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reproduced valley phenomenon
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John Chaillet committed Oct 19, 2021
1 parent 25ff99c commit ca34adb
Showing 1 changed file with 40 additions and 37 deletions.
77 changes: 40 additions & 37 deletions ODEsImmunity.R
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Original file line number Diff line number Diff line change
Expand Up @@ -15,28 +15,31 @@ SEAI<-function(t,y,p){
AD = y[10]
with(as.list(p),{
N = y[5]+y[6]+y[7]+y[8]+y[9]+y[10]
m = (PSU+PSD+PRU+PRD)/N
I = 1-exp(-m)
eps = (((PSD+PSU+((PRD+PRU)*(wr))))/(PSD+PSU+PRD+PRU))
dPSU.dt = -(b*(PSU/N)*ws*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (b*(PSD/N)*ws*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (muSU)*(PSU)
dPSD.dt = -(b*(PSD/N)*ws*(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)) - (muSD)*(PSD)
dPRU.dt = -(b*(PRU/N)*wr*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (b*(PRD/N)*(NU+SU+AU)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (muRU)*(PRU)
dPRD.dt = -(b*(PRD/N)*wr*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (b*(PRU/N)*(ND+SD+AD)*(1/K)*(((PSU+PSD+PRU+PRD)/N)-K)) - (muRD)*(PRD)
dNU.dt = (del*N*(1-(N/L))) + (ND/Tau)-(b*eps*NU*(d+rho1))-(muNU*NU)# - (del*NU)
dND.dt = (b*eps*NU*d)-(ND/Tau)-(b*eps*ND*rho2)-(muND*ND)# - (del*ND)
dSU.dt = (b*eps*omega1*AU*SU)+(b*eps*NU*rho1)+(SD/Tau)-(b*eps*SU*(d+rho3))# - (del*SU)
dSD.dt = (b*eps*omega2*AD*SD)+(b*eps*ND*rho2)+(b*eps*SU*d)-(SD/Tau)-(b*eps*SD*rho4)# - (del*SD)
dAU.dt = (AD/Tau)+(b*eps*SU*rho3)-(b*eps*omega1*AU*SU)# - (del*AU)
dAD.dt = (b*eps*SD*rho4)-(b*eps*omega2*AD*SD)-(AD/Tau)# - (del*AD)
dNU.dt = (del*N)+ (ND/Tau)-(b*I*eps*NU*(d+rho1))-(muNU*NU) - (del*att*NU)
dND.dt = (b*I*eps*NU*d)-(ND/Tau)-(b*I*eps*ND*rho2)-(muND*ND) - (del*att*ND)
dSU.dt = (b*I*eps*NU*rho1)+(SD/Tau)-(b*I*eps*SU*(d+rho3)) - (del*att*SU)
dSD.dt = (b*I*eps*ND*rho2)+(b*I*eps*SU*d)-(SD/Tau)-(b*I*eps*SD*rho4) - (del*att*SD)
dAU.dt = (AD/Tau)+(b*I*eps*SU*rho3)-(b*I*eps*omega1*AU*d) - (del*att*AU)
dAD.dt = (b*I*eps*SD*rho4)+(b*I*eps*omega1*AU*d)-(AD/Tau) - (del*att*AD)
return(list(c(dPSU.dt,dPSD.dt,dPRU.dt,dPRD.dt,dNU.dt,dND.dt,dSU.dt,dSD.dt,dAU.dt,dAD.dt)))
})
}

b = 0.2239*365
b = 20000

nstrains = 20

del = (1/60)
muND = 0.05*20
muNU = 0.1*20
att = 0
del = 0
muND = 0
muNU = 0
rho1 = 0.5 #prob of immunity gain from NU to SU
rho2 = 0.5 #prob of immunity gain from ND to SD
rho3 = 1/nstrains #prob of immunity gain from SU to AU
Expand All @@ -45,32 +48,32 @@ omega1 = 1/100 #prob of appearance of new antigen
omega2 = 1/100 #prob of appearance of new antigen only in resistant strains


L = 5000
L = 10000

ws = 1
wr = 1-0.6
muSU = 1
#muSU=0.05
muSD = 20
#muSD=0.99
muRD = 1
#muRD = 0.05
muRU = 1
#muRU = 0.05
Tau = 20/365
#muSU = 1
muSU=0.05
#muSD = 20
muSD=0.99
#muRD = 1
muRD = 0.05
#muRU = 1
muRU = 0.05
Tau = 20#/365
d = 0.9
#m = 3
K=6
p2 = list(b=b,ws=ws,wr=wr,muSU=muSU,muSD=muSD,muRD=muRD,muRU=muRU,Tau=Tau,d=d,del=del,muND=muND,muNU=muNU,rho1=rho1,rho2=rho2,rho3=rho3,rho4=rho4,omega1=omega1,omega2=omega2,L=L)
K=10
p2 = list(b=b,ws=ws,wr=wr,muSU=muSU,muSD=muSD,muRD=muRD,muRU=muRU,Tau=Tau,d=d,del=del,muND=muND,muNU=muNU,rho1=rho1,rho2=rho2,rho3=rho3,rho4=rho4,omega1=omega1,omega2=omega2,L=L,att=att)


t2 = seq(from=0,to=1000,by=1/365)
t2 = seq(from=0,to=5000,by=1)


N0 = c(500,500,500,500,1000,1000,1000,1000,1000,1000)
N0 = c(500,500,500,500,333,333,333,333,333,333)
out2 = ode(y=N0,times=t2,func=SEAI,parms=p2)

#plot(out2[,1],(out2[,2]+out2[,3]+out2[,4]+out2[,5])/6000)
#plot(out2[,1],(out2[,2]+out2[,3]+out2[,4]+out2[,5]))

plot(out2[,1],(out2[,2]),type="l", xlab="Time", ylab="Population", main = "b=0.2239*365,d=0.30")
lines(out2[,1],(out2[,3]),col="RED")
Expand All @@ -80,35 +83,35 @@ plot(out2[,1],(out2[,4]),type="l", xlab = "Time", ylab="Population", main = "b=0
lines(out2[,1],(out2[,5]),col="RED")
legend(x=40,y=6,legend=c("PRU","PRD"),bty="n",lwd = c(2,1),col=c("BLACK","RED"))

plot(out2[,1],(out2[,6]),type="l",ylim=c(0,max(out2[,6])), xlab="Time", ylab="Population", main = "b=0.2239*365,d=0.30")
plot(out2[,1],(out2[,6]),type="l", xlab="Time", ylab="Population", main = "b=0.2239*365,d=0.30")
lines(out2[,1],(out2[,7]),col="RED")
legend(x=40,y=1000,legend=c("NU","ND"),bty="n",lwd=c(2,1),col=c("BLACK","RED"))

plot(out2[,1],(out2[,8]),type="l",ylim=c(0,max(out2[,8])), xlab="Time", ylab="Population", main = "b=0.2239*365,d=0.30")
plot(out2[,1],(out2[,8]),type="l", xlab="Time",ylab="Population", main = "b=0.2239*365,d=0.30")
lines(out2[,1],(out2[,9]),col="RED")
legend(x=40,y=1000,legend=c("SU","SD"),bty="n",lwd=c(2,1),col=c("BLACK","RED"))

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


out3eq = vector(mode = "numeric", length = 21)
out3eq2 = vector(mode = "numeric", length = 21)
bvalues = c(0,0.15,0.20,0.25,0.27,0.30,0.32,0.35,0.37,0.40,0.45,0.50,0.55,0.60,0.70,0.80,0.90,1,2,3,4,5,6,7,8)
out3eq = vector(mode = "numeric", length = 22)
out3eq2 = 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(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)
wrvalues = 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)
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)
for (i in 1:21){
#b=bvalues[i]*365
for (i in 1:22){
b=bvalues[i]*10
#wr=wrvalues[i]
d=dvalues[i]
p3 = list(b=b,ws=ws,wr=wr,muSU=muSU,muSD=muSD,muRD=muRD,muRU=muRU,Tau=Tau,d=d,del=del,muND=muND,muNU=muNU,rho1=rho1,rho2=rho2,rho3=rho3,rho4=rho4,omega1=omega1,omega2=omega2,L=L)
#d=dvalues[i]
p3 = list(b=b,ws=ws,wr=wr,muSU=muSU,muSD=muSD,muRD=muRD,muRU=muRU,Tau=Tau,d=d,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=p3)
#out3eq[i] = out3[3999,2] + out3[3999,3]+out3[3999,4] + out3[3999,5]
out3eq2[i] = (out3[30000,4]+out3[30000,5])/(out3[30000,2] + out3[30000,3] + out3[30000,4] + out3[30000,5])
out3eq2[i] = (out3[3999,4]+out3[3999,5])/(out3[3999,2] + out3[3999,3] + out3[3999,4] + out3[3999,5])
}

plot(dvalues,out3eq2)
plot(bvalues,out3eq2,xlab="b/10")
print(out3eq2)


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