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John Chaillet
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Oct 18, 2021
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| require(deSolve) | ||
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| SEAI<-function(t,y,p){ | ||
| PSU = y[1] | ||
| PSD = y[2] | ||
| #PS = y[3] | ||
| PRU = y[3] | ||
| PRD = y[4] | ||
| #PR = y[6] | ||
| NU = y[5] | ||
| ND = y[6] | ||
| SU = y[7] | ||
| SD = y[8] | ||
| AU = y[9] | ||
| AD = y[10] | ||
| with(as.list(p),{ | ||
| N = y[5]+y[6]+y[7]+y[8]+y[9]+y[10] | ||
| 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) | ||
| return(list(c(dPSU.dt,dPSD.dt,dPRU.dt,dPRD.dt,dNU.dt,dND.dt,dSU.dt,dSD.dt,dAU.dt,dAD.dt))) | ||
| }) | ||
| } | ||
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| b = 0.2239*365 | ||
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| nstrains = 20 | ||
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| del = (1/60) | ||
| muND = 0.05*20 | ||
| muNU = 0.1*20 | ||
| 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 | ||
| rho4 = 1/nstrains #prob of immunity gain from SD to AD | ||
| omega1 = 1/100 #prob of appearance of new antigen | ||
| omega2 = 1/100 #prob of appearance of new antigen only in resistant strains | ||
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| L = 5000 | ||
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| 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 | ||
| 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) | ||
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| t2 = seq(from=0,to=1000,by=1/365) | ||
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| N0 = c(500,500,500,500,1000,1000,1000,1000,1000,1000) | ||
| out2 = ode(y=N0,times=t2,func=SEAI,parms=p2) | ||
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| #plot(out2[,1],(out2[,2]+out2[,3]+out2[,4]+out2[,5])/6000) | ||
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| 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") | ||
| legend(x=40,y=20000,legend=c("PSU","PSD"),bty="n",lwd = c(2,1),col=c("BLACK","RED")) | ||
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| plot(out2[,1],(out2[,4]),type="l", xlab = "Time", ylab="Population", main = "b=0.2239*365,d=0.30") | ||
| 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")) | ||
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| 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") | ||
| 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")) | ||
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| 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") | ||
| 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")) | ||
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| 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") | ||
| lines(out2[,1],out2[,11],col="RED") | ||
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| 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) | ||
| #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 | ||
| #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) | ||
| 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]) | ||
| } | ||
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| plot(dvalues,out3eq2) | ||
| print(out3eq2) | ||
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