chavez, Cooke, Huang, and Levin." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart; with(DEtools): with(plots)
:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "Variables:  S=susceptibles,
 In=infectives (HIV positive), A=full blown AIDS, Z=HIV positive not i
nfectious did not" }}{PARA 0 "" 0 "" {TEXT -1 12 "develop AIDS" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 110 "Paramete
rs:  B=immigration rate into susceptibles,  mu= natural death rate,  l
ambda= probabilitiy of acquiring" }}{PARA 0 "" 0 "" {TEXT -1 119 "infe
ction from a randomly chosen partner = beta*In/N where beta=transmissi
on probability, c= number of sexual partners," }}{PARA 0 "" 0 "" 
{TEXT -1 66 "d=AIDS death rate, v= rate of conversion from HIV positiv
e to AIDS" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "N(t) := S(t)+I
n(t)+A(t)+Z(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "odes :=
 diff(S(t),t)= B - mu*S(t) -beta*In(t)*S(t)/N(t),diff(In(t),t)=beta*In
(t)*S(t)/N(t)-(v+mu)*In(t), diff(A(t),t)=p*v*In(t)-(d+mu)*A(t),diff(Z(
t),t)=(1-p)*v*In(t)-mu*Z(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 45 "ICs := A(0)=0, Z(0)=0, S(0)=99900, In(0)=100;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 70 "B:= 13333.3; v:=0.2; mu := 1.0/32; d:= 1.
0; p:=0.3; beta:=5.15*v;c:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 82 "soln:=dsolve(\{odes,ICs\},\{S(t),In(t),Z(t),A(t)\},type=numeric,
output=listprocedure);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "s
 := subs(soln,S(t)); i:=subs(soln,In(t));a:=subs(soln,A(t)); z:=subs(s
oln,Z(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(\{i(t),a
(t)\},t=0..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "12" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 
1 1 }