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changed initial condition of sinusoidal function
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Jack Chaillet committed Dec 3, 2021
1 parent 048f0cb commit a619969
Showing 1 changed file with 58 additions and 33 deletions.
91 changes: 58 additions & 33 deletions ODESRecombination-copy.R
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Original file line number Diff line number Diff line change
Expand Up @@ -155,6 +155,7 @@ SEAI<-function(t,y,p){
ratr = ((PRU+PRD)*wr)/(PSU+PSD+((PRU+PRD)*wr))
ratr1 = (PRU+PRD)/(PSU+PSD+PRU+PRD)
rats = (PSU+PSD)/(PSU+PSD+((PRU+PRD)*wr))
rats1 = (PSU+PSD)/(PSU+PSD+PRU+PRD)
#P1 = ratr1
#ps = 0.34
#gammainit = (ratr1*1)+(rats*ps)
Expand Down Expand Up @@ -215,13 +216,23 @@ SEAI<-function(t,y,p){
#dPSD.dt = -((1-sigma1)*b*((PSU+PSD)/N)*ws*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))-(sigma2*b*(PRD/N)*wr*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))-(sigma2*b*(PRU/N)*wr*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))- (b*(PSU/N)*ws*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (b*(PSD/N)*ws*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (muSD)*(PSD)#-(del*att*(1/N)*(ND+SD+AD)*PSD)
#dPRU.dt = -((1-sigma2)*b*((PRU+PRD)/N)*wr*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))-(sigma1*b*(PSD/N)*ws*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))-(sigma1*b*(PSU/N)*ws*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))- (b*(PRU/N)*wr*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (b*(PRD/N)*wr*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (muRU)*(PRU)#-(del*att*(1/N)*(NU+SU+AU)*PRU)
#dPRD.dt = -((1-sigma2)*b*((PRU+PRD)/N)*wr*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))-(sigma1*b*(PSD/N)*ws*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))-(sigma1*b*(PSU/N)*ws*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K))- (b*(PRU/N)*wr*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (b*(PRD/N)*wr*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (muRD)*(PRD)#-(del*att*(1/N)*(ND+SD+AD)*PRD)
dPSU.dt = ((NU+SU+AU)/N)*((1-r)*delS+r*delP*((1-x)^n))-muSU*PSU
dPSD.dt = ((ND+SD+AD)/N)*((1-r)*delS+r*delP*((1-x)^n))-muSD*PSD
dPRU.dt = ((NU+SU+AU)/N)*((1-r)*delR+r*delP*(x^n))-muRU*PRU
dPRD.dt = ((ND+SD+AD)/N)*((1-r)*delR+r*delP*(x^n))-muRD*PRD
e = ((NU+SU+AU)/N)*((1-r)*delS+r*delP*((1-x)^n))-muSU*PSU+((ND+SD+AD)/N)*((1-r)*delS+r*delP*((1-x)^n))-muSD*PSD+((NU+SU+AU)/N)*((1-r)*delR+r*delP*(x^n))-muRU*PRU+((ND+SD+AD)/N)*((1-r)*delR+r*delP*(x^n))-muRD*PRD
er = ((NU+SU+AU)/N)*((1-r)*delR+r*delP*(x^n))-muRU*PRU+((ND+SD+AD)/N)*((1-r)*delR+r*delP*(x^n))-muRD*PRD
es = ((NU+SU+AU)/N)*((1-r)*delS+r*delP*((1-x)^n))-muSU*PSU+((ND+SD+AD)/N)*((1-r)*delS+r*delP*((1-x)^n))-muSD*PSD
gammavec = c((n/n-1),x)
gammavec2 = c(0,x)
if (x<0){
gamma = max(gammavec2)
}else{
gamma = min(gammavec)
}
#x1 = ((PRU+PRD+PSU+PSD)*x-(PRU+PRD)*(1-wr))/(PSD+PSU+((PRD+PRU)*(wr)))
#x1 = (x2^n)/(1+x2^n)
x1 = gamma*(rats1)+ratr1*wr
dPSU.dt = ((NU+SU+AU)/N)*((1-r)*delS+r*delP*(1-x1^n))-muSU*PSU
dPSD.dt = ((ND+SD+AD)/N)*((1-r)*delS+r*delP*(1-x1^n))-muSD*PSD
dPRU.dt = ((NU+SU+AU)/N)*((1-r)*delR+r*delP*(x1^n))-muRU*PRU
dPRD.dt = ((ND+SD+AD)/N)*((1-r)*delR+r*delP*(x1^n))-muRD*PRD
e = ((NU+SU+AU)/N)*((1-r)*delS+r*delP*(1-x1^n))-muSU*PSU+((ND+SD+AD)/N)*((1-r)*delS+r*delP*(1-x1^n))-muSD*PSD+((NU+SU+AU)/N)*((1-r)*delR+r*delP*(x1^n))-muRU*PRU+((ND+SD+AD)/N)*((1-r)*delR+r*delP*(x1^n))-muRD*PRD
er = ((NU+SU+AU)/N)*((1-r)*delR+r*delP*(x1^n))-muRU*PRU+((ND+SD+AD)/N)*((1-r)*delR+r*delP*(x1^n))-muRD*PRD
es = ((NU+SU+AU)/N)*((1-r)*delS+r*delP*(1-x1^n))-muSU*PSU+((ND+SD+AD)/N)*((1-r)*delS+r*delP*(1-x1^n))-muSD*PSD
#dNU.dt = (del*(AU+AD))+(ND/Tau)-(b*I*eps*NU*(d+rho1))-(muNU*NU) - (del*att*NU)
dNU.dt = del+(ND/Tau)-(b*I*eps*NU*(d1+rho1))-(muNU*NU*I*b*eps) - (del*att*NU)
dND.dt = (b*I*eps*NU*d1)-(ND/Tau)-(ratr*b*I*eps*ND*rho2)-(muND*ratr*ND*I*b*eps) - (del*att*ND)
Expand All @@ -234,12 +245,13 @@ SEAI<-function(t,y,p){
#dgamma.dt = (1/(PSU+PSD+((1-S)*(PRU+PRD))))*((1/rats)-(gamma))*(dPRD.dt+dPRU.dt)
#dgamma.dt = ratr + rats*((gamma)-ratr)-((1/(PSU+PSD+((1-S)*(PRU+PRD))))*(dPRD.dt+dPRU.dt)*((gamma)-ratr))
#dgamma.dt = -(dPRD.dt+dPRU.dt)/(dPSD.dt+dPSU.dt)
dx.dt = (1/((PSU+PSD+PRU+PRD)+(e)))*((er)-(x*(e))+((es)*((x*(PSD+PSD+PRU+PRD)-(PRU+PRD))/(PSU+PSD))))
#dx.dt = (1/((PSU+PSD+PRU+PRD)+(e)))*((er)-(x*(e))+((es)*((x*(PSD+PSD+PRU+PRD)-(PRU+PRD))/(PSU+PSD))))
dx.dt = (delP*(x1-x)+delR*(x-1))/((PSU+PSD)+delS)
return(list(c(dPSU.dt,dPSD.dt,dPRU.dt,dPRD.dt,dNU.dt,dND.dt,dSU.dt,dSD.dt,dAU.dt,dAD.dt,dx.dt)))
})
}

b = 10^(-1.5)
b = 10

nstrains = 150

Expand All @@ -258,7 +270,7 @@ omega2 = omega1 #prob of appearance of new antigen only in resistant strains
L = 10000

ws = 1
wr = 1-0.6
wr = 1-0.1
S = 1-wr
#muSU = 1
muSU=1/250#0.001
Expand Down Expand Up @@ -338,75 +350,88 @@ plot(out2[,1],(out2[,8]),ylim=c(0,max(out2[,9])),type="l", xlab="Time",ylab="Pop
lines(out2[,1],(out2[,9]),col="RED")
legend("bottomright",legend=c("SU","SD"),bty="n",lwd=c(2,1),col=c("BLACK","RED"))

plot(out2[,1],out2[,10],type="l",xlab="Time",ylab="Asymptomatic Population (A)", main="b=0.2239*365,d=0.30")
plot(out2[,1],out2[,10],ylim=c(0,max(out2[,10])),type="l",xlab="Time",ylab="Asymptomatic Population (A)", main="b=0.2239*365,d=0.30")
lines(out2[,1],out2[,11],col="RED")

plot(out2[,1],(out2[,2]+out2[,3]+out2[,4]+out2[,5])/(out2[,6]+out2[,7]+out2[,8]+out2[,9]+out2[,10]+out2[,11]))

M = (out2[,2]+out2[,3]+out2[,4]+out2[,5])/(out2[,6]+out2[,7]+out2[,8]+out2[,9]+out2[,10]+out2[,11])
plot(out2[,1],0.5*(1-(((M*exp(-M)))/(1-exp(-M)))))

plot(out2[,1],out2[,12],type="l")
print(out2[,12][35000])

I1 = (1/(K*(out3[,6]+out3[,7]+out3[,8]+out3[,9]+out3[,10]+out3[,11])))*(-(((out3[,3]+out3[,2]+out3[,4] + out3[,5])/(out3[,6]+out3[,7]+out3[,8]+out3[,9]+out3[,10]+out3[,11]))-K))

plot(out2[,1],I1)

#out3eq = vector(mode = "numeric", length = 17)
out3eq2 = vector(mode = "numeric", length = 11)
#out3eq3 = vector(mode = "numeric", length = 8)
#out3eq4 = vector(mode = "numeric", length = 8)
#out3eq5 = vector(mode="numeric", length=23)
#out3eq6 = vector(mode="numeric", length=8)
#out3eq = vector(mode = "numeric", length = 18)
out3eq2 = vector(mode = "numeric", length = 16)
#out3eq3 = vector(mode = "numeric", length = 18)
#out3eq4 = vector(mode = "numeric", length = 18)
#out3eq5 = vector(mode="numeric", length=18)
#out3eq7 = vector(mode="numeric", length=18)
#out4 = vector(mode="numeric", length=22)
#bvalues = c(0,0.0001,0.0005,0.05,0.10,0.15,0.20,0.25,0.27,0.30,0.32,0.35,0.37,0.40,0.45,0.50,0.55,0.60,0.70,0.80,0.90,1)
bvalues = c(-2,-1.5, -1,-0.9,-0.8,-0.6,-0.4,-0.2,-0.1,0,0.2)#,0.4)#,0.6,0.8,1)#,1.5,2)#,2,3,4)
bvalues = c(-2.5,-2,-1.5, -1,-0.9,-0.8,-0.6,-0.4,-0.2,-0.1,0,0.2,0.4,0.6,0.8,1,1.5,2)#,3,4)
#bvalues = c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2)
#bvalues = c(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)
#bvalues = seq(from=-2.5,to=0.5,by=1)
wrvalues = c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1)
#wrvalues = c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1)
wrvalues = c(0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 1)
#wrvalues = c(0.20,0.22,0.24,0.26,0.28,0.30,0.32,0.34,0.36,0.38,0.40)
dvalues = c(0,0.10,0.15,0.20,0.25,0.27,0.30,0.32,0.35,0.37,0.40,0.45,0.50,0.55,0.60,0.65,0.70,0.75,0.80,0.85,0.90,1)
muSUvalues = c(0,0.10,0.15,0.20,0.25,0.27,0.30,0.32,0.35,0.37,0.40,0.45,0.50,0.55,0.60,0.65,0.70,0.75,0.80,0.85,0.90,1)
delvalues = c(10,20,40,50,60,70,90,100,150,200,250,300,350,400,450,500,550,600,700,800,900,1000)
rho3values = c(0.0005,0.002,0.004,0.005,0.007,0.008,0.01,0.02,0.04,0.05,0.06,0.07,0.08,0.09,0.10,0.11)
omegavalues = c(0.01,0.012,0.014,0.016,0.018,0.02,0.022,0.024,0.026,0.028,0.030,0.032,0.034,0.036,0.038,0.040)#,0.042,0.044,0.046,0.048,0.050,0.052)
for (i in 1:11){
for (i in 1:16){
#del=delvalues[i]
b=10^(bvalues[i])
#b=10^(bvalues[i])
#wr=wrvalues[i]
#d1=dvalues[i]
#d2=d1
#d3=d1
#muSU = muSUvalues[i]*0.1
#rho3 = rho3values[i]
rho3 = rho3values[i]
rho4=rho3
#omega1 = omegavalues[i]
p2 = list(b=b,ws=ws,muSU=muSU,muSD=muSD,muRD=muRD,muRU=muRU,Tau=Tau,d1=d1,d2=d2,d3=d3,del=del,muND=muND,muNU=muNU,rho1=rho1,rho2=rho2,rho3=rho3,rho4=rho4,omega1=omega1,omega2=omega2,L=L,att=att)
out3 = ode(y=N0,times=t2,func=SEAI,parms=p2)
#out3eq[i] = out3[3999,3]+out3[3999,2] +out3[3999,4] + out3[3999,5]
#out3eq[i] = out3[39999,3]+out3[39999,2] +out3[39999,4] + out3[39999,5]
out3eq2[i] = (out3[39999,4]+out3[39999,5])/(out3[39999,2] + out3[39999,3] + out3[39999,4] + out3[39999,5])
#out3eq3[i] = (out3[3999,6]+out3[3999,7])/(out3[3999,6]+out3[3999,7]+out3[3999,8]+out3[3999,9]+out3[3999,10]+out3[3999,11])
#out3eq4[i] = (out3[3999,8]+out3[3999,9])/(out3[3999,6]+out3[3999,7]+out3[3999,8]+out3[3999,9]+out3[3999,10]+out3[3999,11])
#out3eq5[i] =(out3[3999,10]+out3[3999,11])/(out3[3999,6]+out3[3999,7]+out3[3999,8]+out3[3999,9]+out3[3999,10]+out3[3999,11])
#out3eq4[i] = (out3[39999,8]+out3[39999,9])/(out3[39999,6]+out3[39999,7]+out3[39999,8]+out3[39999,9]+out3[39999,10]+out3[39999,11])
#out3eq5[i] =(out3[39999,10]+out3[39999,11])/(out3[39999,6]+out3[39999,7]+out3[39999,8]+out3[39999,9]+out3[39999,10]+out3[39999,11])
#out4 [i] = (1/(K*(out3[399999,6]+out3[399999,7]+out3[399999,8]+out3[399999,9]+out3[399999,10]+out3[399999,11])))*(-(((out3[3999,3]+out3[3999,2]+out3[3999,4] + out3[3999,5])/(out3[3999,6]+out3[3999,7]+out3[3999,8]+out3[3999,9]+out3[3999,10]+out3[3999,11]))-K))
#out4[i] = (1/(K*(K)))*(-(((out3[3999,3]+out3[3999,2]+out3[3999,4] + out3[3999,5])/(out3[3999,6]+out3[3999,7]+out3[3999,8]+out3[3999,9]+out3[3999,10]+out3[3999,11]))-K))
#out3eq6[i] = (out3[3999,6]+out3[3999,7]+out3[3999,8]+out3[3999,9]+out3[3999,10]+out3[3999,11])
#out3eq7[i] = (out3[39999,7]+out3[39999,9]+out3[39999,11])/(out3[39999,6]+out3[39999,7]+out3[39999,8]+out3[39999,9]+out3[39999,10]+out3[39999,11])
}

#plot(bvalues,out3eq2,xlab="b/10",ylab="Proportion resistant")
#plot(bvalues,1-out4)#,ylab="Proportion Resistant")
plot(bvalues,out3eq2)
plot(rho3values,out3eq2)
#print(out3eq2)
print(out3eq2)

mat6 = matrix(data=0,nrow=11,ncol=11)
mat6 = matrix(data=0,nrow=16,ncol=16)
#mat7 = matrix(data=0,nrow=11,ncol=17)
#mat8 = matrix(data=0,nrow=11,ncol=11)
#mat9 = matrix(data=0,nrow=11,ncol=18)
#mat10 = matrix(data=0,nrow=11,ncol=18)
#mat11 = matrix(data=0,nrow=11,ncol=18)
#mat12 = matrix(data=0,nrow=11,ncol=18)
for (i in 1:11){
for (j in 1:11){
for (i in 1:16){
for (j in 1:16){
#d = dvalues[i]
# A = Avalues[j]
#rho3=rho3values[i]
wr = wrvalues[i]
rho3=rho3values[i]
rho4=rho3
#wr = wrvalues[i]
#muSU = muSUvalues[i]*0.01
b = 10^(bvalues[j])
#omega1 = omegavalues[j]
#b = 10^(bvalues[j])
omega1 = omegavalues[j]
p2 = list(b=b,ws=ws,wr=wr,muSU=muSU,muSD=muSD,muRD=muRD,muRU=muRU,Tau=Tau,d1=d1,d2=d2,d3=d3,del=del,muND=muND,muNU=muNU,rho1=rho1,rho2=rho2,rho3=rho3,rho4=rho4,omega1=omega1,omega2=omega2,L=L,att=att)
out5 = ode(y=N0,times=t2,func=SEAI,parms=p2)
# PTotal = out5[3999,2] + out5[3999,3] + out5[3999,4] + out5[3999,5]
Expand Down

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