{VERSION 4 0 "IBM INTEL NT" "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 "Geneva" 0 10 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "H eading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } 1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Monaco" 0 9 0 0 255 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 257 1 {CSTYLE "" -1 -1 "Geneva" 0 12 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 258 1 {CSTYLE "" -1 -1 "Geneva" 0 10 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "T his is all the Maple syntax in" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 4 "" 0 "" {TEXT -1 24 "Chapter 10, Section 10.5" }}{PARA 4 "" 0 "" {TEXT -1 75 "An Introduction to the Mathematics of Biology, with Co mputer Algebra Models" }}{PARA 4 "" 0 "" {TEXT -1 34 "by Yeargers, Sho nkwiler, & Herod. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 376 " This worksheet provides a Maple 6 version of the s yntax in Section 10.5. The share library is not used in this version a s it is in the text. Rather, we use the numerical calculations in dsol ve(numeric). We plot the graphs after each new mutation is added. This gives more graphs than 10.5.1, 10.5.2, and 10.5.3. We indicate whic h plots correspond to those in the text." }}{PARA 0 "" 0 "" {TEXT -1 56 " The following lines appear on page 352 of the text" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "a:=5: b:=4: c:=5: g:=1: h:=1: k:=1:\nNdiv:=c *g/(a*k-b*h);" }}}{PARA 0 "" 0 "" {TEXT -1 124 "The following syntax m akes an initialization for the first mutation. It replaces the initial ization on page 354 of the text." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "initial:=v1(0)=5/100,v2(0)=0,v3(0)=0,\n\011v4(0)=0,v5(0)=0,v6 (0)=0,\n\011x1(0)=0,x2(0)=0,x3(0)=0,\n\011x4(0)=0,x5(0)=0,x6(0)=0,\n \011\011z(0)=0;" }}}{PARA 0 "" 0 "" {TEXT -1 103 "The following syntax sets up the differential equations and replaces thesyntax on page 353 of the text." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 870 "sol1:=dsol ve(\{diff(v1(t),t)=(a-b*z(t)-c*x1(t))*v1(t),\n\011diff(v2(t),t)=(a-b*z (t)-c*x2(t))*v2(t),\n\011diff(v3(t),t)=(a-b*z(t)-c*x3(t))*v3(t),\n\011 diff(v4(t),t)=(a-b*z(t)-c*x4(t))*v4(t),\n\011diff(v5(t),t)=(a-b*z(t)-c *x5(t))*v5(t),\n\011diff(v6(t),t)=(a-b*z(t)-c*x6(t))*v6(t),\n\011diff( x1(t),t)=g*v1(t)-k*x1(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011d iff(x2(t),t)=g*v2(t)-k*x2(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n \011diff(x3(t),t)=g*v3(t)-k*x3(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t) ),\n\011diff(x4(t),t)=g*v4(t)-k*x4(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v 6(t)),\n\011diff(x5(t),t)=g*v5(t)-k*x5(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5( t)+v6(t)),\n\011diff(x6(t),t)=g*v6(t)-k*x6(t)*(v1(t)+v2(t)+v3(t)+v4(t) +v5(t)+v6(t)),\n\011diff(z(t),t)=(h-k*z(t))*(v1(t)+v2(t)+v3(t)+v4(t)+v 5(t)+v6(t)),\n\011\011initial\},\n\011\{v1(t),v2(t),v3(t),v4(t),v5(t), v6(t),\n\011\011x1(t),x2(t),x3(t),x4(t),x5(t),x6(t),z(t)\},\n\011numer ic,output=listprocedure);" }}}{PARA 0 "" 0 "" {TEXT -1 60 "The followi ng lines will set up the plot as in Figure 10.5.1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v1sol1:=subs(sol1,v1(t)); \n v2sol1:=subs(s ol1,v2(t));\n v3sol1:=subs(sol1,v3(t));\n v4sol1:=subs(sol1,v4(t)); \n v5sol1:=subs(sol1,v5(t));\n v6sol1:=subs(sol1,v6(t));\n x1sol1:= subs(sol1,x1(t)); \n x2sol1:=subs(sol1,x2(t));\n x3sol1:=subs(sol1,x 3(t));\n x4sol1:=subs(sol1,x4(t));\n x5sol1:=subs(sol1,x5(t));\n x6 sol1:=subs(sol1,x6(t));\n zsol1:=subs(sol1,z(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(['t','v1sol1(t)','t'=0..10]);" }}} {PARA 0 "" 0 "" {TEXT -1 128 "The following syntax intitializes the sy stem to allow for a second mutation. This replaces the syntax at the b ottom of page 354." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 180 "initi al:=v1(1/2)=v1sol1(1/2),v2(1/2)=1/100,v3(1/2)=0,\n\011v4(1/2)=0,v5(1/2 )=0,v6(1/2)=0,\n\011x1(1/2)=x1sol1(1/2),x2(1/2)=0,x3(1/2)=0,\n\011x4(1 /2)=0,x5(1/2)=0,x6(1/2)=0,\n\011\011z(1/2)=zsol1(1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 870 "sol2:=dsolve(\{diff(v1(t),t)=(a-b* z(t)-c*x1(t))*v1(t),\n\011diff(v2(t),t)=(a-b*z(t)-c*x2(t))*v2(t),\n \011diff(v3(t),t)=(a-b*z(t)-c*x3(t))*v3(t),\n\011diff(v4(t),t)=(a-b*z( t)-c*x4(t))*v4(t),\n\011diff(v5(t),t)=(a-b*z(t)-c*x5(t))*v5(t),\n\011d iff(v6(t),t)=(a-b*z(t)-c*x6(t))*v6(t),\n\011diff(x1(t),t)=g*v1(t)-k*x1 (t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x2(t),t)=g*v2(t)- k*x2(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x3(t),t)=g*v3 (t)-k*x3(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x4(t),t)= g*v4(t)-k*x4(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x5(t) ,t)=g*v5(t)-k*x5(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x 6(t),t)=g*v6(t)-k*x6(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011di ff(z(t),t)=(h-k*z(t))*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011\011 initial\},\n\011\{v1(t),v2(t),v3(t),v4(t),v5(t),v6(t),\n\011\011x1(t), x2(t),x3(t),x4(t),x5(t),x6(t),z(t)\},\n\011numeric,output=listprocedur e);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v1sol2:=subs(sol2,v 1(t)); \n v2sol2:=subs(sol2,v2(t));\n v3sol2:=subs(sol2,v3(t));\n v 4sol2:=subs(sol2,v4(t));\n v5sol2:=subs(sol2,v5(t));\n v6sol2:=subs( sol2,v6(t));\n x1sol2:=subs(sol2,x1(t)); \n x2sol2:=subs(sol2,x2(t)) ;\n x3sol2:=subs(sol2,x3(t));\n x4sol2:=subs(sol2,x4(t));\n x5sol2: =subs(sol2,x5(t));\n x6sol2:=subs(sol2,x6(t));\n zsol2:=subs(sol2,z( t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "plot(\{['t','v1sol 1(t)','t'=0..1/2],['t','v1sol2(t)','t'=1/2..10],\n\011['t','v2sol2(t)' ,'t'=1/2..10]\},color=black);" }}}{PARA 0 "" 0 "" {TEXT -1 181 "The fo llowing syntax intitializes for a third mutation. It follows the first infection and first mutation until t = 1. At that time, a new mutatio n occurrs. It is initialized as v3." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "initial:=v1(1)=v1sol2(1),v2(1)=v2sol2(1),v3(1)=1/100 ,\n\011v4(1)=0,v5(1)=0,v6(1)=0,\n\011x1(1)=x1sol2(1),x2(1)=x2sol2(1),x 3(1)=0,\n\011x4(1)=0,x5(1)=0,x6(1)=0,\n\011\011z(1)=zsol2(1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 870 "sol3:=dsolve(\{diff(v1(t),t )=(a-b*z(t)-c*x1(t))*v1(t),\n\011diff(v2(t),t)=(a-b*z(t)-c*x2(t))*v2(t ),\n\011diff(v3(t),t)=(a-b*z(t)-c*x3(t))*v3(t),\n\011diff(v4(t),t)=(a- b*z(t)-c*x4(t))*v4(t),\n\011diff(v5(t),t)=(a-b*z(t)-c*x5(t))*v5(t),\n \011diff(v6(t),t)=(a-b*z(t)-c*x6(t))*v6(t),\n\011diff(x1(t),t)=g*v1(t) -k*x1(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x2(t),t)=g*v 2(t)-k*x2(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x3(t),t) =g*v3(t)-k*x3(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x4(t ),t)=g*v4(t)-k*x4(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff( x5(t),t)=g*v5(t)-k*x5(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011d iff(x6(t),t)=g*v6(t)-k*x6(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n \011diff(z(t),t)=(h-k*z(t))*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n \011\011initial\},\n\011\{v1(t),v2(t),v3(t),v4(t),v5(t),v6(t),\n\011 \011x1(t),x2(t),x3(t),x4(t),x5(t),x6(t),z(t)\},\n\011numeric,output=li stprocedure);" }}}{PARA 0 "" 0 "" {TEXT -1 50 "We set up the a to make the plot of Figure 10.5.2." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v1sol3:=subs(sol3,v1(t)); \n v2sol3:=subs(sol3,v2(t));\n v3sol3 :=subs(sol3,v3(t));\n v4sol3:=subs(sol3,v4(t));\n v5sol3:=subs(sol3, v5(t));\n v6sol3:=subs(sol3,v6(t));\n x1sol3:=subs(sol3,x1(t)); \n \+ x2sol3:=subs(sol3,x2(t));\n x3sol3:=subs(sol3,x3(t));\n x4sol3:=subs (sol3,x4(t));\n x5sol3:=subs(sol3,x5(t));\n x6sol3:=subs(sol3,x6(t)) ;\n zsol3:=subs(sol3,z(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 199 "plot(\{['t','v1sol1(t)','t'=0..1/2],['t','v1sol2(t)','t'=1/2..1 ],\n \011['t','v1sol3(t)','t'=1..10],\n\011['t','v2sol2(t)','t'=1/2.. 1],['t','v2sol3(t)','t'=1..10],\n\011['t','v3sol3(t)','t'=1..10]\},col or=black);" }}}{PARA 0 "" 0 "" {TEXT -1 190 "The following syntax inti tializes for a 3rd mutation. It follows the first infection and the fi rst two mutations until t = 3/2. At that time, a new mutation occurrs. It is initialized as v4." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 220 "initial:=v1(3/2)=v1sol3(3/2),v2(3/2)=v2sol3(3/2),v3(3/2)=v3sol3(3 /2),\n\011v4(3/2)=1/100,v5(3/2)=0,v6(3/2)=0,\n\011x1(3/2)=x1sol3(3/2), x2(3/2)=x2sol3(3/2),x3(3/2)=x3sol3(3/2),\n\011x4(3/2)=0,x5(3/2)=0,x6(3 /2)=0,\n\011\011z(3/2)=zsol3(3/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 870 "sol4:=dsolve(\{diff(v1(t),t)=(a-b*z(t)-c*x1(t))*v1(t ),\n\011diff(v2(t),t)=(a-b*z(t)-c*x2(t))*v2(t),\n\011diff(v3(t),t)=(a- b*z(t)-c*x3(t))*v3(t),\n\011diff(v4(t),t)=(a-b*z(t)-c*x4(t))*v4(t),\n \011diff(v5(t),t)=(a-b*z(t)-c*x5(t))*v5(t),\n\011diff(v6(t),t)=(a-b*z( t)-c*x6(t))*v6(t),\n\011diff(x1(t),t)=g*v1(t)-k*x1(t)*(v1(t)+v2(t)+v3( t)+v4(t)+v5(t)+v6(t)),\n\011diff(x2(t),t)=g*v2(t)-k*x2(t)*(v1(t)+v2(t) +v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x3(t),t)=g*v3(t)-k*x3(t)*(v1(t)+v 2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x4(t),t)=g*v4(t)-k*x4(t)*(v1( t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x5(t),t)=g*v5(t)-k*x5(t)* (v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x6(t),t)=g*v6(t)-k*x6 (t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(z(t),t)=(h-k*z(t) )*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011\011initial\},\n\011\{v1 (t),v2(t),v3(t),v4(t),v5(t),v6(t),\n\011\011x1(t),x2(t),x3(t),x4(t),x5 (t),x6(t),z(t)\},\n\011numeric,output=listprocedure);" }}}{PARA 0 "" 0 "" {TEXT -1 76 "We set up to make the plot of the first infection an d these three mutations." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v1sol4:=subs(sol4,v1(t)); \n v2sol4:=subs(sol4,v2(t));\n v3sol4:=su bs(sol4,v3(t));\n v4sol4:=subs(sol4,v4(t));\n v5sol4:=subs(sol4,v5(t ));\n v6sol4:=subs(sol4,v6(t));\n x1sol4:=subs(sol4,x1(t)); \n x2so l4:=subs(sol4,x2(t));\n x3sol4:=subs(sol4,x3(t));\n x4sol4:=subs(sol 4,x4(t));\n x5sol4:=subs(sol4,x5(t));\n x6sol4:=subs(sol4,x6(t));\n \+ zsol4:=subs(sol4,z(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 324 "plot(\{['t','v1sol1(t)','t'=0..1/2],['t','v1sol2(t)','t'=1/2..1], \n \011['t','v1sol3(t)','t'=1..3/2],['t','v1sol4(t)','t'=3/2..10],\n \011['t','v2sol2(t)','t'=1/2..1],['t','v2sol3(t)','t'=1..3/2],\n['t',' v2sol4(t)','t'=3/2..10],\n\011['t','v3sol3(t)','t'=1..3/2],['t','v3sol 4(t)','t'=3/2..10],\n['t','v4sol4(t)','t'=3/2..10]\},color=black);" }} }{PARA 0 "" 0 "" {TEXT -1 190 "The following syntax intitializes for a 4rd mutation. It follows the first infection and the first three muta tions until t = 2. At that time, a new mutation occurrs. It is initial ized as v5." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "initial:=v1( 2)=v1sol4(2),v2(2)=v2sol4(2),v3(2)=v3sol4(2),\n\011v4(2)=v4sol4(2),v5( 2)=1/100,v6(2)=0,\n\011x1(2)=x1sol4(2),x2(2)=x2sol4(2),x3(2)=x3sol4(2) ,\n\011x4(2)=x4sol4(2),x5(2)=0,x6(2)=0,\n\011\011z(2)=zsol4(2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 870 "sol5:=dsolve(\{diff(v1(t),t )=(a-b*z(t)-c*x1(t))*v1(t),\n\011diff(v2(t),t)=(a-b*z(t)-c*x2(t))*v2(t ),\n\011diff(v3(t),t)=(a-b*z(t)-c*x3(t))*v3(t),\n\011diff(v4(t),t)=(a- b*z(t)-c*x4(t))*v4(t),\n\011diff(v5(t),t)=(a-b*z(t)-c*x5(t))*v5(t),\n \011diff(v6(t),t)=(a-b*z(t)-c*x6(t))*v6(t),\n\011diff(x1(t),t)=g*v1(t) -k*x1(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x2(t),t)=g*v 2(t)-k*x2(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x3(t),t) =g*v3(t)-k*x3(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x4(t ),t)=g*v4(t)-k*x4(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff( x5(t),t)=g*v5(t)-k*x5(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011d iff(x6(t),t)=g*v6(t)-k*x6(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n \011diff(z(t),t)=(h-k*z(t))*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n \011\011initial\},\n\011\{v1(t),v2(t),v3(t),v4(t),v5(t),v6(t),\n\011 \011x1(t),x2(t),x3(t),x4(t),x5(t),x6(t),z(t)\},\n\011numeric,output=li stprocedure);" }}}{PARA 0 "" 0 "" {TEXT -1 75 "We set up to make the p lot of the first infection and these four mutations." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v1sol5:=subs(sol5,v1(t)); \n v2sol5:=su bs(sol5,v2(t));\n v3sol5:=subs(sol5,v3(t));\n v4sol5:=subs(sol5,v4(t ));\n v5sol5:=subs(sol5,v5(t));\n v6sol5:=subs(sol5,v6(t));\n x1sol 5:=subs(sol5,x1(t)); \n x2sol5:=subs(sol5,x2(t));\n x3sol5:=subs(sol 5,x3(t));\n x4sol5:=subs(sol5,x4(t));\n x5sol5:=subs(sol5,x5(t));\n \+ x6sol5:=subs(sol5,x6(t));\n zsol5:=subs(sol5,z(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 463 "plot(\{['t','v1sol1(t)','t'=0..1/2 ],['t','v1sol2(t)','t'=1/2..1],\n \011['t','v1sol3(t)','t'=1..3/2],[' t','v1sol4(t)','t'=3/2..2],\n['t','v1sol5(t)','t'=2..10],\n\011['t','v 2sol2(t)','t'=1/2..1],['t','v2sol3(t)','t'=1..3/2],\n['t','v2sol4(t)', 't'=3/2..2],['t','v2sol5(t)','t'=2..10],\n\011['t','v3sol3(t)','t'=1.. 3/2],['t','v3sol4(t)','t'=3/2..2],\n['t','v3sol5(t)','t'=2..10],\n['t' ,'v4sol4(t)','t'=3/2..2],['t','v4sol5(t)','t'=2..10],\n['t','v5sol5(t) ','t'=2..10]\},color=black);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 191 "The following syntax intitiali zes for a 5th mutation. It follows the first infection and the first f our mutations until t = 5/2. At that time, a new mutation occurrs. It \+ is initialized as v6." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 260 "in itial:=v1(5/2)=v1sol5(5/2),v2(5/2)=v2sol5(5/2),v3(5/2)=v3sol5(5/2),\n \011v4(5/2)=v4sol5(5/2),v5(5/2)=v5sol5(5/2),v6(5/2)=1/100,\n\011x1(5/2 )=x1sol5(5/2),x2(5/2)=x2sol5(5/2),x3(5/2)=x3sol5(5/2),\n\011x4(5/2)=x4 sol5(5/2),x5(5/2)=x5sol5(5/2),x6(5/2)=0,\n\011\011z(5/2)=zsol5(5/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 870 "sol6:=dsolve(\{diff(v1(t ),t)=(a-b*z(t)-c*x1(t))*v1(t),\n\011diff(v2(t),t)=(a-b*z(t)-c*x2(t))*v 2(t),\n\011diff(v3(t),t)=(a-b*z(t)-c*x3(t))*v3(t),\n\011diff(v4(t),t)= (a-b*z(t)-c*x4(t))*v4(t),\n\011diff(v5(t),t)=(a-b*z(t)-c*x5(t))*v5(t), \n\011diff(v6(t),t)=(a-b*z(t)-c*x6(t))*v6(t),\n\011diff(x1(t),t)=g*v1( t)-k*x1(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x2(t),t)=g *v2(t)-k*x2(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x3(t), t)=g*v3(t)-k*x3(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011diff(x4 (t),t)=g*v4(t)-k*x4(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n\011dif f(x5(t),t)=g*v5(t)-k*x5(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)),\n \011diff(x6(t),t)=g*v6(t)-k*x6(t)*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t) ),\n\011diff(z(t),t)=(h-k*z(t))*(v1(t)+v2(t)+v3(t)+v4(t)+v5(t)+v6(t)), \n\011\011initial\},\n\011\{v1(t),v2(t),v3(t),v4(t),v5(t),v6(t),\n\011 \011x1(t),x2(t),x3(t),x4(t),x5(t),x6(t),z(t)\},\n\011numeric,output=li stprocedure);" }}}{PARA 0 "" 0 "" {TEXT -1 75 "We set up to make the p lot of the first infection and these five mutations." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 361 "v1sol6:=subs(sol6,v1(t)); \n v2sol6:=su bs(sol6,v2(t));\n v3sol6:=subs(sol6,v3(t));\n v4sol6:=subs(sol6,v4(t ));\n v5sol6:=subs(sol6,v5(t));\n v6sol6:=subs(sol6,v6(t));\n x1sol 6:=subs(sol6,x1(t)); \n x2sol6:=subs(sol6,x2(t));\n x3sol6:=subs(sol 6,x3(t));\n x4sol6:=subs(sol6,x4(t));\n x5sol6:=subs(sol6,x5(t));\n \+ x6sol6:=subs(sol6,x6(t));\n zsol6:=subs(sol6,z(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 657 "plot(\{['t','v1sol1(t)','t'=0..1/2 ],['t','v1sol2(t)','t'=1/2..1],\n \011['t','v1sol3(t)','t'=1..3/2],[' t','v1sol4(t)','t'=3/2..2],\n\011['t','v1sol5(t)','t'=2..5/2],['t','v1 sol6(t)','t'=5/2..15],\n\011['t','v2sol2(t)','t'=1/2..1],['t','v2sol3( t)','t'=1..3/2],\n\011['t','v2sol4(t)','t'=3/2..2],['t','v2sol5(t)','t '=2..5/2],\n\011['t','v2sol6(t)','t'=5/2..15],\n\011['t','v3sol3(t)',' t'=1..3/2],['t','v3sol4(t)','t'=3/2..2],\n\011['t','v3sol5(t)','t'=2.. 5/2],['t','v3sol6(t)','t'=5/2..15],\n\011['t','v4sol4(t)','t'=3/2..2], ['t','v4sol5(t)','t'=2..5/2],\n\011['t','v4sol6(t)','t'=5/2..15],\n \011['t','v5sol5(t)','t'=2..5/2],['t','v5sol6(t)','t'=5/2..15],\n\011[ 't','v6sol6(t)','t'=5/2..15]\},color=red);" }}}{PARA 0 "" 0 "" {TEXT -1 119 " Maple 6 syntax to replace that at the bottom of page 355 and \+ 356 follows. The resulting plot appears as Figure 10.5.4." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 357 "plot(\{['t','x1sol1(t)','t'=0..1/2 ],\n['t','x1sol2(t)+x2sol2(t)','t'=1/2..1],\n['t','x1sol3(t)+x2sol3(t) +x3sol3(t)','t'=1..3/2],\n['t','x1sol4(t)+x2sol4(t)+x3sol4(t)+x4sol4(t )','t'=3/2..2],\n['t','x1sol5(t)+x2sol5(t)+x3sol5(t)+x4sol5(t)+x5sol5( t)','t'=2..5/2],\n['t','x1sol6(t)+x2sol6(t)+x3sol6(t)+x4sol6(t)+x5sol6 (t)\n +x6sol6(t)','t'=5/2..10]\},color=BLACK);" }}}{PARA 0 "" 0 " " {TEXT -1 101 "Maple 6 syntax to draw the Figure 10.5.5 follows. This replaces the syntax in the middle of page 356." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 191 "plot(\{['t','zsol1(t)','t'=0..1/2],['t','zsol 2(t)','t'=1/2..1],\n['t','zsol3(t)','t'=1..3/2],['t','zsol4(t)','t'=3/ 2..2],\n['t','zsol5(t)','t'=2..5/2],['t','zsol6(t)','t'=5/2..10]\},col or=BLACK);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{MARK "1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }