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1d_model_code_int.R
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source("9_mixing_matrix_gmix.R")
## Model flows
## The subsaripts denote the number of times someone as been exposed through either infection or vaccination
COVID_sero_vax <- function(t, start, params){
with(as.list(c(start,params)),{
sd <- input(t)
# Derived variables
#Rural child
Ncr0v0 = sum(Scr0v0, Ecr1v0, Acr1v0, Icr1v0, Hcr1v0, Rpcr1v0, W1Rpcr1v0,W2Rpcr1v0,W3Rpcr1v0,Rncr1v0) #Unvax and no prior exposure
Ncr1v0 = sum(Spcr1v0, Sncr1v0, Ecr2v0, Acr2v0, Icr2v0, Hcr2v0, Rpcr2v0, Rncr2v0) #Unvax and one prior
Ncr2v0 = sum(Spcr2v0, Sncr2v0, Ecr3v0, Acr3v0, Icr3v0, Hcr3v0, Rpcr3v0, Rncr3v0) #Unvax and two prior
Ncr0v1 = sum(Spcr0v1,Vpcr0v1, W1Vpcr0v1,W2Vpcr0v1,W3Vpcr0v1,Vncr0v1,Sncr0v1, Ecr1v1, Acr1v1, Icr1v1, Hcr1v1, Rpcr1v1, Rncr1v1) #vax 1 dose and no prior exposure
Ncr1v1 = sum(Spcr1v1, Sncr1v1, Ecr2v1, Acr2v1, Icr2v1, Hcr2v1, Rpcr2v1, Rncr2v1) #vax 1 dose and one prior
Ncr2v1 = sum(Spcr2v1, Sncr2v1, Ecr3v1, Acr3v1, Icr3v1, Hcr3v1, Rpcr3v1, Rncr3v1) #vax 1 dose and two prior
Ncr0v2 = sum(Spcr0v2, Vpcr0v2, Vncr0v2,Sncr0v2, Ecr1v2, Acr1v2, Icr1v2, Hcr1v2, Rpcr1v2, Rncr1v2) #vax 2 dose and no prior exposure
Ncr1v2 = sum(Spcr1v2, Sncr1v2, Ecr2v2, Acr2v2, Icr2v2, Hcr2v2, Rpcr2v2, Rncr2v2) #vax 2 dose and one prior
Ncr2v2 = sum(Spcr2v2, Sncr2v2, Ecr3v2, Acr3v2, Icr3v2, Hcr3v2, Rpcr3v2, Rncr3v2) #vax 2 doseand two prior
Ncr0v3 = sum(Spcr0v3, Vpcr0v3, Vncr0v3,Sncr0v3, Ecr1v3, Acr1v3, Icr1v3, Hcr1v3, Rpcr1v3, Rncr1v3) #vax 3 dose and no prior exposure
Ncr1v3 = sum(Spcr1v3, Sncr1v3, Ecr2v3, Acr2v3, Icr2v3, Hcr2v3, Rpcr2v3, Rncr2v3) #vax 3 dose and one prior
Ncr2v3 = sum(Spcr2v3, Sncr2v3, Ecr3v3, Acr3v3, Icr3v3, Hcr3v3, Rpcr3v3, Rncr3v3) #vax 3 dose and two prior
#Urban child
Ncu0v0 = sum(Scu0v0, Ecu1v0, Acu1v0, Icu1v0, Hcu1v0, Rpcu1v0,W1Rpcu1v0,W2Rpcu1v0,W3Rpcu1v0, Rncu1v0) #Unvax and no prior exposure
Ncu1v0 = sum(Spcu1v0, Sncu1v0, Ecu2v0, Acu2v0, Icu2v0, Hcu2v0, Rpcu2v0, Rncu2v0) #Unvax and one prior
Ncu2v0 = sum(Spcu2v0, Sncu2v0, Ecu3v0, Acu3v0, Icu3v0, Hcu3v0, Rpcu3v0, Rncu3v0) #Unvax and two prior
Ncu0v1 = sum(Spcu0v1,Vpcu0v1, W1Vpcu0v1,W2Vpcu0v1,W3Vpcu0v1,Vncu0v1,Sncu0v1, Ecu1v1, Acu1v1, Icu1v1, Hcu1v1, Rpcu1v1, Rncu1v1) #vax 1 dose and no prior exposure
Ncu1v1 = sum(Spcu1v1, Sncu1v1, Ecu2v1, Acu2v1, Icu2v1, Hcu2v1, Rpcu2v1, Rncu2v1) #vax 1 dose and one prior
Ncu2v1 = sum(Spcu2v1, Sncu2v1, Ecu3v1, Acu3v1, Icu3v1, Hcu3v1, Rpcu3v1, Rncu3v1) #vax 1 dose and two prior
Ncu0v2 = sum(Spcu0v2, Vpcu0v2, Vncu0v2,Sncu0v2,Ecu1v2, Acu1v2, Icu1v2, Hcu1v2, Rpcu1v2, Rncu1v2) #vax 2 dose and no prior exposure
Ncu1v2 = sum(Spcu1v2, Sncu1v2, Ecu2v2, Acu2v2, Icu2v2, Hcu2v2, Rpcu2v2, Rncu2v2) #vax 2 dose and one prior
Ncu2v2 = sum(Spcu2v2, Sncu2v2, Ecu3v2, Acu3v2, Icu3v2, Hcu3v2, Rpcu3v2, Rncu3v2) #vax 2 doseand two prior
Ncu0v3 = sum(Spcu0v3, Vpcu0v3, Vncu0v3,Sncu0v3,Ecu1v3, Acu1v3, Icu1v3, Hcu1v3, Rpcu1v3, Rncu1v3) #vax 3 dose and no prior exposure
Ncu1v3 = sum(Spcu1v3, Sncu1v3, Ecu2v3, Acu2v3, Icu2v3, Hcu2v3, Rpcu2v3, Rncu2v3) #vax 3 dose and one prior
Ncu2v3 = sum(Spcu2v3, Sncu2v3, Ecu3v3, Acu3v3, Icu3v3, Hcu3v3, Rpcu3v3, Rncu3v3) #vax 3 dose and two prior
#Rural adult
Nar0v0 = sum(Sar0v0, Ear1v0, Aar1v0, Iar1v0, Har1v0, Rpar1v0,W1Rpar1v0,W2Rpar1v0,W3Rpar1v0, Rnar1v0) #Unvax and no prior exposure
Nar1v0 = sum(Spar1v0, Snar1v0, Ear2v0, Aar2v0, Iar2v0, Har2v0, Rpar2v0, Rnar2v0) #Unvax and one prior
Nar2v0 = sum(Spar2v0, Snar2v0, Ear3v0, Aar3v0, Iar3v0, Har3v0, Rpar3v0, Rnar3v0) #Unvax and two prior
Nar0v1 = sum(Spar0v1,Vpar0v1, W1Vpar0v1,W2Vpar0v1,W3Vpar0v1,Vnar0v1, Snar0v1, Ear1v1, Aar1v1, Iar1v1, Har1v1, Rpar1v1, Rnar1v1) #vax 1 dose and no prior exposure
Nar1v1 = sum(Spar1v1, Snar1v1, Ear2v1, Aar2v1, Iar2v1, Har2v1, Rpar2v1, Rnar2v1) #vax 1 dose and one prior
Nar2v1 = sum(Spar2v1, Snar2v1, Ear3v1, Aar3v1, Iar3v1, Har3v1, Rpar3v1, Rnar3v1) #vax 1 dose and two prior
Nar0v2 = sum(Spar0v2, Vpar0v2, Vnar0v2, Snar0v2, Ear1v2, Aar1v2, Iar1v2, Har1v2, Rpar1v2, Rnar1v2) #vax 2 dose and no prior exposure
Nar1v2 = sum(Spar1v2, Snar1v2, Ear2v2, Aar2v2, Iar2v2, Har2v2, Rpar2v2, Rnar2v2) #vax 2 dose and one prior
Nar2v2 = sum(Spar2v2, Snar2v2, Ear3v2, Aar3v2, Iar3v2, Har3v2, Rpar3v2, Rnar3v2) #vax 2 doseand two prior
Nar0v3 = sum(Spar0v3, Vpar0v3, Vnar0v3,Snar0v3, Ear1v3, Aar1v3, Iar1v3, Har1v3, Rpar1v3, Rnar1v3) #vax 3 dose and no prior exposure
Nar1v3 = sum(Spar1v3, Snar1v3, Ear2v3, Aar2v3, Iar2v3, Har2v3, Rpar2v3, Rnar2v3) #vax 3 dose and one prior
Nar2v3 = sum(Spar2v3, Snar2v3, Ear3v3, Aar3v3, Iar3v3, Har3v3, Rpar3v3, Rnar3v3) #vax 3 dose and two prior
#Urban adult
Nau0v0 = sum(Sau0v0, Eau1v0, Aau1v0, Iau1v0, Hau1v0, Rpau1v0, W1Rpau1v0,W2Rpau1v0,W3Rpau1v0, Rnau1v0) #Unvax and no prior exposure
Nau1v0 = sum(Spau1v0, Snau1v0, Eau2v0, Aau2v0, Iau2v0, Hau2v0, Rpau2v0, Rnau2v0) #Unvax and one prior
Nau2v0 = sum(Spau2v0, Snau2v0, Eau3v0, Aau3v0, Iau3v0, Hau3v0, Rpau3v0, Rnau3v0) #Unvax and two prior
Nau0v1 = sum(Spau0v1,Vpau0v1, W1Vpau0v1,W2Vpau0v1,W3Vpau0v1,Vnau0v1,Snau0v1, Eau1v1, Aau1v1, Iau1v1, Hau1v1, Rpau1v1, Rnau1v1) #vax 1 dose and no prior exposure
Nau1v1 = sum(Spau1v1, Snau1v1, Eau2v1, Aau2v1, Iau2v1, Hau2v1, Rpau2v1, Rnau2v1) #vax 1 dose and one prior
Nau2v1 = sum(Spau2v1, Snau2v1, Eau3v1, Aau3v1, Iau3v1, Hau3v1, Rpau3v1, Rnau3v1) #vax 1 dose and two prior
Nau0v2 = sum(Spau0v2, Vpau0v2, Vnau0v2,Snau0v2, Eau1v2, Aau1v2, Iau1v2, Hau1v2, Rpau1v2, Rnau1v2) #vax 2 dose and no prior exposure
Nau1v2 = sum(Spau1v2, Snau1v2, Eau2v2, Aau2v2, Iau2v2, Hau2v2, Rpau2v2, Rnau2v2) #vax 2 dose and one prior
Nau2v2 = sum(Spau2v2, Snau2v2, Eau3v2, Aau3v2, Iau3v2, Hau3v2, Rpau3v2, Rnau3v2) #vax 2 doseand two prior
Nau0v3 = sum(Spau0v3, Vpau0v3, Vnau0v3,Snau0v3, Eau1v3, Aau1v3, Iau1v3, Hau1v3, Rpau1v3, Rnau1v3) #vax 3 dose and no prior exposure
Nau1v3 = sum(Spau1v3, Snau1v3, Eau2v3, Aau2v3, Iau2v3, Hau2v3, Rpau2v3, Rnau2v3) #vax 3 dose and one prior
Nau2v3 = sum(Spau2v3, Snau2v3, Eau3v3, Aau3v3, Iau3v3, Hau3v3, Rpau3v3, Rnau3v3) #vax 3 dose and two prior
#Rural elderly
Ner0v0 = sum(Ser0v0, Eer1v0, Aer1v0, Ier1v0, Her1v0, Rper1v0,W1Rper1v0,W2Rper1v0,W3Rper1v0, Rner1v0) #Unvax and no prior exposure
Ner1v0 = sum(Sper1v0, Sner1v0, Eer2v0, Aer2v0, Ier2v0, Her2v0, Rper2v0, Rner2v0) #Unvax and one prior
Ner2v0 = sum(Sper2v0, Sner2v0, Eer3v0, Aer3v0, Ier3v0, Her3v0, Rper3v0, Rner3v0) #Unvax and two prior
Ner0v1 = sum(Sper0v1,Vper0v1, W1Vper0v1,W2Vper0v1,W3Vper0v1,Vner0v1, Sner0v1, Eer1v1, Aer1v1, Ier1v1, Her1v1, Rper1v1, Rner1v1) #vax 1 dose and no prior exposure
Ner1v1 = sum(Sper1v1, Sner1v1, Eer2v1, Aer2v1, Ier2v1, Her2v1, Rper2v1, Rner2v1) #vax 1 dose and one prior
Ner2v1 = sum(Sper2v1, Sner2v1, Eer3v1, Aer3v1, Ier3v1, Her3v1, Rper3v1, Rner3v1) #vax 1 dose and two prior
Ner0v2 = sum(Sper0v2, Vper0v2, Vner0v2,Sner0v2, Eer1v2, Aer1v2, Ier1v2, Her1v2, Rper1v2, Rner1v2) #vax 2 dose and no prior exposure
Ner1v2 = sum(Sper1v2, Sner1v2, Eer2v2, Aer2v2, Ier2v2, Her2v2, Rper2v2, Rner2v2) #vax 2 dose and one prior
Ner2v2 = sum(Sper2v2, Sner2v2, Eer3v2, Aer3v2, Ier3v2, Her3v2, Rper3v2, Rner3v2) #vax 2 doseand two prior
Ner0v3 = sum(Sper0v3, Vper0v3, Vner0v3,Sner0v3, Eer1v3, Aer1v3, Ier1v3, Her1v3, Rper1v3, Rner1v3) #vax 3 dose and no prior exposure
Ner1v3 = sum(Sper1v3, Sner1v3, Eer2v3, Aer2v3, Ier2v3, Her2v3, Rper2v3, Rner2v3) #vax 3 dose and one prior
Ner2v3 = sum(Sper2v3, Sner2v3, Eer3v3, Aer3v3, Ier3v3, Her3v3, Rper3v3, Rner3v3) #vax 3 dose and two prior
#Urban elderly
Neu0v0 = sum(Seu0v0, Eeu1v0, Aeu1v0, Ieu1v0, Heu1v0, Rpeu1v0, W1Rpeu1v0,W2Rpeu1v0,W3Rpeu1v0, Rneu1v0) #Unvax and no prior exposure
Neu1v0 = sum(Speu1v0, Sneu1v0, Eeu2v0, Aeu2v0, Ieu2v0, Heu2v0, Rpeu2v0, Rneu2v0) #Unvax and one prior
Neu2v0 = sum(Speu2v0, Sneu2v0, Eeu3v0, Aeu3v0, Ieu3v0, Heu3v0, Rpeu3v0, Rneu3v0) #Unvax and two prior
Neu0v1 = sum(Speu0v1,Vpeu0v1, W1Vpeu0v1,W2Vpeu0v1,W3Vpeu0v1,Vneu0v1, Sneu0v1, Eeu1v1, Aeu1v1, Ieu1v1, Heu1v1, Rpeu1v1, Rneu1v1) #vax 1 dose and no prior exposure
Neu1v1 = sum(Speu1v1, Sneu1v1, Eeu2v1, Aeu2v1, Ieu2v1, Heu2v1, Rpeu2v1, Rneu2v1) #vax 1 dose and one prior
Neu2v1 = sum(Speu2v1, Sneu2v1, Eeu3v1, Aeu3v1, Ieu3v1, Heu3v1, Rpeu3v1, Rneu3v1) #vax 1 dose and two prior
Neu0v2 = sum(Speu0v2, Vpeu0v2, Vneu0v2,Sneu0v2, Eeu1v2, Aeu1v2, Ieu1v2, Heu1v2, Rpeu1v2, Rneu1v2) #vax 2 dose and no prior exposure
Neu1v2 = sum(Speu1v2, Sneu1v2, Eeu2v2, Aeu2v2, Ieu2v2, Heu2v2, Rpeu2v2, Rneu2v2) #vax 2 dose and one prior
Neu2v2 = sum(Speu2v2, Sneu2v2, Eeu3v2, Aeu3v2, Ieu3v2, Heu3v2, Rpeu3v2, Rneu3v2) #vax 2 doseand two prior
Neu0v3 = sum(Speu0v3, Vpeu0v3, Vneu0v3, Sneu0v3, Eeu1v3, Aeu1v3, Ieu1v3, Heu1v3, Rpeu1v3, Rneu1v3) #vax 3 dose and no prior exposure
Neu1v3 = sum(Speu1v3, Sneu1v3, Eeu2v3, Aeu2v3, Ieu2v3, Heu2v3, Rpeu2v3, Rneu2v3) #vax 3 dose and one prior
Neu2v3 = sum(Speu2v3, Sneu2v3, Eeu3v3, Aeu3v3, Ieu3v3, Heu3v3, Rpeu3v3, Rneu3v3) #vax 3 dose and two prior
##Population sums
Nchildr = sum(Ncr0v0,Ncr1v0,Ncr2v0,Ncr0v1,Ncr1v1,Ncr2v1,Ncr0v2,Ncr1v2,Ncr2v2,Ncr0v3,Ncr1v3,Ncr2v3)
Nadultr = sum(Nar0v0,Nar1v0,Nar2v0,Nar0v1,Nar1v1,Nar2v1,Nar0v2,Nar1v2,Nar2v2,Nar0v3,Nar1v3,Nar2v3)
Noldr = sum(Ner0v0,Ner1v0,Ner2v0,Ner0v1,Ner1v1,Ner2v1,Ner0v2,Ner1v2,Ner2v2,Ner0v3,Ner1v3,Ner2v3)
Nchildu = sum(Ncu0v0,Ncu1v0,Ncu2v0,Ncu0v1,Ncu1v1,Ncu2v1,Ncu0v2,Ncu1v2,Ncu2v2,Ncu0v3,Ncu1v3,Ncu2v3)
Nadultu = sum(Nau0v0,Nau1v0,Nau2v0,Nau0v1,Nau1v1,Nau2v1,Nau0v2,Nau1v2,Nau2v2,Nau0v3,Nau1v3,Nau2v3)
Noldu = sum(Neu0v0,Neu1v0,Neu2v0,Neu0v1,Neu1v1,Neu2v1,Neu0v2,Neu1v2,Neu2v2,Neu0v3,Neu1v3,Neu2v3)
## Vax values (0 unless triggered)
## Vax values (0 unless triggered)
delta1_cr<-0; delta1_cu<-0; delta1_ar<-0; delta1_au<-0; delta1_er <- 0; delta1_eu <-0
delta2_cr<-0; delta2_cu<-0; delta2_ar<-0; delta2_au<-0; delta2_er <- 0; delta2_eu <-0
delta3_cr<-0; delta3_cu<-0
##Social distancing stuff
#create the seasonality parameter
#years = t/365
#seas = 1 + beta1 *(cos(2*3.141593*years + 1)) #seasonal forcing
##r0_hyp <- r00
#sd <- (r0_hyp)/r0
#if ((t/365)%%1>(270/365)){
#yr<-floor(years)
# if(yr==0){
# r0_hyp <- r00
# } else if(yr==1){
# r0_hyp <- r01
# } else if(yr==2){
# r0_hyp <- r02
# } else if(yr==3){
# r0_hyp <- r03
# } else if(yr==4){
# r0_hyp <- r04
# } else if(yr==5){
# r0_hyp <- r05
# } else if(yr==6){
# r0_hyp <- r06
# } else if (yr==7){
# r0_hyp <- r07
# } else if (yr==8){
# r0_hyp <- r08
# } else {
# r0_hyp <- r09
# }
#sd <- ((r0_hyp)/r0)*seas
#} else {
# sd <- 1.8/r0
#}
#if(t<=100){
# sd <- sd2
#} else if(t<=320){
# sd <- rel_newvar
#} else {
# sd <- rel_newvar ##keep on for now and see what happens
#}
### imunne escape factor for those with either prior exposur or prior vaccination
#if (t <= 100){
imm_esc_factor <- imm_esc_factor_omi
#} else {
# imm_esc_factor <- imm_esc_factor_newvar
#}
if(t >=vax_first){
if((t/vax_int)%%1>(vax_start)&(t/vax_int)%%1<=(vax_end)){
delta3_ar <-0
delta3_au <-0
delta3_er <-0.02
delta3_eu <-0.02
} else{
delta3_ar <-0
delta3_au <-0
delta3_er <-0
delta3_eu <-0
}
}else{
delta3_ar <-0
delta3_au <-0
delta3_er <-0
delta3_eu <-0
}
#StartODES
# Force of infection
# Foi_cr: Interpreted as FOI exerted on child rural susceptibles
foi_cr_0v0 = beta_c * ((CM[1,1]*(Icr1v0 +Icr2v0 +Icr3v0 +Icr1v1 +Icr2v1 +Icr3v1 + Icr1v2 +Icr2v2 +Icr3v2 +Icr1v3 +Icr2v3 +Icr3v3 + alpha*(Acr1v0 +Acr2v0 +Acr3v0 +Acr1v1 +Acr2v1 +Acr3v1 + Acr1v2 +Acr2v2 +Acr3v2 +Acr1v3 +Acr2v3 +Acr3v3))/Nchildr) + # first part is rural infectious -> rural suscepible
(CM[2,1]*(Iar1v0 +Iar2v0 +Iar3v0 +Iar1v1 +Iar2v1 +Iar3v1 + Iar1v2 +Iar2v2 +Iar3v2 +Iar1v3 +Iar2v3 +Iar3v3 + alpha*(Aar1v0 +Aar2v0 +Aar3v0 +Aar1v1 +Aar2v1 +Aar3v1 + Aar1v2 +Aar2v2 +Aar3v2 +Aar1v3 +Aar2v3 +Aar3v3))/Nadultr) +
(CM[3,1]*(Ier1v0 +Ier2v0 +Ier3v0 +Ier1v1 +Ier2v1 +Ier3v1 + Ier1v2 +Ier2v2 +Ier3v2 +Ier1v3 +Ier2v3 +Ier3v3 + alpha*(Aer1v0 +Aer2v0 +Aer3v0 +Aer1v1 +Aer2v1 +Aer3v1 + Aer1v2 +Aer2v2 +Aer3v2 +Aer1v3 +Aer2v3 +Aer3v3))/Noldr) +
#second part is urban infectious -> rural susceptible
(CM[4,1]*(Icu1v0 +Icu2v0 +Icu3v0 +Icu1v1 +Icu2v1 +Icu3v1 + Icu1v2 +Icu2v2 +Icu3v2 +Icu1v3 +Icu2v3 +Icu3v3 + alpha*(Acu1v0 +Acu2v0 +Acu3v0 +Acu1v1 +Acu2v1 +Acu3v1 + Acu1v2 +Acu2v2 +Acu3v2 +Acu1v3 +Acu2v3 +Acu3v3))/Nchildu) +
(CM[5,1]*(Iau1v0 +Iau2v0 +Iau3v0 +Iau1v1 +Iau2v1 +Iau3v1 + Iau1v2 +Iau2v2 +Iau3v2 +Iau1v3 +Iau2v3 +Iau3v3 + alpha*(Aau1v0 +Aau2v0 +Aau3v0 +Aau1v1 +Aau2v1 +Aau3v1 + Aau1v2 +Aau2v2 +Aau3v2 +Aau1v3 +Aau2v3 +Aau3v3))/Nadultu) +
(CM[6,1]*(Ieu1v0 +Ieu2v0 +Ieu3v0 +Ieu1v1 +Ieu2v1 +Ieu3v1 + Ieu1v2 +Ieu2v2 +Ieu3v2 +Ieu1v3 +Ieu2v3 +Ieu3v3 + alpha*(Aeu1v0 +Aeu2v0 +Aeu3v0 +Aeu1v1 +Aeu2v1 +Aeu3v1 + Aeu1v2 +Aeu2v2 +Aeu3v2 +Aeu1v3 +Aeu2v3 +Aeu3v3))/Noldu))
foi_ar_0v0 = beta_a * ((CM[1,2]*(Icr1v0 +Icr2v0 +Icr3v0 +Icr1v1 +Icr2v1 +Icr3v1 + Icr1v2 +Icr2v2 +Icr3v2 +Icr1v3 +Icr2v3 +Icr3v3 + alpha*(Acr1v0 +Acr2v0 +Acr3v0 +Acr1v1 +Acr2v1 +Acr3v1 + Acr1v2 +Acr2v2 +Acr3v2 +Acr1v3 +Acr2v3 +Acr3v3))/Nchildr) + # first part is rural infectious -> rural suscepible
(CM[2,2]*(Iar1v0 +Iar2v0 +Iar3v0 +Iar1v1 +Iar2v1 +Iar3v1 + Iar1v2 +Iar2v2 +Iar3v2 +Iar1v3 +Iar2v3 +Iar3v3 + alpha*(Aar1v0 +Aar2v0 +Aar3v0 +Aar1v1 +Aar2v1 +Aar3v1 + Aar1v2 +Aar2v2 +Aar3v2 +Aar1v3 +Aar2v3 +Aar3v3))/Nadultr) +
(CM[3,2]*(Ier1v0 +Ier2v0 +Ier3v0 +Ier1v1 +Ier2v1 +Ier3v1 + Ier1v2 +Ier2v2 +Ier3v2 +Ier1v3 +Ier2v3 +Ier3v3 + alpha*(Aer1v0 +Aer2v0 +Aer3v0 +Aer1v1 +Aer2v1 +Aer3v1 + Aer1v2 +Aer2v2 +Aer3v2 +Aer1v3 +Aer2v3 +Aer3v3))/Noldr) +
#second part is urban infectious -> rural susceptible
(CM[4,2]*(Icu1v0 +Icu2v0 +Icu3v0 +Icu1v1 +Icu2v1 +Icu3v1 + Icu1v2 +Icu2v2 +Icu3v2 +Icu1v3 +Icu2v3 +Icu3v3 + alpha*(Acu1v0 +Acu2v0 +Acu3v0 +Acu1v1 +Acu2v1 +Acu3v1 + Acu1v2 +Acu2v2 +Acu3v2 +Acu1v3 +Acu2v3 +Acu3v3))/Nchildu) +
(CM[5,2]*(Iau1v0 +Iau2v0 +Iau3v0 +Iau1v1 +Iau2v1 +Iau3v1 + Iau1v2 +Iau2v2 +Iau3v2 +Iau1v3 +Iau2v3 +Iau3v3 + alpha*(Aau1v0 +Aau2v0 +Aau3v0 +Aau1v1 +Aau2v1 +Aau3v1 + Aau1v2 +Aau2v2 +Aau3v2 +Aau1v3 +Aau2v3 +Aau3v3))/Nadultu) +
(CM[6,2]*(Ieu1v0 +Ieu2v0 +Ieu3v0 +Ieu1v1 +Ieu2v1 +Ieu3v1 + Ieu1v2 +Ieu2v2 +Ieu3v2 +Ieu1v3 +Ieu2v3 +Ieu3v3 + alpha*(Aeu1v0 +Aeu2v0 +Aeu3v0 +Aeu1v1 +Aeu2v1 +Aeu3v1 + Aeu1v2 +Aeu2v2 +Aeu3v2 +Aeu1v3 +Aeu2v3 +Aeu3v3))/Noldu))
foi_er_0v0 = beta_e * ((CM[1,3]*(Icr1v0 +Icr2v0 +Icr3v0 +Icr1v1 +Icr2v1 +Icr3v1 + Icr1v2 +Icr2v2 +Icr3v2 +Icr1v3 +Icr2v3 +Icr3v3 + alpha*(Acr1v0 +Acr2v0 +Acr3v0 +Acr1v1 +Acr2v1 +Acr3v1 + Acr1v2 +Acr2v2 +Acr3v2 +Acr1v3 +Acr2v3 +Acr3v3))/Nchildr) + # first part is rural infectious -> rural suscepible
(CM[2,3]*(Iar1v0 +Iar2v0 +Iar3v0 +Iar1v1 +Iar2v1 +Iar3v1 + Iar1v2 +Iar2v2 +Iar3v2 +Iar1v3 +Iar2v3 +Iar3v3 + alpha*(Aar1v0 +Aar2v0 +Aar3v0 +Aar1v1 +Aar2v1 +Aar3v1 + Aar1v2 +Aar2v2 +Aar3v2 +Aar1v3 +Aar2v3 +Aar3v3))/Nadultr) +
(CM[3,3]*(Ier1v0 +Ier2v0 +Ier3v0 +Ier1v1 +Ier2v1 +Ier3v1 + Ier1v2 +Ier2v2 +Ier3v2 +Ier1v3 +Ier2v3 +Ier3v3 + alpha*(Aer1v0 +Aer2v0 +Aer3v0 +Aer1v1 +Aer2v1 +Aer3v1 + Aer1v2 +Aer2v2 +Aer3v2 +Aer1v3 +Aer2v3 +Aer3v3))/Noldr) +
#second part is urban infectious -> rural susceptible
(CM[4,3]*(Icu1v0 +Icu2v0 +Icu3v0 +Icu1v1 +Icu2v1 +Icu3v1 + Icu1v2 +Icu2v2 +Icu3v2 +Icu1v3 +Icu2v3 +Icu3v3 + alpha*(Acu1v0 +Acu2v0 +Acu3v0 +Acu1v1 +Acu2v1 +Acu3v1 + Acu1v2 +Acu2v2 +Acu3v2 +Acu1v3 +Acu2v3 +Acu3v3))/Nchildu) +
(CM[5,3]*(Iau1v0 +Iau2v0 +Iau3v0 +Iau1v1 +Iau2v1 +Iau3v1 + Iau1v2 +Iau2v2 +Iau3v2 +Iau1v3 +Iau2v3 +Iau3v3 + alpha*(Aau1v0 +Aau2v0 +Aau3v0 +Aau1v1 +Aau2v1 +Aau3v1 + Aau1v2 +Aau2v2 +Aau3v2 +Aau1v3 +Aau2v3 +Aau3v3))/Nadultu) +
(CM[6,3]*(Ieu1v0 +Ieu2v0 +Ieu3v0 +Ieu1v1 +Ieu2v1 +Ieu3v1 + Ieu1v2 +Ieu2v2 +Ieu3v2 +Ieu1v3 +Ieu2v3 +Ieu3v3 + alpha*(Aeu1v0 +Aeu2v0 +Aeu3v0 +Aeu1v1 +Aeu2v1 +Aeu3v1 + Aeu1v2 +Aeu2v2 +Aeu3v2 +Aeu1v3 +Aeu2v3 +Aeu3v3))/Noldu))
foi_cu_0v0 = beta_c * ((CM[1,4]*(Icr1v0 +Icr2v0 +Icr3v0 +Icr1v1 +Icr2v1 +Icr3v1 + Icr1v2 +Icr2v2 +Icr3v2 +Icr1v3 +Icr2v3 +Icr3v3 + alpha*(Acr1v0 +Acr2v0 +Acr3v0 +Acr1v1 +Acr2v1 +Acr3v1 + Acr1v2 +Acr2v2 +Acr3v2 +Acr1v3 +Acr2v3 +Acr3v3))/Nchildr) + # first part is rural infectious -> rural suscepible
(CM[2,4]*(Iar1v0 +Iar2v0 +Iar3v0 +Iar1v1 +Iar2v1 +Iar3v1 + Iar1v2 +Iar2v2 +Iar3v2 +Iar1v3 +Iar2v3 +Iar3v3 + alpha*(Aar1v0 +Aar2v0 +Aar3v0 +Aar1v1 +Aar2v1 +Aar3v1 + Aar1v2 +Aar2v2 +Aar3v2 +Aar1v3 +Aar2v3 +Aar3v3))/Nadultr) +
(CM[3,4]*(Ier1v0 +Ier2v0 +Ier3v0 +Ier1v1 +Ier2v1 +Ier3v1 + Ier1v2 +Ier2v2 +Ier3v2 +Ier1v3 +Ier2v3 +Ier3v3 + alpha*(Aer1v0 +Aer2v0 +Aer3v0 +Aer1v1 +Aer2v1 +Aer3v1 + Aer1v2 +Aer2v2 +Aer3v2 +Aer1v3 +Aer2v3 +Aer3v3))/Noldr) +
#second part is urban infectious -> urban susceptible
(CM[4,4]*(Icu1v0 +Icu2v0 +Icu3v0 +Icu1v1 +Icu2v1 +Icu3v1 + Icu1v2 +Icu2v2 +Icu3v2 +Icu1v3 +Icu2v3 +Icu3v3 + alpha*(Acu1v0 +Acu2v0 +Acu3v0 +Acu1v1 +Acu2v1 +Acu3v1 + Acu1v2 +Acu2v2 +Acu3v2 +Acu1v3 +Acu2v3 +Acu3v3))/Nchildu) +
(CM[5,4]*(Iau1v0 +Iau2v0 +Iau3v0 +Iau1v1 +Iau2v1 +Iau3v1 + Iau1v2 +Iau2v2 +Iau3v2 +Iau1v3 +Iau2v3 +Iau3v3 + alpha*(Aau1v0 +Aau2v0 +Aau3v0 +Aau1v1 +Aau2v1 +Aau3v1 + Aau1v2 +Aau2v2 +Aau3v2 +Aau1v3 +Aau2v3 +Aau3v3))/Nadultu) +
(CM[6,4]*(Ieu1v0 +Ieu2v0 +Ieu3v0 +Ieu1v1 +Ieu2v1 +Ieu3v1 + Ieu1v2 +Ieu2v2 +Ieu3v2 +Ieu1v3 +Ieu2v3 +Ieu3v3 + alpha*(Aeu1v0 +Aeu2v0 +Aeu3v0 +Aeu1v1 +Aeu2v1 +Aeu3v1 + Aeu1v2 +Aeu2v2 +Aeu3v2 +Aeu1v3 +Aeu2v3 +Aeu3v3))/Noldu))
foi_au_0v0 = beta_a * ((CM[1,5]*(Icr1v0 +Icr2v0 +Icr3v0 +Icr1v1 +Icr2v1 +Icr3v1 + Icr1v2 +Icr2v2 +Icr3v2 +Icr1v3 +Icr2v3 +Icr3v3 + alpha*(Acr1v0 +Acr2v0 +Acr3v0 +Acr1v1 +Acr2v1 +Acr3v1 + Acr1v2 +Acr2v2 +Acr3v2 +Acr1v3 +Acr2v3 +Acr3v3))/Nchildr) + # first part is rural infectious -> rural suscepible
(CM[2,5]*(Iar1v0 +Iar2v0 +Iar3v0 +Iar1v1 +Iar2v1 +Iar3v1 + Iar1v2 +Iar2v2 +Iar3v2 +Iar1v3 +Iar2v3 +Iar3v3 + alpha*(Aar1v0 +Aar2v0 +Aar3v0 +Aar1v1 +Aar2v1 +Aar3v1 + Aar1v2 +Aar2v2 +Aar3v2 +Aar1v3 +Aar2v3 +Aar3v3))/Nadultr) +
(CM[3,5]*(Ier1v0 +Ier2v0 +Ier3v0 +Ier1v1 +Ier2v1 +Ier3v1 + Ier1v2 +Ier2v2 +Ier3v2 +Ier1v3 +Ier2v3 +Ier3v3 + alpha*(Aer1v0 +Aer2v0 +Aer3v0 +Aer1v1 +Aer2v1 +Aer3v1 + Aer1v2 +Aer2v2 +Aer3v2 +Aer1v3 +Aer2v3 +Aer3v3))/Noldr) +
#second part is urban infectious -> urban susceptible
(CM[4,5]*(Icu1v0 +Icu2v0 +Icu3v0 +Icu1v1 +Icu2v1 +Icu3v1 + Icu1v2 +Icu2v2 +Icu3v2 +Icu1v3 +Icu2v3 +Icu3v3 + alpha*(Acu1v0 +Acu2v0 +Acu3v0 +Acu1v1 +Acu2v1 +Acu3v1 + Acu1v2 +Acu2v2 +Acu3v2 +Acu1v3 +Acu2v3 +Acu3v3))/Nchildu) +
(CM[5,5]*(Iau1v0 +Iau2v0 +Iau3v0 +Iau1v1 +Iau2v1 +Iau3v1 + Iau1v2 +Iau2v2 +Iau3v2 +Iau1v3 +Iau2v3 +Iau3v3 + alpha*(Aau1v0 +Aau2v0 +Aau3v0 +Aau1v1 +Aau2v1 +Aau3v1 + Aau1v2 +Aau2v2 +Aau3v2 +Aau1v3 +Aau2v3 +Aau3v3))/Nadultu) +
(CM[6,5]*(Ieu1v0 +Ieu2v0 +Ieu3v0 +Ieu1v1 +Ieu2v1 +Ieu3v1 + Ieu1v2 +Ieu2v2 +Ieu3v2 +Ieu1v3 +Ieu2v3 +Ieu3v3 + alpha*(Aeu1v0 +Aeu2v0 +Aeu3v0 +Aeu1v1 +Aeu2v1 +Aeu3v1 + Aeu1v2 +Aeu2v2 +Aeu3v2 +Aeu1v3 +Aeu2v3 +Aeu3v3))/Noldu))
foi_eu_0v0 = beta_e * ((CM[1,6]*(Icr1v0 +Icr2v0 +Icr3v0 +Icr1v1 +Icr2v1 +Icr3v1 + Icr1v2 +Icr2v2 +Icr3v2 +Icr1v3 +Icr2v3 +Icr3v3 + alpha*(Acr1v0 +Acr2v0 +Acr3v0 +Acr1v1 +Acr2v1 +Acr3v1 + Acr1v2 +Acr2v2 +Acr3v2 +Acr1v3 +Acr2v3 +Acr3v3))/Nchildr) + # first part is rural infectious -> rural suscepible
(CM[2,6]*(Iar1v0 +Iar2v0 +Iar3v0 +Iar1v1 +Iar2v1 +Iar3v1 + Iar1v2 +Iar2v2 +Iar3v2 +Iar1v3 +Iar2v3 +Iar3v3 + alpha*(Aar1v0 +Aar2v0 +Aar3v0 +Aar1v1 +Aar2v1 +Aar3v1 + Aar1v2 +Aar2v2 +Aar3v2 +Aar1v3 +Aar2v3 +Aar3v3))/Nadultr) +
(CM[3,6]*(Ier1v0 +Ier2v0 +Ier3v0 +Ier1v1 +Ier2v1 +Ier3v1 + Ier1v2 +Ier2v2 +Ier3v2 +Ier1v3 +Ier2v3 +Ier3v3 + alpha*(Aer1v0 +Aer2v0 +Aer3v0 +Aer1v1 +Aer2v1 +Aer3v1 + Aer1v2 +Aer2v2 +Aer3v2 +Aer1v3 +Aer2v3 +Aer3v3))/Noldr) +
#second part is urban infectious -> urban susceptible
(CM[4,6]*(Icu1v0 +Icu2v0 +Icu3v0 +Icu1v1 +Icu2v1 +Icu3v1 + Icu1v2 +Icu2v2 +Icu3v2 +Icu1v3 +Icu2v3 +Icu3v3 + alpha*(Acu1v0 +Acu2v0 +Acu3v0 +Acu1v1 +Acu2v1 +Acu3v1 + Acu1v2 +Acu2v2 +Acu3v2 +Acu1v3 +Acu2v3 +Acu3v3))/Nchildu) +
(CM[5,6]*(Iau1v0 +Iau2v0 +Iau3v0 +Iau1v1 +Iau2v1 +Iau3v1 + Iau1v2 +Iau2v2 +Iau3v2 +Iau1v3 +Iau2v3 +Iau3v3 + alpha*(Aau1v0 +Aau2v0 +Aau3v0 +Aau1v1 +Aau2v1 +Aau3v1 + Aau1v2 +Aau2v2 +Aau3v2 +Aau1v3 +Aau2v3 +Aau3v3))/Nadultu) +
(CM[6,6]*(Ieu1v0 +Ieu2v0 +Ieu3v0 +Ieu1v1 +Ieu2v1 +Ieu3v1 + Ieu1v2 +Ieu2v2 +Ieu3v2 +Ieu1v3 +Ieu2v3 +Ieu3v3 + alpha*(Aeu1v0 +Aeu2v0 +Aeu3v0 +Aeu1v1 +Aeu2v1 +Aeu3v1 + Aeu1v2 +Aeu2v2 +Aeu3v2 +Aeu1v3 +Aeu2v3 +Aeu3v3))/Noldu))
foi_cr_0v1 = foi_cr_0v0 * (1-vei1) *imm_esc_factor
foi_cu_0v1 = foi_cu_0v0 * (1-vei1) *imm_esc_factor
foi_ar_0v1 = foi_ar_0v0 * (1-vei1) *imm_esc_factor
foi_au_0v1 = foi_au_0v0 * (1-vei1) *imm_esc_factor
foi_er_0v1 = foi_er_0v0 * (1-vei1) *imm_esc_factor
foi_eu_0v1 = foi_eu_0v0 * (1-vei1) *imm_esc_factor
foi_cr_0v2 = foi_cr_0v0 * (1-vei2) *imm_esc_factor
foi_cu_0v2 = foi_cu_0v0 * (1-vei2) *imm_esc_factor
foi_ar_0v2 = foi_ar_0v0 * (1-vei2) *imm_esc_factor
foi_au_0v2 = foi_au_0v0 * (1-vei2) *imm_esc_factor
foi_er_0v2 = foi_er_0v0 * (1-vei2) *imm_esc_factor
foi_eu_0v2 = foi_eu_0v0 * (1-vei2) *imm_esc_factor
foi_cr_0v3 = foi_cr_0v0 * (1-vei3) *imm_esc_factor
foi_cu_0v3 = foi_cu_0v0 * (1-vei3) *imm_esc_factor
foi_ar_0v3 = foi_ar_0v0 * (1-vei3) *imm_esc_factor
foi_au_0v3 = foi_au_0v0 * (1-vei3) *imm_esc_factor
foi_er_0v3 = foi_er_0v0 * (1-vei3) *imm_esc_factor
foi_eu_0v3 = foi_eu_0v0 * (1-vei3) *imm_esc_factor
### After first exposure
foi_cr_1v0 = foi_cr_0v0 * red_inf_1 *imm_esc_factor*0.7
foi_cu_1v0 = foi_cu_0v0 * red_inf_1 *imm_esc_factor*0.7
foi_ar_1v0 = foi_ar_0v0 * red_inf_1 *imm_esc_factor
foi_au_1v0 = foi_au_0v0 * red_inf_1 *imm_esc_factor
foi_er_1v0 = foi_er_0v0 * red_inf_1 *imm_esc_factor
foi_eu_1v0 = foi_eu_0v0 * red_inf_1 *imm_esc_factor
foi_cr_1v1 = foi_cr_0v1 * red_inf_1 *imm_esc_factor
foi_cu_1v1 = foi_cu_0v1 * red_inf_1 *imm_esc_factor
foi_ar_1v1 = foi_ar_0v1 * red_inf_1 *imm_esc_factor
foi_au_1v1 = foi_au_0v1 * red_inf_1 *imm_esc_factor
foi_er_1v1 = foi_er_0v1 * red_inf_1 *imm_esc_factor
foi_eu_1v1 = foi_eu_0v1 * red_inf_1 *imm_esc_factor
foi_cr_1v2 = foi_cr_0v2 * red_inf_1 *imm_esc_factor
foi_cu_1v2 = foi_cu_0v2 * red_inf_1 *imm_esc_factor
foi_ar_1v2 = foi_ar_0v2 * red_inf_1 *imm_esc_factor
foi_au_1v2 = foi_au_0v2 * red_inf_1 *imm_esc_factor
foi_er_1v2 = foi_er_0v2 * red_inf_1 *imm_esc_factor
foi_eu_1v2 = foi_eu_0v2 * red_inf_1 *imm_esc_factor
foi_cr_1v3 = foi_cr_0v3 * red_inf_1 *imm_esc_factor
foi_cu_1v3 = foi_cu_0v3 * red_inf_1 *imm_esc_factor
foi_ar_1v3 = foi_ar_0v3 * red_inf_1 *imm_esc_factor
foi_au_1v3 = foi_au_0v3 * red_inf_1 *imm_esc_factor
foi_er_1v3 = foi_er_0v3 * red_inf_1 *imm_esc_factor
foi_eu_1v3 = foi_eu_0v3 * red_inf_1 *imm_esc_factor
### After second exposure
foi_cr_2v0 = foi_cr_0v0 * red_inf_2 *imm_esc_factor*0.7
foi_cu_2v0 = foi_cu_0v0 * red_inf_2*imm_esc_factor*0.7
foi_ar_2v0 = foi_ar_0v0 * red_inf_2*imm_esc_factor
foi_au_2v0 = foi_au_0v0 * red_inf_2*imm_esc_factor
foi_er_2v0 = foi_er_0v0 * red_inf_2*imm_esc_factor
foi_eu_2v0 = foi_eu_0v0 * red_inf_2*imm_esc_factor
foi_cr_2v1 = foi_cr_0v1 * red_inf_2 *imm_esc_factor
foi_cu_2v1 = foi_cu_0v1 * red_inf_2*imm_esc_factor
foi_ar_2v1 = foi_ar_0v1 * red_inf_2*imm_esc_factor
foi_au_2v1 = foi_au_0v1 * red_inf_2*imm_esc_factor
foi_er_2v1 = foi_er_0v1 * red_inf_2*imm_esc_factor
foi_eu_2v1 = foi_eu_0v1 * red_inf_2*imm_esc_factor
foi_cr_2v2 = foi_cr_0v2 * red_inf_2*imm_esc_factor
foi_cu_2v2 = foi_cu_0v2 * red_inf_2*imm_esc_factor
foi_ar_2v2 = foi_ar_0v2 * red_inf_2*imm_esc_factor
foi_au_2v2 = foi_au_0v2 * red_inf_2*imm_esc_factor
foi_er_2v2 = foi_er_0v2 * red_inf_2*imm_esc_factor
foi_eu_2v2 = foi_eu_0v2 * red_inf_2*imm_esc_factor
foi_cr_2v3 = foi_cr_0v3 * red_inf_2*imm_esc_factor
foi_cu_2v3 = foi_cu_0v3 * red_inf_2*imm_esc_factor
foi_ar_2v3 = foi_ar_0v3 * red_inf_2*imm_esc_factor
foi_au_2v3 = foi_au_0v3 * red_inf_2*imm_esc_factor
foi_er_2v3 = foi_er_0v3 * red_inf_2*imm_esc_factor
foi_eu_2v3 = foi_eu_0v3 * red_inf_2*imm_esc_factor
################################
##Unvaccinated and unexposed####
################################
#Susceptible
dScr0v0 = -Scr0v0 * sd * foi_cr_0v0 - delta1_cr * Scr0v0
dScu0v0 = -Scu0v0 * sd * foi_cu_0v0 - delta1_cu * Scu0v0
dSar0v0 = -Sar0v0 * sd * foi_ar_0v0 - delta1_ar * Sar0v0
dSau0v0 = -Sau0v0 * sd * foi_au_0v0 - delta1_au * Sau0v0
dSer0v0 = -Ser0v0 * sd * foi_er_0v0 - delta1_er * Ser0v0
dSeu0v0 = -Seu0v0 * sd * foi_eu_0v0 - delta1_eu * Seu0v0
#Exposed
dEcr1v0 = Scr0v0 * sd * foi_cr_0v0 - sigma*Ecr1v0 - delta1_cr*Ecr1v0
dEcu1v0 = Scu0v0 * sd * foi_cu_0v0 - sigma*Ecu1v0 - delta1_cu*Ecu1v0
dEar1v0 = Sar0v0 * sd * foi_ar_0v0 - sigma*Ear1v0 - delta1_ar*Ear1v0
dEau1v0 = Sau0v0 * sd * foi_au_0v0 - sigma*Eau1v0 - delta1_au*Eau1v0
dEer1v0 = Ser0v0 * sd * foi_er_0v0 - sigma*Eer1v0 - delta1_er*Eer1v0
dEeu1v0 = Seu0v0 * sd * foi_eu_0v0 - sigma*Eeu1v0 - delta1_eu*Eeu1v0
# Asymptomatic
dAcr1v0 = (1-nu_c)*sigma*Ecr1v0 - gamma_A * Acr1v0 - delta1_cr*Acr1v0
dAcu1v0 = (1-nu_c)*sigma*Ecu1v0 - gamma_A * Acu1v0 - delta1_cu*Acu1v0
dAar1v0 = (1-nu_a)*sigma*Ear1v0 - gamma_A * Aar1v0 - delta1_ar*Aar1v0
dAau1v0 = (1-nu_a)*sigma*Eau1v0 - gamma_A * Aau1v0 - delta1_au*Aau1v0
dAer1v0 = (1-nu_e)*sigma*Eer1v0 - gamma_A * Aer1v0 - delta1_er*Aer1v0
dAeu1v0 = (1-nu_e)*sigma*Eeu1v0 - gamma_A * Aeu1v0 - delta1_eu*Aeu1v0
#Symptomatic
dIcr1v0 = nu_c*sigma*Ecr1v0 - gamma_I * Icr1v0
dIcu1v0 = nu_c*sigma*Ecu1v0 - gamma_I * Icu1v0
dIar1v0 = nu_a*sigma*Ear1v0 - gamma_I * Iar1v0
dIau1v0 = nu_a*sigma*Eau1v0 - gamma_I * Iau1v0
dIer1v0 = nu_e*sigma*Eer1v0 - gamma_I * Ier1v0
dIeu1v0 = nu_e*sigma*Eeu1v0 - gamma_I * Ieu1v0
# Hospitalized
dHcr1v0 = phi_c*gamma_I*Icr1v0 - gamma_H * Hcr1v0
dHcu1v0 = phi_c*gamma_I*Icu1v0 - gamma_H * Hcu1v0
dHar1v0 = phi_a*gamma_I*Iar1v0 - gamma_H * Har1v0
dHau1v0 = phi_a*gamma_I*Iau1v0 - gamma_H * Hau1v0
dHer1v0 = phi_e*gamma_I*Ier1v0 - gamma_H * Her1v0
dHeu1v0 = phi_e*gamma_I*Ieu1v0 - gamma_H * Heu1v0
# Recovered and seroconverted
dRpcr1v0 = pi*(1-phi_c)*gamma_I*Icr1v0 + pi*gamma_A*Acr1v0 + pi*(1-mu_c)*gamma_H*Hcr1v0 -4*kappa1*Rpcr1v0 - omega_pc*Rpcr1v0 - delta1_cr*Rpcr1v0
dRpcu1v0 = pi*(1-phi_c)*gamma_I*Icu1v0 + pi*gamma_A*Acu1v0 + pi*(1-mu_c)*gamma_H*Hcu1v0 -4*kappa1*Rpcu1v0 - omega_pc*Rpcu1v0 - delta1_cu*Rpcu1v0
dRpar1v0 = pi*(1-phi_a)*gamma_I*Iar1v0 + pi*gamma_A*Aar1v0 + pi*(1-mu_a)*gamma_H*Har1v0 -4*kappa1*Rpar1v0 - omega_pa*Rpar1v0 - delta1_ar*Rpar1v0
dRpau1v0 = pi*(1-phi_a)*gamma_I*Iau1v0 + pi*gamma_A*Aau1v0 + pi*(1-mu_a)*gamma_H*Hau1v0 -4*kappa1*Rpau1v0 - omega_pa*Rpau1v0 - delta1_au*Rpau1v0
dRper1v0 = pi*(1-phi_e)*gamma_I*Ier1v0 + pi*gamma_A*Aer1v0 + pi*(1-mu_e)*gamma_H*Her1v0 -4*kappa1*Rper1v0 - omega_pe*Rper1v0 - delta1_er*Rper1v0
dRpeu1v0 = pi*(1-phi_e)*gamma_I*Ieu1v0 + pi*gamma_A*Aeu1v0 + pi*(1-mu_e)*gamma_H*Heu1v0 -4*kappa1*Rpeu1v0 - omega_pe*Rpeu1v0 - delta1_eu*Rpeu1v0
#Recovered and not seropositive
dRncr1v0 = (1-pi)*(1-phi_c)*gamma_I*Icr1v0 + (1-pi)*gamma_A*Acr1v0 + (1-pi)*(1-mu_c)*gamma_H*Hcr1v0 + 4*kappa1*W3Rpcr1v0 - omega_nc*Rncr1v0 - delta1_cr*Rncr1v0
dRncu1v0 = (1-pi)*(1-phi_c)*gamma_I*Icu1v0 + (1-pi)*gamma_A*Acu1v0 + (1-pi)*(1-mu_c)*gamma_H*Hcu1v0 + 4*kappa1*W3Rpcu1v0 - omega_nc*Rncu1v0 - delta1_cu*Rncu1v0
dRnar1v0 = (1-pi)*(1-phi_a)*gamma_I*Iar1v0 + (1-pi)*gamma_A*Aar1v0 + (1-pi)*(1-mu_a)*gamma_H*Har1v0 + 4*kappa1*W3Rpar1v0 - omega_na*Rnar1v0 - delta1_ar*Rnar1v0
dRnau1v0 = (1-pi)*(1-phi_a)*gamma_I*Iau1v0 + (1-pi)*gamma_A*Aau1v0 + (1-pi)*(1-mu_a)*gamma_H*Hau1v0 + 4*kappa1*W3Rpau1v0 - omega_na*Rnau1v0 - delta1_au*Rnau1v0
dRner1v0 = (1-pi)*(1-phi_e)*gamma_I*Ier1v0 + (1-pi)*gamma_A*Aer1v0 + (1-pi)*(1-mu_e)*gamma_H*Her1v0 + 4*kappa1*W3Rper1v0 - omega_ne*Rner1v0 - delta1_er*Rner1v0
dRneu1v0 = (1-pi)*(1-phi_e)*gamma_I*Ieu1v0 + (1-pi)*gamma_A*Aeu1v0 + (1-pi)*(1-mu_e)*gamma_H*Heu1v0 + 4*kappa1*W3Rpeu1v0 - omega_ne*Rneu1v0 - delta1_eu*Rneu1v0
#Deaths
dDcr1v0 = mu_c*gamma_H*Hcr1v0
dDcu1v0 = mu_c*gamma_H*Hcu1v0
dDar1v0 = mu_a*gamma_H*Har1v0
dDau1v0 = mu_a*gamma_H*Hau1v0
dDer1v0 = mu_e*gamma_H*Her1v0
dDeu1v0 = mu_e*gamma_H*Heu1v0
################################
##Unvaccinated and exposed once####
################################
#Susceptible
dSpcr1v0 = omega_pc*Rpcr1v0 + omega_pc*W1Rpcr1v0 +omega_pc*W2Rpcr1v0 +omega_pc*W3Rpcr1v0 -kappa1*Spcr1v0 - Spcr1v0 * sd * foi_cr_1v0 - delta1_cr * Spcr1v0 +omega4_pc*Spcr2v0 ##Note vaccination rate here doesnt differ by previous vax status
dSpcu1v0 = omega_pc*Rpcu1v0 + omega_pc*W1Rpcu1v0 +omega_pc*W2Rpcu1v0 +omega_pc*W3Rpcu1v0-kappa1*Spcu1v0 - Spcu1v0 * sd * foi_cu_1v0 - delta1_cu * Spcu1v0 + omega4_pc*Spcu2v0
dSpar1v0 = omega_pa*Rpar1v0 + omega_pa*W1Rpar1v0 +omega_pa*W2Rpar1v0 +omega_pa*W3Rpar1v0 -kappa1*Spar1v0 - Spar1v0 * sd * foi_ar_1v0 - delta1_ar * Spar1v0
dSpau1v0 = omega_pa*Rpau1v0 + omega_pa*W1Rpau1v0 +omega_pa*W2Rpau1v0 +omega_pa*W3Rpau1v0 -kappa1*Spau1v0 - Spau1v0 * sd * foi_au_1v0 - delta1_au * Spau1v0
dSper1v0 = omega_pe*Rper1v0 + omega_pe*W1Rper1v0 +omega_pe*W2Rper1v0 +omega_pe*W3Rper1v0 -kappa1*Sper1v0 - Sper1v0 * sd * foi_er_1v0 - delta1_er * Sper1v0
dSpeu1v0 = omega_pe*Rpeu1v0 + omega_pe*W1Rpeu1v0 +omega_pe*W2Rpeu1v0 +omega_pe*W3Rpeu1v0 -kappa1*Speu1v0 - Speu1v0 * sd * foi_eu_1v0 - delta1_eu * Speu1v0
dSncr1v0 = omega_nc*Rncr1v0 + kappa1*Spcr1v0 -Sncr1v0 * sd * foi_cr_1v0 - delta1_cr * Sncr1v0 + omega4_nc*Sncr2v0##Note vaccination rate here doesnt differ by previous vax status
dSncu1v0 = omega_nc*Rncu1v0 + kappa1*Spcu1v0 -Sncu1v0 * sd * foi_cu_1v0 - delta1_cu * Sncu1v0 + omega4_nc*Sncu2v0
dSnar1v0 = omega_na*Rnar1v0 + kappa1*Spar1v0 -Snar1v0 * sd * foi_ar_1v0 - delta1_ar * Snar1v0
dSnau1v0 = omega_na*Rnau1v0 + kappa1*Spau1v0 -Snau1v0 * sd * foi_au_1v0 - delta1_au * Snau1v0
dSner1v0 = omega_ne*Rner1v0 + kappa1*Sper1v0 -Sner1v0 * sd * foi_er_1v0 - delta1_er * Sner1v0
dSneu1v0 = omega_ne*Rneu1v0 + kappa1*Speu1v0 -Sneu1v0 * sd * foi_eu_1v0 - delta1_eu * Sneu1v0
#Exposed
dEcr2v0 = Spcr1v0 * sd * foi_cr_1v0 + Sncr1v0 * sd * foi_cr_1v0 - sigma * Ecr2v0 - delta1_cr*Ecr2v0
dEcu2v0 = Spcu1v0 * sd * foi_cu_1v0 + Sncu1v0 * sd * foi_cu_1v0 - sigma * Ecu2v0 - delta1_cu*Ecu2v0
dEar2v0 = Spar1v0 * sd * foi_ar_1v0 + Snar1v0 * sd * foi_ar_1v0 - sigma * Ear2v0 - delta1_ar*Ear2v0
dEau2v0 = Spau1v0 * sd * foi_au_1v0 + Snau1v0 * sd * foi_au_1v0 - sigma * Eau2v0 - delta1_au*Eau2v0
dEer2v0 = Sper1v0 * sd * foi_er_1v0 + Sner1v0 * sd * foi_er_1v0 - sigma * Eer2v0 - delta1_er*Eer2v0
dEeu2v0 = Speu1v0 * sd * foi_eu_1v0 + Sneu1v0 * sd * foi_eu_1v0 - sigma * Eeu2v0 - delta1_eu*Eeu2v0
# Asymptomatic
dAcr2v0 = (1-nu_c)*sigma*Ecr2v0 - gamma_A * Acr2v0 - delta1_cr*Acr2v0
dAcu2v0 = (1-nu_c)*sigma*Ecu2v0 - gamma_A * Acu2v0 - delta1_cu*Acu2v0
dAar2v0 = (1-nu_a)*sigma*Ear2v0 - gamma_A * Aar2v0 - delta1_ar*Aar2v0
dAau2v0 = (1-nu_a)*sigma*Eau2v0 - gamma_A * Aau2v0 - delta1_au*Aau2v0
dAer2v0 = (1-nu_e)*sigma*Eer2v0 - gamma_A * Aer2v0 - delta1_er*Aer2v0
dAeu2v0 = (1-nu_e)*sigma*Eeu2v0 - gamma_A * Aeu2v0 - delta1_eu*Aeu2v0
#Symptomatic
dIcr2v0 = nu_c*sigma*Ecr2v0 - gamma_I * Icr2v0
dIcu2v0 = nu_c*sigma*Ecu2v0 - gamma_I * Icu2v0
dIar2v0 = nu_a*sigma*Ear2v0 - gamma_I * Iar2v0
dIau2v0 = nu_a*sigma*Eau2v0 - gamma_I * Iau2v0
dIer2v0 = nu_e*sigma*Eer2v0 - gamma_I * Ier2v0
dIeu2v0 = nu_e*sigma*Eeu2v0 - gamma_I * Ieu2v0
# Hospitalized
dHcr2v0 = phi_c*gamma_I*Icr2v0 - gamma_H * Hcr2v0
dHcu2v0 = phi_c*gamma_I*Icu2v0 - gamma_H * Hcu2v0
dHar2v0 = phi_a*gamma_I*Iar2v0 - gamma_H * Har2v0
dHau2v0 = phi_a*gamma_I*Iau2v0 - gamma_H * Hau2v0
dHer2v0 = phi_e*gamma_I*Ier2v0 - gamma_H * Her2v0
dHeu2v0 = phi_e*gamma_I*Ieu2v0 - gamma_H * Heu2v0
# Recovered and seroconverted
dRpcr2v0 = pi*(1-phi_c)*gamma_I*Icr2v0 + pi*gamma_A*Acr2v0 + pi*(1-mu_c)*gamma_H*Hcr2v0 -kappa2*Rpcr2v0 - omega_pc*Rpcr2v0 - delta1_cr*Rpcr2v0
dRpcu2v0 = pi*(1-phi_c)*gamma_I*Icu2v0 + pi*gamma_A*Acu2v0 + pi*(1-mu_c)*gamma_H*Hcu2v0 -kappa2*Rpcu2v0 - omega_pc*Rpcu2v0 - delta1_cu*Rpcu2v0
dRpar2v0 = pi*(1-phi_a)*gamma_I*Iar2v0 + pi*gamma_A*Aar2v0 + pi*(1-mu_a)*gamma_H*Har2v0 -kappa2*Rpar2v0 - omega_pa*Rpar2v0 - delta1_ar*Rpar2v0
dRpau2v0 = pi*(1-phi_a)*gamma_I*Iau2v0 + pi*gamma_A*Aau2v0 + pi*(1-mu_a)*gamma_H*Hau2v0 -kappa2*Rpau2v0 - omega_pa*Rpau2v0 - delta1_au*Rpau2v0
dRper2v0 = pi*(1-phi_e)*gamma_I*Ier2v0 + pi*gamma_A*Aer2v0 + pi*(1-mu_e)*gamma_H*Her2v0 -kappa2*Rper2v0 - omega_pe*Rper2v0 - delta1_er*Rper2v0
dRpeu2v0 = pi*(1-phi_e)*gamma_I*Ieu2v0 + pi*gamma_A*Aeu2v0 + pi*(1-mu_e)*gamma_H*Heu2v0 -kappa2*Rpeu2v0 - omega_pe*Rpeu2v0 - delta1_eu*Rpeu2v0
#Recovered and not seropositive
dRncr2v0 = (1-pi)*(1-phi_c)*gamma_I*Icr2v0 + (1-pi)*gamma_A*Acr2v0 + (1-pi)*(1-mu_c)*gamma_H*Hcr2v0 + kappa2*Rpcr2v0 - omega_nc*Rncr2v0 - delta1_cr*Rncr2v0
dRncu2v0 = (1-pi)*(1-phi_c)*gamma_I*Icu2v0 + (1-pi)*gamma_A*Acu2v0 + (1-pi)*(1-mu_c)*gamma_H*Hcu2v0 + kappa2*Rpcu2v0 - omega_nc*Rncu2v0 - delta1_cu*Rncu2v0
dRnar2v0 = (1-pi)*(1-phi_a)*gamma_I*Iar2v0 + (1-pi)*gamma_A*Aar2v0 + (1-pi)*(1-mu_a)*gamma_H*Har2v0 + kappa2*Rpar2v0 - omega_na*Rnar2v0 - delta1_ar*Rnar2v0
dRnau2v0 = (1-pi)*(1-phi_a)*gamma_I*Iau2v0 + (1-pi)*gamma_A*Aau2v0 + (1-pi)*(1-mu_a)*gamma_H*Hau2v0 + kappa2*Rpau2v0 - omega_na*Rnau2v0 - delta1_au*Rnau2v0
dRner2v0 = (1-pi)*(1-phi_e)*gamma_I*Ier2v0 + (1-pi)*gamma_A*Aer2v0 + (1-pi)*(1-mu_e)*gamma_H*Her2v0 + kappa2*Rper2v0 - omega_ne*Rner2v0 - delta1_er*Rner2v0
dRneu2v0 = (1-pi)*(1-phi_e)*gamma_I*Ieu2v0 + (1-pi)*gamma_A*Aeu2v0 + (1-pi)*(1-mu_e)*gamma_H*Heu2v0 + kappa2*Rpeu2v0 - omega_ne*Rneu2v0 - delta1_eu*Rneu2v0
#Deaths
dDcr2v0 = mu_c*gamma_H*Hcr2v0
dDcu2v0 = mu_c*gamma_H*Hcu2v0
dDar2v0 = mu_a*gamma_H*Har2v0
dDau2v0 = mu_a*gamma_H*Hau2v0
dDer2v0 = mu_e*gamma_H*Her2v0
dDeu2v0 = mu_e*gamma_H*Heu2v0
################################
##Unvaccinated and exposed twice####
################################
#Susceptible
dSpcr2v0 = omega_pc*Rpcr2v0 -kappa2*Spcr2v0 - Spcr2v0 * sd * foi_cr_2v0 - delta1_cr * Spcr2v0 + omega2_pc*Rpcr3v0 - omega4_pc*Spcr2v0 ##Note vaccination rate here doesnt differ by previous vax status
dSpcu2v0 = omega_pc*Rpcu2v0 -kappa2*Spcu2v0 - Spcu2v0 * sd * foi_cu_2v0 - delta1_cu * Spcu2v0 + omega2_pc*Rpcu3v0 - omega4_pc*Spcu2v0
dSpar2v0 = omega_pa*Rpar2v0 -kappa2*Spar2v0 - Spar2v0 * sd * foi_ar_2v0 - delta1_ar * Spar2v0 + omega2_pa*Rpar3v0
dSpau2v0 = omega_pa*Rpau2v0 -kappa2*Spau2v0 - Spau2v0 * sd * foi_au_2v0 - delta1_au * Spau2v0 + omega2_pa*Rpau3v0
dSper2v0 = omega_pe*Rper2v0 -kappa2*Sper2v0 - Sper2v0 * sd * foi_er_2v0 - delta1_er * Sper2v0 + omega2_pe*Rper3v0
dSpeu2v0 = omega_pe*Rpeu2v0 -kappa2*Speu2v0 - Speu2v0 * sd * foi_eu_2v0 - delta1_eu * Speu2v0 + omega2_pe*Rpeu3v0
dSncr2v0 = omega_nc*Rncr2v0 + kappa2*Spcr2v0 -Sncr2v0 * sd * foi_cr_2v0 - delta1_cr * Sncr2v0 + omega2_nc*Rncr3v0- omega4_nc*Sncr2v0
dSncu2v0 = omega_nc*Rncu2v0 + kappa2*Spcu2v0 -Sncu2v0 * sd * foi_cu_2v0 - delta1_cu * Sncu2v0 + omega2_nc*Rncu3v0- omega4_nc*Sncu2v0
dSnar2v0 = omega_na*Rnar2v0 + kappa2*Spar2v0 -Snar2v0 * sd * foi_ar_2v0 - delta1_ar * Snar2v0 + omega2_na*Rnar3v0
dSnau2v0 = omega_na*Rnau2v0 + kappa2*Spau2v0 -Snau2v0 * sd * foi_au_2v0 - delta1_au * Snau2v0 + omega2_na*Rnau3v0
dSner2v0 = omega_ne*Rner2v0 + kappa2*Sper2v0 -Sner2v0 * sd * foi_er_2v0 - delta1_er * Sner2v0 + omega2_ne*Rner3v0
dSneu2v0 = omega_ne*Rneu2v0 + kappa2*Speu2v0 -Sneu2v0 * sd * foi_eu_2v0 - delta1_eu * Sneu2v0 + omega2_ne*Rneu3v0
#Exposed
dEcr3v0 = Spcr2v0 * sd * foi_cr_2v0 + Sncr2v0 * sd * foi_cr_2v0 - sigma * Ecr3v0 - delta1_cr*Ecr3v0
dEcu3v0 = Spcu2v0 * sd * foi_cu_2v0 + Sncu2v0 * sd * foi_cu_2v0 - sigma * Ecu3v0 - delta1_cu*Ecu3v0
dEar3v0 = Spar2v0 * sd * foi_ar_2v0 + Snar2v0 * sd * foi_ar_2v0 - sigma * Ear3v0 - delta1_ar*Ear3v0
dEau3v0 = Spau2v0 * sd * foi_au_2v0 + Snau2v0 * sd * foi_au_2v0 - sigma * Eau3v0 - delta1_au*Eau3v0
dEer3v0 = Sper2v0 * sd * foi_er_2v0 + Sner2v0 * sd * foi_er_2v0 - sigma * Eer3v0 - delta1_er*Eer3v0
dEeu3v0 = Speu2v0 * sd * foi_eu_2v0 + Sneu2v0 * sd * foi_eu_2v0 - sigma * Eeu3v0 - delta1_eu*Eeu3v0
# Asymptomatic
dAcr3v0 = (1-nu_c)*sigma*Ecr3v0 - gamma_A * Acr3v0 - delta1_cr*Acr3v0
dAcu3v0 = (1-nu_c)*sigma*Ecu3v0 - gamma_A * Acu3v0 - delta1_cu*Acu3v0
dAar3v0 = (1-nu_a)*sigma*Ear3v0 - gamma_A * Aar3v0 - delta1_ar*Aar3v0
dAau3v0 = (1-nu_a)*sigma*Eau3v0 - gamma_A * Aau3v0 - delta1_au*Aau3v0
dAer3v0 = (1-nu_e)*sigma*Eer3v0 - gamma_A * Aer3v0 - delta1_er*Aer3v0
dAeu3v0 = (1-nu_e)*sigma*Eeu3v0 - gamma_A * Aeu3v0 - delta1_eu*Aeu3v0
#Symptomatic
dIcr3v0 = nu_c*sigma*Ecr3v0 - gamma_I * Icr3v0
dIcu3v0 = nu_c*sigma*Ecu3v0 - gamma_I * Icu3v0
dIar3v0 = nu_a*sigma*Ear3v0 - gamma_I * Iar3v0
dIau3v0 = nu_a*sigma*Eau3v0 - gamma_I * Iau3v0
dIer3v0 = nu_e*sigma*Eer3v0 - gamma_I * Ier3v0
dIeu3v0 = nu_e*sigma*Eeu3v0 - gamma_I * Ieu3v0
# Hospitalized
dHcr3v0 = phi_c*gamma_I*Icr3v0 - gamma_H * Hcr3v0
dHcu3v0 = phi_c*gamma_I*Icu3v0 - gamma_H * Hcu3v0
dHar3v0 = phi_a*gamma_I*Iar3v0 - gamma_H * Har3v0
dHau3v0 = phi_a*gamma_I*Iau3v0 - gamma_H * Hau3v0
dHer3v0 = phi_e*gamma_I*Ier3v0 - gamma_H * Her3v0
dHeu3v0 = phi_e*gamma_I*Ieu3v0 - gamma_H * Heu3v0
# Recovered and seroconverted
dRpcr3v0 = pi*(1-phi_c)*gamma_I*Icr3v0 + pi*gamma_A*Acr3v0 + pi*(1-mu_c)*gamma_H*Hcr3v0 -kappa3*Rpcr3v0 - omega2_pc*Rpcr3v0 - delta1_cr*Rpcr3v0
dRpcu3v0 = pi*(1-phi_c)*gamma_I*Icu3v0 + pi*gamma_A*Acu3v0 + pi*(1-mu_c)*gamma_H*Hcu3v0 -kappa3*Rpcu3v0 - omega2_pc*Rpcu3v0 - delta1_cu*Rpcu3v0
dRpar3v0 = pi*(1-phi_a)*gamma_I*Iar3v0 + pi*gamma_A*Aar3v0 + pi*(1-mu_a)*gamma_H*Har3v0 -kappa3*Rpar3v0 - omega2_pa*Rpar3v0 - delta1_ar*Rpar3v0
dRpau3v0 = pi*(1-phi_a)*gamma_I*Iau3v0 + pi*gamma_A*Aau3v0 + pi*(1-mu_a)*gamma_H*Hau3v0 -kappa3*Rpau3v0 - omega2_pa*Rpau3v0 - delta1_au*Rpau3v0
dRper3v0 = pi*(1-phi_e)*gamma_I*Ier3v0 + pi*gamma_A*Aer3v0 + pi*(1-mu_e)*gamma_H*Her3v0 -kappa3*Rper3v0 - omega2_pe*Rper3v0 - delta1_er*Rper3v0
dRpeu3v0 = pi*(1-phi_e)*gamma_I*Ieu3v0 + pi*gamma_A*Aeu3v0 + pi*(1-mu_e)*gamma_H*Heu3v0 -kappa3*Rpeu3v0 - omega2_pe*Rpeu3v0 - delta1_eu*Rpeu3v0
#Recovered and not seropositive
dRncr3v0 = (1-pi)*(1-phi_c)*gamma_I*Icr3v0 + (1-pi)*gamma_A*Acr3v0 + (1-pi)*(1-mu_c)*gamma_H*Hcr3v0 + kappa3*Rpcr3v0 - omega2_nc*Rncr3v0 - delta1_cr*Rncr3v0
dRncu3v0 = (1-pi)*(1-phi_c)*gamma_I*Icu3v0 + (1-pi)*gamma_A*Acu3v0 + (1-pi)*(1-mu_c)*gamma_H*Hcu3v0 + kappa3*Rpcu3v0 - omega2_nc*Rncu3v0 - delta1_cu*Rncu3v0
dRnar3v0 = (1-pi)*(1-phi_a)*gamma_I*Iar3v0 + (1-pi)*gamma_A*Aar3v0 + (1-pi)*(1-mu_a)*gamma_H*Har3v0 + kappa3*Rpar3v0 - omega2_na*Rnar3v0 - delta1_ar*Rnar3v0
dRnau3v0 = (1-pi)*(1-phi_a)*gamma_I*Iau3v0 + (1-pi)*gamma_A*Aau3v0 + (1-pi)*(1-mu_a)*gamma_H*Hau3v0 + kappa3*Rpau3v0 - omega2_na*Rnau3v0 - delta1_au*Rnau3v0
dRner3v0 = (1-pi)*(1-phi_e)*gamma_I*Ier3v0 + (1-pi)*gamma_A*Aer3v0 + (1-pi)*(1-mu_e)*gamma_H*Her3v0 + kappa3*Rper3v0 - omega2_ne*Rner3v0 - delta1_er*Rner3v0
dRneu3v0 = (1-pi)*(1-phi_e)*gamma_I*Ieu3v0 + (1-pi)*gamma_A*Aeu3v0 + (1-pi)*(1-mu_e)*gamma_H*Heu3v0 + kappa3*Rpeu3v0 - omega2_ne*Rneu3v0 - delta1_eu*Rneu3v0
#Deaths
dDcr3v0 = mu_c*gamma_H*Hcr3v0
dDcu3v0 = mu_c*gamma_H*Hcu3v0
dDar3v0 = mu_a*gamma_H*Har3v0
dDau3v0 = mu_a*gamma_H*Hau3v0
dDer3v0 = mu_e*gamma_H*Her3v0
dDeu3v0 = mu_e*gamma_H*Heu3v0
################################
##Vaccinated one dose and unexposed####
################################
#Susceptible and seropositive with S-spike and total IGg
dSpcr0v1 = omegav_pc *Vpcr0v1+ omegav_pc*W1Vpcr0v1+ omegav_pc*W2Vpcr0v1+ omegav_pc*W3Vpcr0v1 -Spcr0v1 * sd * foi_cr_0v1 - delta2_cr * Spcr0v1 -kappa1 * Spcr0v1
dSpcu0v1 = omegav_pc *Vpcu0v1+ omegav_pc*W1Vpcu0v1+ omegav_pc*W2Vpcu0v1+ omegav_pc*W3Vpcu0v1 -Spcu0v1 * sd * foi_cu_0v1 - delta2_cu * Spcu0v1 -kappa1 * Spcu0v1
dSpar0v1 = omegav_pa *Vpar0v1+ omegav_pa*W1Vpar0v1+ omegav_pa*W2Vpar0v1+ omegav_pa*W3Vpar0v1 -Spar0v1 * sd * foi_ar_0v1 - delta2_ar * Spar0v1 -kappa1 * Spar0v1
dSpau0v1 = omegav_pa *Vpau0v1+ omegav_pa*W1Vpau0v1+ omegav_pa*W2Vpau0v1+ omegav_pa*W3Vpau0v1 -Spau0v1 * sd * foi_au_0v1 - delta2_au * Spau0v1 -kappa1 * Spau0v1
dSper0v1 = omegav_pe *Vper0v1+ omegav_pe*W1Vper0v1+ omegav_pe*W2Vper0v1+ omegav_pe*W3Vper0v1 -Sper0v1 * sd * foi_er_0v1 - delta2_er * Sper0v1 -kappa1 * Sper0v1
dSpeu0v1 = omegav_pe *Vpeu0v1+ omegav_pe*W1Vpeu0v1+ omegav_pe*W2Vpeu0v1+ omegav_pe*W3Vpeu0v1 -Speu0v1 * sd * foi_eu_0v1 - delta2_eu * Speu0v1 -kappa1 * Speu0v1
# Susceptible and seronegative for S-spike and total IGg
dSncr0v1 = omegav_nc *Vncr0v1 - Sncr0v1 * sd * foi_cr_0v1 - delta2_cr * Sncr0v1 +kappa1 * Spcr0v1
dSncu0v1 = omegav_nc *Vncu0v1 - Sncu0v1 * sd * foi_cu_0v1 - delta2_cu * Sncu0v1 +kappa1 * Spcu0v1
dSnar0v1 = omegav_na *Vnar0v1 - Snar0v1 * sd * foi_ar_0v1 - delta2_ar * Snar0v1 +kappa1 * Spar0v1
dSnau0v1 = omegav_na *Vnau0v1 - Snau0v1 * sd * foi_au_0v1 - delta2_au * Snau0v1 +kappa1 * Spau0v1
dSner0v1 = omegav_ne *Vner0v1 - Sner0v1 * sd * foi_er_0v1 - delta2_er * Sner0v1 +kappa1 * Sper0v1
dSneu0v1 = omegav_ne *Vneu0v1 - Sneu0v1 * sd * foi_eu_0v1 - delta2_eu * Sneu0v1 +kappa1 * Speu0v1
#Exposed
dEcr1v1 = Spcr0v1*sd*foi_cr_0v1+Sncr0v1 * sd * foi_cr_0v1 - sigma * Ecr1v1 - delta2_cr*Ecr1v1 +delta1_cr*Ecr1v0
dEcu1v1 = Spcu0v1*sd*foi_cu_0v1+Sncu0v1 * sd * foi_cu_0v1- sigma * Ecu1v1 - delta2_cu*Ecu1v1 +delta1_cu*Ecu1v0
dEar1v1 = Spar0v1*sd*foi_ar_0v1+Snar0v1 * sd * foi_ar_0v1- sigma * Ear1v1 - delta2_ar*Ear1v1 +delta1_ar*Ear1v0
dEau1v1 = Spau0v1*sd*foi_au_0v1+Snau0v1 * sd * foi_au_0v1- sigma * Eau1v1 - delta2_au*Eau1v1 +delta1_au*Eau1v0
dEer1v1 = Sper0v1*sd*foi_er_0v1+Sner0v1 * sd * foi_er_0v1- sigma * Eer1v1 - delta2_er*Eer1v1 +delta1_er*Eer1v0
dEeu1v1 = Speu0v1*sd*foi_eu_0v1+Sneu0v1 * sd * foi_eu_0v1- sigma * Eeu1v1 - delta2_eu*Eeu1v1 +delta1_eu*Eeu1v0
# Asymptomatic
dAcr1v1 = (1-nu_c)*sigma*Ecr1v1 - gamma_A * Acr1v1 - delta2_cr*Acr1v1 +delta1_cr*Acr1v0
dAcu1v1 = (1-nu_c)*sigma*Ecu1v1 - gamma_A * Acu1v1 - delta2_cu*Acu1v1 +delta1_cu*Acu1v0
dAar1v1 = (1-nu_a)*sigma*Ear1v1 - gamma_A * Aar1v1 - delta2_ar*Aar1v1 +delta1_ar*Aar1v0
dAau1v1 = (1-nu_a)*sigma*Eau1v1 - gamma_A * Aau1v1 - delta2_au*Aau1v1 +delta1_au*Aau1v0
dAer1v1 = (1-nu_e)*sigma*Eer1v1 - gamma_A * Aer1v1 - delta2_er*Aer1v1 +delta1_er*Aer1v0
dAeu1v1 = (1-nu_e)*sigma*Eeu1v1 - gamma_A * Aeu1v1 - delta2_eu*Aeu1v1 +delta1_eu*Aeu1v0
#Symptomatic
dIcr1v1 = nu_c*sigma*Ecr1v1 - gamma_I * Icr1v1
dIcu1v1 = nu_c*sigma*Ecu1v1 - gamma_I * Icu1v1
dIar1v1 = nu_a*sigma*Ear1v1 - gamma_I * Iar1v1
dIau1v1 = nu_a*sigma*Eau1v1 - gamma_I * Iau1v1
dIer1v1 = nu_e*sigma*Eer1v1 - gamma_I * Ier1v1
dIeu1v1 = nu_e*sigma*Eeu1v1 - gamma_I * Ieu1v1
# Hospitalized
dHcr1v1 = phi_cv1*gamma_I*Icr1v1 - gamma_H * Hcr1v1
dHcu1v1 = phi_cv1*gamma_I*Icu1v1 - gamma_H * Hcu1v1
dHar1v1 = phi_av1*gamma_I*Iar1v1 - gamma_H * Har1v1
dHau1v1 = phi_av1*gamma_I*Iau1v1 - gamma_H * Hau1v1
dHer1v1 = phi_ev1*gamma_I*Ier1v1 - gamma_H * Her1v1
dHeu1v1 = phi_ev1*gamma_I*Ieu1v1 - gamma_H * Heu1v1
# Recovered and seroconverted
dRpcr1v1 = pi*(1-phi_cv1)*gamma_I*Icr1v1 + pi*gamma_A*Acr1v1 + pi*(1-mu_c)*gamma_H*Hcr1v1 -kappa2*Rpcr1v1 - omega_pc*Rpcr1v1 - delta2_cr*Rpcr1v1 +delta1_cr*Rpcr1v0+delta1_cr*W1Rpcr1v0+delta1_cr*W2Rpcr1v0+delta1_cr*W3Rpcr1v0+delta1_cr*Rncr1v0*rho_v1 +delta1_cr*Spcr1v0+delta1_cr*Sncr1v0*rho_v1
dRpcu1v1 = pi*(1-phi_cv1)*gamma_I*Icu1v1 + pi*gamma_A*Acu1v1 + pi*(1-mu_c)*gamma_H*Hcu1v1 -kappa2*Rpcu1v1 - omega_pc*Rpcu1v1 - delta2_cu*Rpcu1v1 +delta1_cu*Rpcu1v0+delta1_cu*W1Rpcu1v0+delta1_cu*W2Rpcu1v0+delta1_cu*W3Rpcu1v0+delta1_cu*Rncu1v0*rho_v1 +delta1_cu*Spcu1v0+delta1_cu*Sncu1v0*rho_v1
dRpar1v1 = pi*(1-phi_av1)*gamma_I*Iar1v1 + pi*gamma_A*Aar1v1 + pi*(1-mu_a)*gamma_H*Har1v1 -kappa2*Rpar1v1 - omega_pa*Rpar1v1 - delta2_ar*Rpar1v1 +delta1_ar*Rpar1v0+delta1_ar*W1Rpar1v0+delta1_ar*W2Rpar1v0+delta1_ar*W3Rpar1v0+delta1_ar*Rnar1v0*rho_v1 +delta1_ar*Spar1v0+delta1_ar*Snar1v0*rho_v1
dRpau1v1 = pi*(1-phi_av1)*gamma_I*Iau1v1 + pi*gamma_A*Aau1v1 + pi*(1-mu_a)*gamma_H*Hau1v1 -kappa2*Rpau1v1 - omega_pa*Rpau1v1 - delta2_au*Rpau1v1 +delta1_au*Rpau1v0+delta1_au*W1Rpau1v0+delta1_au*W2Rpau1v0+delta1_au*W3Rpau1v0+delta1_au*Rnau1v0*rho_v1 +delta1_au*Spau1v0+delta1_au*Snau1v0*rho_v1
dRper1v1 = pi*(1-phi_ev1)*gamma_I*Ier1v1 + pi*gamma_A*Aer1v1 + pi*(1-mu_e)*gamma_H*Her1v1 -kappa2*Rper1v1 - omega_pe*Rper1v1 - delta2_er*Rper1v1 +delta1_er*Rper1v0+delta1_er*W1Rper1v0+delta1_er*W2Rper1v0+delta1_er*W3Rper1v0+delta1_er*Rner1v0*rho_v1 +delta1_er*Sper1v0+delta1_er*Sner1v0*rho_v1
dRpeu1v1 = pi*(1-phi_ev1)*gamma_I*Ieu1v1 + pi*gamma_A*Aeu1v1 + pi*(1-mu_e)*gamma_H*Heu1v1 -kappa2*Rpeu1v1 - omega_pe*Rpeu1v1 - delta2_eu*Rpeu1v1 +delta1_eu*Rpeu1v0+delta1_eu*W1Rpeu1v0+delta1_eu*W2Rpeu1v0+delta1_eu*W3Rpeu1v0+delta1_eu*Rneu1v0*rho_v1 +delta1_eu*Speu1v0+delta1_eu*Sneu1v0*rho_v1
#Recovered and not seropositive
dRncr1v1 = (1-pi)*(1-phi_cv1)*gamma_I*Icr1v1 + (1-pi)*gamma_A*Acr1v1 + (1-pi)*(1-mu_c)*gamma_H*Hcr1v1 + kappa2*Rpcr1v1 - omega_nc*Rncr1v1 - delta2_cr*Rncr1v1 +delta1_cr*Rncr1v0*(1-rho_v1)+delta1_cr*Sncr1v0*(1-rho_v1)
dRncu1v1 = (1-pi)*(1-phi_cv1)*gamma_I*Icu1v1 + (1-pi)*gamma_A*Acu1v1 + (1-pi)*(1-mu_c)*gamma_H*Hcu1v1 + kappa2*Rpcu1v1 - omega_nc*Rncu1v1 - delta2_cu*Rncu1v1 +delta1_cu*Rncu1v0*(1-rho_v1)+delta1_cu*Sncu1v0*(1-rho_v1)
dRnar1v1 = (1-pi)*(1-phi_av1)*gamma_I*Iar1v1 + (1-pi)*gamma_A*Aar1v1 + (1-pi)*(1-mu_a)*gamma_H*Har1v1 + kappa2*Rpar1v1 - omega_na*Rnar1v1 - delta2_ar*Rnar1v1 +delta1_ar*Rnar1v0*(1-rho_v1)+delta1_ar*Snar1v0*(1-rho_v1)
dRnau1v1 = (1-pi)*(1-phi_av1)*gamma_I*Iau1v1 + (1-pi)*gamma_A*Aau1v1 + (1-pi)*(1-mu_a)*gamma_H*Hau1v1 + kappa2*Rpau1v1 - omega_na*Rnau1v1 - delta2_au*Rnau1v1 +delta1_au*Rnau1v0*(1-rho_v1)+delta1_au*Snau1v0*(1-rho_v1)
dRner1v1 = (1-pi)*(1-phi_ev1)*gamma_I*Ier1v1 + (1-pi)*gamma_A*Aer1v1 + (1-pi)*(1-mu_e)*gamma_H*Her1v1 + kappa2*Rper1v1 - omega_ne*Rner1v1 - delta2_er*Rner1v1 +delta1_er*Rner1v0*(1-rho_v1)+delta1_er*Sner1v0*(1-rho_v1)
dRneu1v1 = (1-pi)*(1-phi_ev1)*gamma_I*Ieu1v1 + (1-pi)*gamma_A*Aeu1v1 + (1-pi)*(1-mu_e)*gamma_H*Heu1v1 + kappa2*Rpeu1v1 - omega_ne*Rneu1v1 - delta2_eu*Rneu1v1 +delta1_eu*Rneu1v0*(1-rho_v1)+delta1_eu*Sneu1v0*(1-rho_v1)
#Deaths
dDcr1v1 = mu_c*gamma_H*Hcr1v1
dDcu1v1 = mu_c*gamma_H*Hcu1v1
dDar1v1 = mu_a*gamma_H*Har1v1
dDau1v1 = mu_a*gamma_H*Hau1v1
dDer1v1 = mu_e*gamma_H*Her1v1
dDeu1v1 = mu_e*gamma_H*Heu1v1
################################
##Vaccinated one dose and exposed once####
################################
#Susceptible
dSpcr1v1 = omega_pc*Rpcr1v1 -kappa2*Spcr1v1 - Spcr1v1 * sd * foi_cr_1v1 - delta2_cr * Spcr1v1
dSpcu1v1 = omega_pc*Rpcu1v1 -kappa2*Spcu1v1 - Spcu1v1 * sd * foi_cu_1v1 - delta2_cu * Spcu1v1
dSpar1v1 = omega_pa*Rpar1v1 -kappa2*Spar1v1 - Spar1v1 * sd * foi_ar_1v1 - delta2_ar * Spar1v1
dSpau1v1 = omega_pa*Rpau1v1 -kappa2*Spau1v1 - Spau1v1 * sd * foi_au_1v1 - delta2_au * Spau1v1
dSper1v1 = omega_pe*Rper1v1 -kappa2*Sper1v1 - Sper1v1 * sd * foi_er_1v1 - delta2_er * Sper1v1
dSpeu1v1 = omega_pe*Rpeu1v1 -kappa2*Speu1v1 - Speu1v1 * sd * foi_eu_1v1 - delta2_eu * Speu1v1
dSncr1v1 = omega_nc*Rncr1v1 + kappa2*Spcr1v1 -Sncr1v1 * sd * foi_cr_1v1 - delta2_cr * Sncr1v1
dSncu1v1 = omega_nc*Rncu1v1 + kappa2*Spcu1v1 -Sncu1v1 * sd * foi_cu_1v1 - delta2_cu * Sncu1v1
dSnar1v1 = omega_na*Rnar1v1 + kappa2*Spar1v1 -Snar1v1 * sd * foi_ar_1v1 - delta2_ar * Snar1v1
dSnau1v1 = omega_na*Rnau1v1 + kappa2*Spau1v1 -Snau1v1 * sd * foi_au_1v1 - delta2_au * Snau1v1
dSner1v1 = omega_ne*Rner1v1 + kappa2*Sper1v1 -Sner1v1 * sd * foi_er_1v1 - delta2_er * Sner1v1
dSneu1v1 = omega_ne*Rneu1v1 + kappa2*Speu1v1 -Sneu1v1 * sd * foi_eu_1v1 - delta2_eu * Sneu1v1
#Exposed
dEcr2v1 = Spcr1v1 * sd * foi_cr_1v1 + Sncr1v1 * sd * foi_cr_1v1 - sigma * Ecr2v1 - delta2_cr*Ecr2v1 +delta1_cr*Ecr2v0
dEcu2v1 = Spcu1v1 * sd * foi_cu_1v1 + Sncu1v1 * sd * foi_cu_1v1 - sigma * Ecu2v1 - delta2_cu*Ecu2v1 +delta1_cu*Ecu2v0
dEar2v1 = Spar1v1 * sd * foi_ar_1v1 + Snar1v1 * sd * foi_ar_1v1 - sigma * Ear2v1 - delta2_ar*Ear2v1 +delta1_ar*Ear2v0
dEau2v1 = Spau1v1 * sd * foi_au_1v1 + Snau1v1 * sd * foi_au_1v1 - sigma * Eau2v1 - delta2_au*Eau2v1 +delta1_au*Eau2v0
dEer2v1 = Sper1v1 * sd * foi_er_1v1 + Sner1v1 * sd * foi_er_1v1 - sigma * Eer2v1 - delta2_er*Eer2v1 +delta1_er*Eer2v0
dEeu2v1 = Speu1v1 * sd * foi_eu_1v1 + Sneu1v1 * sd * foi_eu_1v1 - sigma * Eeu2v1 - delta2_eu*Eeu2v1 +delta1_eu*Eeu2v0
# Asymptomatic
dAcr2v1 = (1-nu_c)*sigma*Ecr2v1 - gamma_A * Acr2v1 - delta2_cr*Acr2v1 + delta1_cr*Acr2v0
dAcu2v1 = (1-nu_c)*sigma*Ecu2v1 - gamma_A * Acu2v1 - delta2_cu*Acu2v1 + delta1_cu*Acu2v0
dAar2v1 = (1-nu_a)*sigma*Ear2v1 - gamma_A * Aar2v1 - delta2_ar*Aar2v1 + delta1_ar*Aar2v0
dAau2v1 = (1-nu_a)*sigma*Eau2v1 - gamma_A * Aau2v1 - delta2_au*Aau2v1 + delta1_au*Aau2v0
dAer2v1 = (1-nu_e)*sigma*Eer2v1 - gamma_A * Aer2v1 - delta2_er*Aer2v1 + delta1_er*Aer2v0
dAeu2v1 = (1-nu_e)*sigma*Eeu2v1 - gamma_A * Aeu2v1 - delta2_eu*Aeu2v1 + delta1_eu*Aeu2v0
#Symptomatic
dIcr2v1 = nu_c*sigma*Ecr2v1 - gamma_I * Icr2v1
dIcu2v1 = nu_c*sigma*Ecu2v1 - gamma_I * Icu2v1
dIar2v1 = nu_a*sigma*Ear2v1 - gamma_I * Iar2v1
dIau2v1 = nu_a*sigma*Eau2v1 - gamma_I * Iau2v1
dIer2v1 = nu_e*sigma*Eer2v1 - gamma_I * Ier2v1
dIeu2v1 = nu_e*sigma*Eeu2v1 - gamma_I * Ieu2v1
# Hospitalized
dHcr2v1 = phi_cv1*gamma_I*Icr2v1 - gamma_H * Hcr2v1
dHcu2v1 = phi_cv1*gamma_I*Icu2v1 - gamma_H * Hcu2v1
dHar2v1 = phi_av1*gamma_I*Iar2v1 - gamma_H * Har2v1
dHau2v1 = phi_av1*gamma_I*Iau2v1 - gamma_H * Hau2v1
dHer2v1 = phi_ev1*gamma_I*Ier2v1 - gamma_H * Her2v1
dHeu2v1 = phi_ev1*gamma_I*Ieu2v1 - gamma_H * Heu2v1
# Recovered and seroconverted
dRpcr2v1 = pi*(1-phi_cv1)*gamma_I*Icr2v1 + pi*gamma_A*Acr2v1 + pi*(1-mu_c)*gamma_H*Hcr2v1 -kappa3*Rpcr2v1 - omega_pc*Rpcr2v1 - delta2_cr*Rpcr2v1 +delta1_cr*Rpcr2v0 + delta1_cr*Rncr2v0*(rho_v2)+ delta1_cr*Spcr2v0+ delta1_cr*Sncr2v0*(rho_v2)
dRpcu2v1 = pi*(1-phi_cv1)*gamma_I*Icu2v1 + pi*gamma_A*Acu2v1 + pi*(1-mu_c)*gamma_H*Hcu2v1 -kappa3*Rpcu2v1 - omega_pc*Rpcu2v1 - delta2_cu*Rpcu2v1 +delta1_cu*Rpcu2v0+ delta1_cu*Rncu2v0*(rho_v2)+ delta1_cu*Spcu2v0+ delta1_cu*Sncu2v0*(rho_v2)
dRpar2v1 = pi*(1-phi_av1)*gamma_I*Iar2v1 + pi*gamma_A*Aar2v1 + pi*(1-mu_a)*gamma_H*Har2v1 -kappa3*Rpar2v1 - omega_pa*Rpar2v1 - delta2_ar*Rpar2v1 +delta1_ar*Rpar2v0+ delta1_ar*Rnar2v0*(rho_v2)+ delta1_ar*Spar2v0+ delta1_ar*Snar2v0*(rho_v2)
dRpau2v1 = pi*(1-phi_av1)*gamma_I*Iau2v1 + pi*gamma_A*Aau2v1 + pi*(1-mu_a)*gamma_H*Hau2v1 -kappa3*Rpau2v1 - omega_pa*Rpau2v1 - delta2_au*Rpau2v1 +delta1_au*Rpau2v0+ delta1_au*Rnau2v0*(rho_v2)+ delta1_au*Spau2v0+ delta1_au*Snau2v0*(rho_v2)
dRper2v1 = pi*(1-phi_ev1)*gamma_I*Ier2v1 + pi*gamma_A*Aer2v1 + pi*(1-mu_e)*gamma_H*Her2v1 -kappa3*Rper2v1 - omega_pe*Rper2v1 - delta2_er*Rper2v1 +delta1_er*Rper2v0+ delta1_er*Rner2v0*(rho_v2)+ delta1_er*Sper2v0+ delta1_er*Sner2v0*(rho_v2)
dRpeu2v1 = pi*(1-phi_ev1)*gamma_I*Ieu2v1 + pi*gamma_A*Aeu2v1 + pi*(1-mu_e)*gamma_H*Heu2v1 -kappa3*Rpeu2v1 - omega_pe*Rpeu2v1 - delta2_eu*Rpeu2v1 +delta1_eu*Rpeu2v0+ delta1_eu*Rneu2v0*(rho_v2)+ delta1_eu*Speu2v0+ delta1_eu*Sneu2v0*(rho_v2)
#Recovered and not seropositive
dRncr2v1 = (1-pi)*(1-phi_cv1)*gamma_I*Icr2v1 + (1-pi)*gamma_A*Acr2v1 + (1-pi)*(1-mu_c)*gamma_H*Hcr2v1 + kappa3*Rpcr2v1 - omega_nc*Rncr2v1 - delta2_cr*Rncr2v1 + delta1_cr*Rncr2v0*(1-rho_v2)+ delta1_cr*Sncr2v0*(1-rho_v2)
dRncu2v1 = (1-pi)*(1-phi_cv1)*gamma_I*Icu2v1 + (1-pi)*gamma_A*Acu2v1 + (1-pi)*(1-mu_c)*gamma_H*Hcu2v1 + kappa3*Rpcu2v1 - omega_nc*Rncu2v1 - delta2_cu*Rncu2v1 + delta1_cu*Rncu2v0*(1-rho_v2)+ delta1_cu*Sncu2v0*(1-rho_v2)
dRnar2v1 = (1-pi)*(1-phi_av1)*gamma_I*Iar2v1 + (1-pi)*gamma_A*Aar2v1 + (1-pi)*(1-mu_a)*gamma_H*Har2v1 + kappa3*Rpar2v1 - omega_na*Rnar2v1 - delta2_ar*Rnar2v1 + delta1_ar*Rnar2v0*(1-rho_v2)+ delta1_ar*Snar2v0*(1-rho_v2)
dRnau2v1 = (1-pi)*(1-phi_av1)*gamma_I*Iau2v1 + (1-pi)*gamma_A*Aau2v1 + (1-pi)*(1-mu_a)*gamma_H*Hau2v1 + kappa3*Rpau2v1 - omega_na*Rnau2v1 - delta2_au*Rnau2v1 + delta1_au*Rnau2v0*(1-rho_v2)+ delta1_au*Snau2v0*(1-rho_v2)
dRner2v1 = (1-pi)*(1-phi_ev1)*gamma_I*Ier2v1 + (1-pi)*gamma_A*Aer2v1 + (1-pi)*(1-mu_e)*gamma_H*Her2v1 + kappa3*Rper2v1 - omega_ne*Rner2v1 - delta2_er*Rner2v1 + delta1_er*Rner2v0*(1-rho_v2)+ delta1_er*Sner2v0*(1-rho_v2)
dRneu2v1 = (1-pi)*(1-phi_ev1)*gamma_I*Ieu2v1 + (1-pi)*gamma_A*Aeu2v1 + (1-pi)*(1-mu_e)*gamma_H*Heu2v1 + kappa3*Rpeu2v1 - omega_ne*Rneu2v1 - delta2_eu*Rneu2v1 + delta1_eu*Rneu2v0*(1-rho_v2)+ delta1_eu*Sneu2v0*(1-rho_v2)
#Deaths
dDcr2v1 = mu_c*gamma_H*Hcr2v1
dDcu2v1 = mu_c*gamma_H*Hcu2v1
dDar2v1 = mu_a*gamma_H*Har2v1
dDau2v1 = mu_a*gamma_H*Hau2v1
dDer2v1 = mu_e*gamma_H*Her2v1
dDeu2v1 = mu_e*gamma_H*Heu2v1
################################
##Vaccinated one dose and exposed twice####
################################
#Susceptible
dSpcr2v1 = omega_pc*Rpcr2v1 -kappa3*Spcr2v1 - Spcr2v1 * sd * foi_cr_2v1 - delta2_cr * Spcr2v1 + omega2_pc*Rpcr3v1
dSpcu2v1 = omega_pc*Rpcu2v1 -kappa3*Spcu2v1 - Spcu2v1 * sd * foi_cu_2v1 - delta2_cu * Spcu2v1 + omega2_pc*Rpcu3v1
dSpar2v1 = omega_pa*Rpar2v1 -kappa3*Spar2v1 - Spar2v1 * sd * foi_ar_2v1 - delta2_ar * Spar2v1 + omega2_pa*Rpar3v1
dSpau2v1 = omega_pa*Rpau2v1 -kappa3*Spau2v1 - Spau2v1 * sd * foi_au_2v1 - delta2_au * Spau2v1 + omega2_pa*Rpau3v1
dSper2v1 = omega_pe*Rper2v1 -kappa3*Sper2v1 - Sper2v1 * sd * foi_er_2v1 - delta2_er * Sper2v1 + omega2_pe*Rper3v1
dSpeu2v1 = omega_pe*Rpeu2v1 -kappa3*Speu2v1 - Speu2v1 * sd * foi_eu_2v1 - delta2_eu * Speu2v1 + omega2_pe*Rpeu3v1
dSncr2v1 = omega_nc*Rncr2v1 + kappa3*Spcr2v1 -Sncr2v1 * sd * foi_cr_2v1 - delta2_cr * Sncr2v1 + omega2_nc*Rncr3v1
dSncu2v1 = omega_nc*Rncu2v1 + kappa3*Spcu2v1 -Sncu2v1 * sd * foi_cu_2v1 - delta2_cu * Sncu2v1 + omega2_nc*Rncu3v1
dSnar2v1 = omega_na*Rnar2v1 + kappa3*Spar2v1 -Snar2v1 * sd * foi_ar_2v1 - delta2_ar * Snar2v1 + omega2_na*Rnar3v1
dSnau2v1 = omega_na*Rnau2v1 + kappa3*Spau2v1 -Snau2v1 * sd * foi_au_2v1 - delta2_au * Snau2v1 + omega2_na*Rnau3v1
dSner2v1 = omega_ne*Rner2v1 + kappa3*Sper2v1 -Sner2v1 * sd * foi_er_2v1 - delta2_er * Sner2v1 + omega2_ne*Rner3v1
dSneu2v1 = omega_ne*Rneu2v1 + kappa3*Speu2v1 -Sneu2v1 * sd * foi_eu_2v1 - delta2_eu * Sneu2v1 + omega2_ne*Rneu3v1
#Exposed
dEcr3v1 = Spcr2v1 * sd * foi_cr_2v1 + Sncr2v1 * sd * foi_cr_2v1 - sigma * Ecr3v1 - delta2_cr*Ecr3v1 + delta1_cr*Ecr3v0
dEcu3v1 = Spcu2v1 * sd * foi_cu_2v1 + Sncu2v1 * sd * foi_cu_2v1 - sigma * Ecu3v1 - delta2_cu*Ecu3v1 + delta1_cu*Ecu3v0
dEar3v1 = Spar2v1 * sd * foi_ar_2v1 + Snar2v1 * sd * foi_ar_2v1 - sigma * Ear3v1 - delta2_ar*Ear3v1 + delta1_ar*Ear3v0
dEau3v1 = Spau2v1 * sd * foi_au_2v1 + Snau2v1 * sd * foi_au_2v1 - sigma * Eau3v1 - delta2_au*Eau3v1 + delta1_au*Eau3v0
dEer3v1 = Sper2v1 * sd * foi_er_2v1 + Sner2v1 * sd * foi_er_2v1 - sigma * Eer3v1 - delta2_er*Eer3v1 + delta1_er*Eer3v0
dEeu3v1 = Speu2v1 * sd * foi_eu_2v1 + Sneu2v1 * sd * foi_eu_2v1 - sigma * Eeu3v1 - delta2_eu*Eeu3v1 + delta1_eu*Eeu3v0
# Asymptomatic
dAcr3v1 = (1-nu_c)*sigma*Ecr3v1 - gamma_A * Acr3v1 - delta2_cr*Acr3v1+ delta1_cr*Acr3v0
dAcu3v1 = (1-nu_c)*sigma*Ecu3v1 - gamma_A * Acu3v1 - delta2_cu*Acu3v1+ delta1_cu*Acu3v0
dAar3v1 = (1-nu_a)*sigma*Ear3v1 - gamma_A * Aar3v1 - delta2_ar*Aar3v1+ delta1_ar*Aar3v0
dAau3v1 = (1-nu_a)*sigma*Eau3v1 - gamma_A * Aau3v1 - delta2_au*Aau3v1+ delta1_au*Aau3v0
dAer3v1 = (1-nu_e)*sigma*Eer3v1 - gamma_A * Aer3v1 - delta2_er*Aer3v1+ delta1_er*Aer3v0
dAeu3v1 = (1-nu_e)*sigma*Eeu3v1 - gamma_A * Aeu3v1 - delta2_eu*Aeu3v1+ delta1_eu*Aeu3v0
#Symptomatic
dIcr3v1 = nu_c*sigma*Ecr3v1 - gamma_I * Icr3v1
dIcu3v1 = nu_c*sigma*Ecu3v1 - gamma_I * Icu3v1
dIar3v1 = nu_a*sigma*Ear3v1 - gamma_I * Iar3v1
dIau3v1 = nu_a*sigma*Eau3v1 - gamma_I * Iau3v1
dIer3v1 = nu_e*sigma*Eer3v1 - gamma_I * Ier3v1
dIeu3v1 = nu_e*sigma*Eeu3v1 - gamma_I * Ieu3v1
# Hospitalized
dHcr3v1 = phi_cv1*gamma_I*Icr3v1 - gamma_H * Hcr3v1
dHcu3v1 = phi_cv1*gamma_I*Icu3v1 - gamma_H * Hcu3v1
dHar3v1 = phi_av1*gamma_I*Iar3v1 - gamma_H * Har3v1
dHau3v1 = phi_av1*gamma_I*Iau3v1 - gamma_H * Hau3v1
dHer3v1 = phi_ev1*gamma_I*Ier3v1 - gamma_H * Her3v1
dHeu3v1 = phi_ev1*gamma_I*Ieu3v1 - gamma_H * Heu3v1
# Recovered and seroconverted
dRpcr3v1 = pi*(1-phi_cv1)*gamma_I*Icr3v1 + pi*gamma_A*Acr3v1 + pi*(1-mu_c)*gamma_H*Hcr3v1 -kappa3*Rpcr3v1 - omega2_pc*Rpcr3v1 - delta2_cr*Rpcr3v1 + delta1_cr*Rpcr3v0+ delta1_cr*Rncr3v0*(rho_v2)
dRpcu3v1 = pi*(1-phi_cv1)*gamma_I*Icu3v1 + pi*gamma_A*Acu3v1 + pi*(1-mu_c)*gamma_H*Hcu3v1 -kappa3*Rpcu3v1 - omega2_pc*Rpcu3v1 - delta2_cu*Rpcu3v1 + delta1_cu*Rpcu3v0+ delta1_cu*Rncu3v0*(rho_v2)
dRpar3v1 = pi*(1-phi_av1)*gamma_I*Iar3v1 + pi*gamma_A*Aar3v1 + pi*(1-mu_a)*gamma_H*Har3v1 -kappa3*Rpar3v1 - omega2_pa*Rpar3v1 - delta2_ar*Rpar3v1 + delta1_ar*Rpar3v0+ delta1_ar*Rnar3v0*(rho_v2)
dRpau3v1 = pi*(1-phi_av1)*gamma_I*Iau3v1 + pi*gamma_A*Aau3v1 + pi*(1-mu_a)*gamma_H*Hau3v1 -kappa3*Rpau3v1 - omega2_pa*Rpau3v1 - delta2_au*Rpau3v1 + delta1_au*Rpau3v0+ delta1_au*Rnau3v0*(rho_v2)
dRper3v1 = pi*(1-phi_ev1)*gamma_I*Ier3v1 + pi*gamma_A*Aer3v1 + pi*(1-mu_e)*gamma_H*Her3v1 -kappa3*Rper3v1 - omega2_pe*Rper3v1 - delta2_er*Rper3v1 + delta1_er*Rper3v0+ delta1_er*Rner3v0*(rho_v2)
dRpeu3v1 = pi*(1-phi_ev1)*gamma_I*Ieu3v1 + pi*gamma_A*Aeu3v1 + pi*(1-mu_e)*gamma_H*Heu3v1 -kappa3*Rpeu3v1 - omega2_pe*Rpeu3v1 - delta2_eu*Rpeu3v1 + delta1_eu*Rpeu3v0+ delta1_eu*Rneu3v0*(rho_v2)
#Recovered and not seropositive
dRncr3v1 = (1-pi)*(1-phi_cv1)*gamma_I*Icr3v1 + (1-pi)*gamma_A*Acr3v1 + (1-pi)*(1-mu_c)*gamma_H*Hcr3v1 + kappa3*Rpcr3v1 - omega2_nc*Rncr3v1 - delta2_cr*Rncr3v1 + delta1_cr*Rncr3v0*(1-rho_v2)
dRncu3v1 = (1-pi)*(1-phi_cv1)*gamma_I*Icu3v1 + (1-pi)*gamma_A*Acu3v1 + (1-pi)*(1-mu_c)*gamma_H*Hcu3v1 + kappa3*Rpcu3v1 - omega2_nc*Rncu3v1 - delta2_cu*Rncu3v1 + delta1_cu*Rncu3v0*(1-rho_v2)
dRnar3v1 = (1-pi)*(1-phi_av1)*gamma_I*Iar3v1 + (1-pi)*gamma_A*Aar3v1 + (1-pi)*(1-mu_a)*gamma_H*Har3v1 + kappa3*Rpar3v1 - omega2_na*Rnar3v1 - delta2_ar*Rnar3v1 + delta1_ar*Rnar3v0*(1-rho_v2)
dRnau3v1 = (1-pi)*(1-phi_av1)*gamma_I*Iau3v1 + (1-pi)*gamma_A*Aau3v1 + (1-pi)*(1-mu_a)*gamma_H*Hau3v1 + kappa3*Rpau3v1 - omega2_na*Rnau3v1 - delta2_au*Rnau3v1 + delta1_au*Rnau3v0*(1-rho_v2)
dRner3v1 = (1-pi)*(1-phi_ev1)*gamma_I*Ier3v1 + (1-pi)*gamma_A*Aer3v1 + (1-pi)*(1-mu_e)*gamma_H*Her3v1 + kappa3*Rper3v1 - omega2_ne*Rner3v1 - delta2_er*Rner3v1 + delta1_er*Rner3v0*(1-rho_v2)
dRneu3v1 = (1-pi)*(1-phi_ev1)*gamma_I*Ieu3v1 + (1-pi)*gamma_A*Aeu3v1 + (1-pi)*(1-mu_e)*gamma_H*Heu3v1 + kappa3*Rpeu3v1 - omega2_ne*Rneu3v1 - delta2_eu*Rneu3v1 + delta1_eu*Rneu3v0*(1-rho_v2)
#Deaths
dDcr3v1 = mu_c*gamma_H*Hcr3v1
dDcu3v1 = mu_c*gamma_H*Hcu3v1
dDar3v1 = mu_a*gamma_H*Har3v1
dDau3v1 = mu_a*gamma_H*Hau3v1
dDer3v1 = mu_e*gamma_H*Her3v1
dDeu3v1 = mu_e*gamma_H*Heu3v1
################################
##Vaccinated two dose and unexposed####
################################
#Susceptible and seropositive with S-spike and total IGg
dSpcr0v2 = omegav_pc*Vpcr0v2 -Spcr0v2 * sd * foi_cr_0v2 - delta3_cr * Spcr0v2 -kappa2 * Spcr0v2 +omega3_pc*Spcr0v3
dSpcu0v2 = omegav_pc*Vpcu0v2 -Spcu0v2 * sd * foi_cu_0v2 - delta3_cu * Spcu0v2 -kappa2 * Spcu0v2 +omega3_pc*Spcu0v3
dSpar0v2 = omegav_pa*Vpar0v2 -Spar0v2 * sd * foi_ar_0v2 - delta3_ar * Spar0v2 -kappa2 * Spar0v2 +omega3_pa*Spar0v3
dSpau0v2 = omegav_pa*Vpau0v2 -Spau0v2 * sd * foi_au_0v2 - delta3_au * Spau0v2 -kappa2 * Spau0v2 +omega3_pa*Spau0v3
dSper0v2 = omegav_pe*Vper0v2 -Sper0v2 * sd * foi_er_0v2 - delta3_er * Sper0v2 -kappa2 * Sper0v2 +omega3_pe*Sper0v3
dSpeu0v2 = omegav_pe*Vpeu0v2 -Speu0v2 * sd * foi_eu_0v2 - delta3_eu * Speu0v2 -kappa2 * Speu0v2 +omega3_pe*Speu0v3
#Susceptible
dSncr0v2 = omegav_nc*Vncr0v2 -Sncr0v2 * sd * foi_cr_0v2 - delta3_cr * Sncr0v2 +kappa2 * Spcr0v2 +omega3_nc*Sncr0v3
dSncu0v2 = omegav_nc*Vncu0v2 -Sncu0v2 * sd * foi_cu_0v2 - delta3_cu * Sncu0v2 +kappa2 * Spcu0v2 +omega3_nc*Sncu0v3
dSnar0v2 = omegav_na*Vnar0v2 -Snar0v2 * sd * foi_ar_0v2 - delta3_ar * Snar0v2 +kappa2 * Spar0v2 +omega3_na*Snar0v3
dSnau0v2 = omegav_na*Vnau0v2 -Snau0v2 * sd * foi_au_0v2 - delta3_au * Snau0v2 +kappa2 * Spau0v2 +omega3_na*Snau0v3
dSner0v2 = omegav_ne*Vner0v2 -Sner0v2 * sd * foi_er_0v2 - delta3_er * Sner0v2 +kappa2 * Sper0v2 +omega3_ne*Sner0v3
dSneu0v2 = omegav_ne*Vneu0v2 -Sneu0v2 * sd * foi_eu_0v2 - delta3_eu * Sneu0v2 +kappa2 * Speu0v2 +omega3_ne*Sneu0v3
#Exposed
dEcr1v2 = Spcr0v2 * sd * foi_cr_0v2 + Sncr0v2 * sd * foi_cr_0v2- sigma * Ecr1v2 - delta3_cr*Ecr1v2 +delta2_cr*Ecr1v1
dEcu1v2 = Spcu0v2 * sd * foi_cu_0v2 + Sncu0v2 * sd * foi_cu_0v2- sigma * Ecu1v2 - delta3_cu*Ecu1v2 +delta2_cu*Ecu1v1
dEar1v2 = Spar0v2 * sd * foi_ar_0v2 + Snar0v2 * sd * foi_ar_0v2- sigma * Ear1v2 - delta3_ar*Ear1v2 +delta2_ar*Ear1v1
dEau1v2 = Spau0v2 * sd * foi_au_0v2 + Snau0v2 * sd * foi_au_0v2- sigma * Eau1v2 - delta3_au*Eau1v2 +delta2_au*Eau1v1
dEer1v2 = Sper0v2 * sd * foi_er_0v2 + Sner0v2 * sd * foi_er_0v2- sigma * Eer1v2 - delta3_er*Eer1v2 +delta2_er*Eer1v1
dEeu1v2 = Speu0v2 * sd * foi_eu_0v2 + Sneu0v2 * sd * foi_eu_0v2- sigma * Eeu1v2 - delta3_eu*Eeu1v2 +delta2_eu*Eeu1v1
# Asymptomatic
dAcr1v2 = (1-nu_c)*sigma*Ecr1v2 - gamma_A * Acr1v2 - delta3_cr*Acr1v2 +delta2_cr*Acr1v1
dAcu1v2 = (1-nu_c)*sigma*Ecu1v2 - gamma_A * Acu1v2 - delta3_cu*Acu1v2 +delta2_cu*Acu1v1
dAar1v2 = (1-nu_a)*sigma*Ear1v2 - gamma_A * Aar1v2 - delta3_ar*Aar1v2 +delta2_ar*Aar1v1
dAau1v2 = (1-nu_a)*sigma*Eau1v2 - gamma_A * Aau1v2 - delta3_au*Aau1v2 +delta2_au*Aau1v1
dAer1v2 = (1-nu_e)*sigma*Eer1v2 - gamma_A * Aer1v2 - delta3_er*Aer1v2 +delta2_er*Aer1v1
dAeu1v2 = (1-nu_e)*sigma*Eeu1v2 - gamma_A * Aeu1v2 - delta3_eu*Aeu1v2 +delta2_eu*Aeu1v1
#Symptomatic
dIcr1v2 = nu_c*sigma*Ecr1v2 - gamma_I * Icr1v2
dIcu1v2 = nu_c*sigma*Ecu1v2 - gamma_I * Icu1v2
dIar1v2 = nu_a*sigma*Ear1v2 - gamma_I * Iar1v2
dIau1v2 = nu_a*sigma*Eau1v2 - gamma_I * Iau1v2
dIer1v2 = nu_e*sigma*Eer1v2 - gamma_I * Ier1v2
dIeu1v2 = nu_e*sigma*Eeu1v2 - gamma_I * Ieu1v2
# Hospitalized
dHcr1v2 = phi_cv2*gamma_I*Icr1v2 - gamma_H * Hcr1v2
dHcu1v2 = phi_cv2*gamma_I*Icu1v2 - gamma_H * Hcu1v2
dHar1v2 = phi_av2*gamma_I*Iar1v2 - gamma_H * Har1v2
dHau1v2 = phi_av2*gamma_I*Iau1v2 - gamma_H * Hau1v2
dHer1v2 = phi_ev2*gamma_I*Ier1v2 - gamma_H * Her1v2
dHeu1v2 = phi_ev2*gamma_I*Ieu1v2 - gamma_H * Heu1v2
# Recovered and seroconverted
dRpcr1v2 = pi*(1-phi_cv2)*gamma_I*Icr1v2 + pi*gamma_A*Acr1v2 + pi*(1-mu_c)*gamma_H*Hcr1v2 -kappa3*Rpcr1v2 - omega_pc*Rpcr1v2 - delta3_cr*Rpcr1v2 +delta2_cr*Rpcr1v1+delta2_cr*Rncr1v1*(rho_v2)+delta2_cr*Spcr1v1 +delta2_cr*Sncr1v1*(rho_v2)
dRpcu1v2 = pi*(1-phi_cv2)*gamma_I*Icu1v2 + pi*gamma_A*Acu1v2 + pi*(1-mu_c)*gamma_H*Hcu1v2 -kappa3*Rpcu1v2 - omega_pc*Rpcu1v2 - delta3_cu*Rpcu1v2 +delta2_cu*Rpcu1v1+delta2_cu*Rncu1v1*(rho_v2)+delta2_cu*Spcu1v1+delta2_cu*Sncu1v1*(rho_v2)
dRpar1v2 = pi*(1-phi_av2)*gamma_I*Iar1v2 + pi*gamma_A*Aar1v2 + pi*(1-mu_a)*gamma_H*Har1v2 -kappa3*Rpar1v2 - omega_pa*Rpar1v2 - delta3_ar*Rpar1v2 +delta2_ar*Rpar1v1+delta2_ar*Rnar1v1*(rho_v2)+delta2_ar*Spar1v1+delta2_ar*Snar1v1*(rho_v2)
dRpau1v2 = pi*(1-phi_av2)*gamma_I*Iau1v2 + pi*gamma_A*Aau1v2 + pi*(1-mu_a)*gamma_H*Hau1v2 -kappa3*Rpau1v2 - omega_pa*Rpau1v2 - delta3_au*Rpau1v2 +delta2_au*Rpau1v1+delta2_au*Rnau1v1*(rho_v2)+delta2_au*Spau1v1+delta2_au*Snau1v1*(rho_v2)
dRper1v2 = pi*(1-phi_ev2)*gamma_I*Ier1v2 + pi*gamma_A*Aer1v2 + pi*(1-mu_e)*gamma_H*Her1v2 -kappa3*Rper1v2 - omega_pe*Rper1v2 - delta3_er*Rper1v2 +delta2_er*Rper1v1+delta2_er*Rner1v1*(rho_v2)+delta2_er*Sper1v1+delta2_er*Sner1v1*(rho_v2)
dRpeu1v2 = pi*(1-phi_ev2)*gamma_I*Ieu1v2 + pi*gamma_A*Aeu1v2 + pi*(1-mu_e)*gamma_H*Heu1v2 -kappa3*Rpeu1v2 - omega_pe*Rpeu1v2 - delta3_eu*Rpeu1v2 +delta2_eu*Rpeu1v1+delta2_eu*Rneu1v1*(rho_v2)+delta2_eu*Speu1v1+delta2_eu*Sneu1v1*(rho_v2)
#Recovered and not seropositive
dRncr1v2 = (1-pi)*(1-phi_cv2)*gamma_I*Icr1v2 + (1-pi)*gamma_A*Acr1v2 + (1-pi)*(1-mu_c)*gamma_H*Hcr1v2 + kappa3*Rpcr1v2 - omega_nc*Rncr1v2 - delta3_cr*Rncr1v2 +delta2_cr*Rncr1v1*(1-rho_v2)+delta2_cr*Sncr1v1*(1-rho_v2)
dRncu1v2 = (1-pi)*(1-phi_cv2)*gamma_I*Icu1v2 + (1-pi)*gamma_A*Acu1v2 + (1-pi)*(1-mu_c)*gamma_H*Hcu1v2 + kappa3*Rpcu1v2 - omega_nc*Rncu1v2 - delta3_cu*Rncu1v2 +delta2_cu*Rncu1v1*(1-rho_v2)+delta2_cu*Sncu1v1*(1-rho_v2)
dRnar1v2 = (1-pi)*(1-phi_av2)*gamma_I*Iar1v2 + (1-pi)*gamma_A*Aar1v2 + (1-pi)*(1-mu_a)*gamma_H*Har1v2 + kappa3*Rpar1v2 - omega_na*Rnar1v2 - delta3_ar*Rnar1v2 +delta2_ar*Rnar1v1*(1-rho_v2)+delta2_ar*Snar1v1*(1-rho_v2)
dRnau1v2 = (1-pi)*(1-phi_av2)*gamma_I*Iau1v2 + (1-pi)*gamma_A*Aau1v2 + (1-pi)*(1-mu_a)*gamma_H*Hau1v2 + kappa3*Rpau1v2 - omega_na*Rnau1v2 - delta3_au*Rnau1v2 +delta2_au*Rnau1v1*(1-rho_v2)+delta2_au*Snau1v1*(1-rho_v2)
dRner1v2 = (1-pi)*(1-phi_ev2)*gamma_I*Ier1v2 + (1-pi)*gamma_A*Aer1v2 + (1-pi)*(1-mu_e)*gamma_H*Her1v2 + kappa3*Rper1v2 - omega_ne*Rner1v2 - delta3_er*Rner1v2 +delta2_er*Rner1v1*(1-rho_v2)+delta2_er*Sner1v1*(1-rho_v2)
dRneu1v2 = (1-pi)*(1-phi_ev2)*gamma_I*Ieu1v2 + (1-pi)*gamma_A*Aeu1v2 + (1-pi)*(1-mu_e)*gamma_H*Heu1v2 + kappa3*Rpeu1v2 - omega_ne*Rneu1v2 - delta3_eu*Rneu1v2 +delta2_eu*Rneu1v1*(1-rho_v2)+delta2_eu*Sneu1v1*(1-rho_v2)
#Deaths
dDcr1v2 = mu_c*gamma_H*Hcr1v2
dDcu1v2 = mu_c*gamma_H*Hcu1v2
dDar1v2 = mu_a*gamma_H*Har1v2
dDau1v2 = mu_a*gamma_H*Hau1v2
dDer1v2 = mu_e*gamma_H*Her1v2
dDeu1v2 = mu_e*gamma_H*Heu1v2
################################
##Vaccinated two dose and exposed once####
################################
#Susceptible
dSpcr1v2 = omega_pc*Rpcr1v2 -kappa3*Spcr1v2 - Spcr1v2 * sd * foi_cr_1v2 - delta3_cr * Spcr1v2 +omega3_pc*Spcr1v3
dSpcu1v2 = omega_pc*Rpcu1v2 -kappa3*Spcu1v2 - Spcu1v2 * sd * foi_cu_1v2 - delta3_cu * Spcu1v2 +omega3_pc*Spcu1v3
dSpar1v2 = omega_pa*Rpar1v2 -kappa3*Spar1v2 - Spar1v2 * sd * foi_ar_1v2 - delta3_ar * Spar1v2 +omega3_pa*Spar1v3 + omega4_pa*Spar2v2
dSpau1v2 = omega_pa*Rpau1v2 -kappa3*Spau1v2 - Spau1v2 * sd * foi_au_1v2 - delta3_au * Spau1v2 +omega3_pa*Spau1v3 + omega4_pa*Spau2v2
dSper1v2 = omega_pe*Rper1v2 -kappa3*Sper1v2 - Sper1v2 * sd * foi_er_1v2 - delta3_er * Sper1v2 +omega3_pe*Sper1v3 + omega4_pe*Sper2v2
dSpeu1v2 = omega_pe*Rpeu1v2 -kappa3*Speu1v2 - Speu1v2 * sd * foi_eu_1v2 - delta3_eu * Speu1v2 +omega3_pe*Speu1v3 + omega4_pe*Speu2v2
dSncr1v2 = omega_nc*Rncr1v2 + kappa3*Spcr1v2 -Sncr1v2 * sd * foi_cr_1v2 - delta3_cr * Sncr1v2 +omega3_nc*Sncr1v3
dSncu1v2 = omega_nc*Rncu1v2 + kappa3*Spcu1v2 -Sncu1v2 * sd * foi_cu_1v2 - delta3_cu * Sncu1v2 +omega3_nc*Sncu1v3
dSnar1v2 = omega_na*Rnar1v2 + kappa3*Spar1v2 -Snar1v2 * sd * foi_ar_1v2 - delta3_ar * Snar1v2 +omega3_na*Snar1v3 +omega4_na*Snar2v2
dSnau1v2 = omega_na*Rnau1v2 + kappa3*Spau1v2 -Snau1v2 * sd * foi_au_1v2 - delta3_au * Snau1v2 +omega3_na*Snau1v3 +omega4_na*Snau2v2
dSner1v2 = omega_ne*Rner1v2 + kappa3*Sper1v2 -Sner1v2 * sd * foi_er_1v2 - delta3_er * Sner1v2 +omega3_ne*Sner1v3 +omega4_ne*Sner2v2
dSneu1v2 = omega_ne*Rneu1v2 + kappa3*Speu1v2 -Sneu1v2 * sd * foi_eu_1v2 - delta3_eu * Sneu1v2 +omega3_ne*Sneu1v3 +omega4_ne*Sneu2v2
#Exposed
dEcr2v2 = Spcr1v2 * sd * foi_cr_1v2 + Sncr1v2 * sd * foi_cr_1v2 - sigma * Ecr2v2 - delta3_cr*Ecr2v2 +delta2_cr*Ecr2v1
dEcu2v2 = Spcu1v2 * sd * foi_cu_1v2 + Sncu1v2 * sd * foi_cu_1v2 - sigma * Ecu2v2 - delta3_cu*Ecu2v2 +delta2_cu*Ecu2v1
dEar2v2 = Spar1v2 * sd * foi_ar_1v2 + Snar1v2 * sd * foi_ar_1v2 - sigma * Ear2v2 - delta3_ar*Ear2v2 +delta2_ar*Ear2v1
dEau2v2 = Spau1v2 * sd * foi_au_1v2 + Snau1v2 * sd * foi_au_1v2 - sigma * Eau2v2 - delta3_au*Eau2v2 +delta2_au*Eau2v1
dEer2v2 = Sper1v2 * sd * foi_er_1v2 + Sner1v2 * sd * foi_er_1v2 - sigma * Eer2v2 - delta3_er*Eer2v2 +delta2_er*Eer2v1
dEeu2v2 = Speu1v2 * sd * foi_eu_1v2 + Sneu1v2 * sd * foi_eu_1v2 - sigma * Eeu2v2 - delta3_eu*Eeu2v2 +delta2_eu*Eeu2v1
# Asymptomatic
dAcr2v2 = (1-nu_c)*sigma*Ecr2v2 - gamma_A * Acr2v2 - delta3_cr*Acr2v2 + delta2_cr*Acr2v1
dAcu2v2 = (1-nu_c)*sigma*Ecu2v2 - gamma_A * Acu2v2 - delta3_cu*Acu2v2 + delta2_cu*Acu2v1
dAar2v2 = (1-nu_a)*sigma*Ear2v2 - gamma_A * Aar2v2 - delta3_ar*Aar2v2 + delta2_ar*Aar2v1
dAau2v2 = (1-nu_a)*sigma*Eau2v2 - gamma_A * Aau2v2 - delta3_au*Aau2v2 + delta2_au*Aau2v1
dAer2v2 = (1-nu_e)*sigma*Eer2v2 - gamma_A * Aer2v2 - delta3_er*Aer2v2 + delta2_er*Aer2v1
dAeu2v2 = (1-nu_e)*sigma*Eeu2v2 - gamma_A * Aeu2v2 - delta3_eu*Aeu2v2 + delta2_eu*Aeu2v1
#Symptomatic
dIcr2v2 = nu_c*sigma*Ecr2v2 - gamma_I * Icr2v2
dIcu2v2 = nu_c*sigma*Ecu2v2 - gamma_I * Icu2v2
dIar2v2 = nu_a*sigma*Ear2v2 - gamma_I * Iar2v2
dIau2v2 = nu_a*sigma*Eau2v2 - gamma_I * Iau2v2
dIer2v2 = nu_e*sigma*Eer2v2 - gamma_I * Ier2v2
dIeu2v2 = nu_e*sigma*Eeu2v2 - gamma_I * Ieu2v2
# Hospitalized
dHcr2v2 = phi_cv2*gamma_I*Icr2v2 - gamma_H * Hcr2v2
dHcu2v2 = phi_cv2*gamma_I*Icu2v2 - gamma_H * Hcu2v2
dHar2v2 = phi_av2*gamma_I*Iar2v2 - gamma_H * Har2v2
dHau2v2 = phi_av2*gamma_I*Iau2v2 - gamma_H * Hau2v2
dHer2v2 = phi_ev2*gamma_I*Ier2v2 - gamma_H * Her2v2
dHeu2v2 = phi_ev2*gamma_I*Ieu2v2 - gamma_H * Heu2v2
# Recovered and seroconverted
dRpcr2v2 = pi*(1-phi_cv2)*gamma_I*Icr2v2 + pi*gamma_A*Acr2v2 + pi*(1-mu_c)*gamma_H*Hcr2v2 -kappa3*Rpcr2v2 - omega_pc*Rpcr2v2 - delta3_cr*Rpcr2v2 +delta2_cr*Rpcr2v1+ delta2_cr*Rncr2v1*rho_v2
dRpcu2v2 = pi*(1-phi_cv2)*gamma_I*Icu2v2 + pi*gamma_A*Acu2v2 + pi*(1-mu_c)*gamma_H*Hcu2v2 -kappa3*Rpcu2v2 - omega_pc*Rpcu2v2 - delta3_cu*Rpcu2v2 +delta2_cu*Rpcu2v1+ delta2_cu*Rncu2v1*rho_v2
dRpar2v2 = pi*(1-phi_av2)*gamma_I*Iar2v2 + pi*gamma_A*Aar2v2 + pi*(1-mu_a)*gamma_H*Har2v2 -kappa3*Rpar2v2 - omega_pa*Rpar2v2 - delta3_ar*Rpar2v2 +delta2_ar*Rpar2v1+ delta2_ar*Rnar2v1*rho_v2
dRpau2v2 = pi*(1-phi_av2)*gamma_I*Iau2v2 + pi*gamma_A*Aau2v2 + pi*(1-mu_a)*gamma_H*Hau2v2 -kappa3*Rpau2v2 - omega_pa*Rpau2v2 - delta3_au*Rpau2v2 +delta2_au*Rpau2v1+ delta2_au*Rnau2v1*rho_v2
dRper2v2 = pi*(1-phi_ev2)*gamma_I*Ier2v2 + pi*gamma_A*Aer2v2 + pi*(1-mu_e)*gamma_H*Her2v2 -kappa3*Rper2v2 - omega_pe*Rper2v2 - delta3_er*Rper2v2 +delta2_er*Rper2v1+ delta2_er*Rner2v1*rho_v2
dRpeu2v2 = pi*(1-phi_ev2)*gamma_I*Ieu2v2 + pi*gamma_A*Aeu2v2 + pi*(1-mu_e)*gamma_H*Heu2v2 -kappa3*Rpeu2v2 - omega_pe*Rpeu2v2 - delta3_eu*Rpeu2v2 +delta2_eu*Rpeu2v1+ delta2_eu*Rneu2v1*rho_v2
#Recovered and not seropositive
dRncr2v2 = (1-pi)*(1-phi_cv2)*gamma_I*Icr2v2 + (1-pi)*gamma_A*Acr2v2 + (1-pi)*(1-mu_c)*gamma_H*Hcr2v2 + kappa3*Rpcr2v2 - omega_nc*Rncr2v2 - delta3_cr*Rncr2v2 + delta2_cr*Rncr2v1*(1-rho_v2)
dRncu2v2 = (1-pi)*(1-phi_cv2)*gamma_I*Icu2v2 + (1-pi)*gamma_A*Acu2v2 + (1-pi)*(1-mu_c)*gamma_H*Hcu2v2 + kappa3*Rpcu2v2 - omega_nc*Rncu2v2 - delta3_cu*Rncu2v2 + delta2_cu*Rncu2v1*(1-rho_v2)
dRnar2v2 = (1-pi)*(1-phi_av2)*gamma_I*Iar2v2 + (1-pi)*gamma_A*Aar2v2 + (1-pi)*(1-mu_a)*gamma_H*Har2v2 + kappa3*Rpar2v2 - omega_na*Rnar2v2 - delta3_ar*Rnar2v2 + delta2_ar*Rnar2v1*(1-rho_v2)
dRnau2v2 = (1-pi)*(1-phi_av2)*gamma_I*Iau2v2 + (1-pi)*gamma_A*Aau2v2 + (1-pi)*(1-mu_a)*gamma_H*Hau2v2 + kappa3*Rpau2v2 - omega_na*Rnau2v2 - delta3_au*Rnau2v2 + delta2_au*Rnau2v1*(1-rho_v2)
dRner2v2 = (1-pi)*(1-phi_ev2)*gamma_I*Ier2v2 + (1-pi)*gamma_A*Aer2v2 + (1-pi)*(1-mu_e)*gamma_H*Her2v2 + kappa3*Rper2v2 - omega_ne*Rner2v2 - delta3_er*Rner2v2 + delta2_er*Rner2v1*(1-rho_v2)
dRneu2v2 = (1-pi)*(1-phi_ev2)*gamma_I*Ieu2v2 + (1-pi)*gamma_A*Aeu2v2 + (1-pi)*(1-mu_e)*gamma_H*Heu2v2 + kappa3*Rpeu2v2 - omega_ne*Rneu2v2 - delta3_eu*Rneu2v2 + delta2_eu*Rneu2v1*(1-rho_v2)
#Deaths
dDcr2v2 = mu_c*gamma_H*Hcr2v2
dDcu2v2 = mu_c*gamma_H*Hcu2v2
dDar2v2 = mu_a*gamma_H*Har2v2
dDau2v2 = mu_a*gamma_H*Hau2v2
dDer2v2 = mu_e*gamma_H*Her2v2
dDeu2v2 = mu_e*gamma_H*Heu2v2
################################
##Vaccinated two dose and exposed twice####
################################
#Susceptible
dSpcr2v2 = omega_pc*Rpcr2v2 -kappa3*Spcr2v2 - Spcr2v2 * sd * foi_cr_2v2 - delta3_cr * Spcr2v2 + delta2_cr*Spcr2v1+ delta2_cr*Sncr2v1*(rho_v2)+ omega2_pc*Rpcr3v2 +omega3_pc*Spcr2v3
dSpcu2v2 = omega_pc*Rpcu2v2 -kappa3*Spcu2v2 - Spcu2v2 * sd * foi_cu_2v2 - delta3_cu * Spcu2v2 + delta2_cu*Spcu2v1+ delta2_cu*Sncu2v1*(rho_v2)+ omega2_pc*Rpcu3v2 +omega3_pc*Spcu2v3
dSpar2v2 = omega_pa*Rpar2v2 -kappa3*Spar2v2 - Spar2v2 * sd * foi_ar_2v2 - delta3_ar * Spar2v2 + delta2_ar*Spar2v1+ delta2_ar*Snar2v1*(rho_v2)+ omega2_pa*Rpar3v2 +omega3_pa*Spar2v3 -omega4_pa*Spar2v2
dSpau2v2 = omega_pa*Rpau2v2 -kappa3*Spau2v2 - Spau2v2 * sd * foi_au_2v2 - delta3_au * Spau2v2 + delta2_au*Spau2v1+ delta2_au*Snau2v1*(rho_v2)+ omega2_pa*Rpau3v2 +omega3_pa*Spau2v3 -omega4_pa*Spau2v2
dSper2v2 = omega_pe*Rper2v2 -kappa3*Sper2v2 - Sper2v2 * sd * foi_er_2v2 - delta3_er * Sper2v2 + delta2_er*Sper2v1+ delta2_er*Sner2v1*(rho_v2)+ omega2_pe*Rper3v2 +omega3_pe*Sper2v3 -omega4_pe*Sper2v2
dSpeu2v2 = omega_pe*Rpeu2v2 -kappa3*Speu2v2 - Speu2v2 * sd * foi_eu_2v2 - delta3_eu * Speu2v2 + delta2_eu*Speu2v1+ delta2_eu*Sneu2v1*(rho_v2)+ omega2_pe*Rpeu3v2 +omega3_pe*Speu2v3 -omega4_pe*Speu2v2
dSncr2v2 = omega_nc*Rncr2v2 + kappa3*Spcr2v2 -Sncr2v2 * sd * foi_cr_2v2 - delta3_cr * Sncr2v2 + delta2_cr*Sncr2v1*(1-rho_v2) + omega2_nc*Rncr3v2 +omega3_nc*Sncr2v3
dSncu2v2 = omega_nc*Rncu2v2 + kappa3*Spcu2v2 -Sncu2v2 * sd * foi_cu_2v2 - delta3_cu * Sncu2v2 + delta2_cu*Sncu2v1*(1-rho_v2) + omega2_nc*Rncu3v2 +omega3_nc*Sncu2v3
dSnar2v2 = omega_na*Rnar2v2 + kappa3*Spar2v2 -Snar2v2 * sd * foi_ar_2v2 - delta3_ar * Snar2v2 + delta2_ar*Snar2v1*(1-rho_v2) + omega2_na*Rnar3v2 +omega3_na*Snar2v3-omega4_na*Snar2v2
dSnau2v2 = omega_na*Rnau2v2 + kappa3*Spau2v2 -Snau2v2 * sd * foi_au_2v2 - delta3_au * Snau2v2 + delta2_au*Snau2v1*(1-rho_v2) + omega2_na*Rnau3v2 +omega3_na*Snau2v3-omega4_na*Snau2v2
dSner2v2 = omega_ne*Rner2v2 + kappa3*Sper2v2 -Sner2v2 * sd * foi_er_2v2 - delta3_er * Sner2v2 + delta2_er*Sner2v1*(1-rho_v2) + omega2_ne*Rner3v2 +omega3_ne*Sner2v3-omega4_ne*Sner2v2
dSneu2v2 = omega_ne*Rneu2v2 + kappa3*Speu2v2 -Sneu2v2 * sd * foi_eu_2v2 - delta3_eu * Sneu2v2 + delta2_eu*Sneu2v1*(1-rho_v2) + omega2_ne*Rneu3v2 +omega3_ne*Sneu2v3-omega4_ne*Sneu2v2
#Exposed
dEcr3v2 = Spcr2v2 * sd * foi_cr_2v2 + Sncr2v2 * sd * foi_cr_2v2 - sigma * Ecr3v2 - delta3_cr*Ecr3v2 + delta2_cr*Ecr3v1
dEcu3v2 = Spcu2v2 * sd * foi_cu_2v2 + Sncu2v2 * sd * foi_cu_2v2 - sigma * Ecu3v2 - delta3_cu*Ecu3v2 + delta2_cu*Ecu3v1
dEar3v2 = Spar2v2 * sd * foi_ar_2v2 + Snar2v2 * sd * foi_ar_2v2 - sigma * Ear3v2 - delta3_ar*Ear3v2 + delta2_ar*Ear3v1
dEau3v2 = Spau2v2 * sd * foi_au_2v2 + Snau2v2 * sd * foi_au_2v2 - sigma * Eau3v2 - delta3_au*Eau3v2 + delta2_au*Eau3v1
dEer3v2 = Sper2v2 * sd * foi_er_2v2 + Sner2v2 * sd * foi_er_2v2 - sigma * Eer3v2 - delta3_er*Eer3v2 + delta2_er*Eer3v1
dEeu3v2 = Speu2v2 * sd * foi_eu_2v2 + Sneu2v2 * sd * foi_eu_2v2 - sigma * Eeu3v2 - delta3_eu*Eeu3v2 + delta2_eu*Eeu3v1
# Asymptomatic
dAcr3v2 = (1-nu_c)*sigma*Ecr3v2 - gamma_A * Acr3v2 - delta3_cr*Acr3v2+ delta2_cr*Acr3v1
dAcu3v2 = (1-nu_c)*sigma*Ecu3v2 - gamma_A * Acu3v2 - delta3_cu*Acu3v2+ delta2_cu*Acu3v1
dAar3v2 = (1-nu_a)*sigma*Ear3v2 - gamma_A * Aar3v2 - delta3_ar*Aar3v2+ delta2_ar*Aar3v1
dAau3v2 = (1-nu_a)*sigma*Eau3v2 - gamma_A * Aau3v2 - delta3_au*Aau3v2+ delta2_au*Aau3v1
dAer3v2 = (1-nu_e)*sigma*Eer3v2 - gamma_A * Aer3v2 - delta3_er*Aer3v2+ delta2_er*Aer3v1
dAeu3v2 = (1-nu_e)*sigma*Eeu3v2 - gamma_A * Aeu3v2 - delta3_eu*Aeu3v2+ delta2_eu*Aeu3v1
#Symptomatic
dIcr3v2 = nu_c*sigma*Ecr3v2 - gamma_I * Icr3v2
dIcu3v2 = nu_c*sigma*Ecu3v2 - gamma_I * Icu3v2
dIar3v2 = nu_a*sigma*Ear3v2 - gamma_I * Iar3v2
dIau3v2 = nu_a*sigma*Eau3v2 - gamma_I * Iau3v2
dIer3v2 = nu_e*sigma*Eer3v2 - gamma_I * Ier3v2
dIeu3v2 = nu_e*sigma*Eeu3v2 - gamma_I * Ieu3v2
# Hospitalized
dHcr3v2 = phi_cv2*gamma_I*Icr3v2 - gamma_H * Hcr3v2
dHcu3v2 = phi_cv2*gamma_I*Icu3v2 - gamma_H * Hcu3v2
dHar3v2 = phi_av2*gamma_I*Iar3v2 - gamma_H * Har3v2
dHau3v2 = phi_av2*gamma_I*Iau3v2 - gamma_H * Hau3v2
dHer3v2 = phi_ev2*gamma_I*Ier3v2 - gamma_H * Her3v2
dHeu3v2 = phi_ev2*gamma_I*Ieu3v2 - gamma_H * Heu3v2
# Recovered and seroconverted
dRpcr3v2 = pi*(1-phi_cv2)*gamma_I*Icr3v2 + pi*gamma_A*Acr3v2 + pi*(1-mu_c)*gamma_H*Hcr3v2 -kappa3*Rpcr3v2 - omega2_pc*Rpcr3v2 - delta3_cr*Rpcr3v2 + delta2_cr*Rpcr3v1+ delta2_cr*Rncr3v1*(rho_v2)
dRpcu3v2 = pi*(1-phi_cv2)*gamma_I*Icu3v2 + pi*gamma_A*Acu3v2 + pi*(1-mu_c)*gamma_H*Hcu3v2 -kappa3*Rpcu3v2 - omega2_pc*Rpcu3v2 - delta3_cu*Rpcu3v2 + delta2_cu*Rpcu3v1+ delta2_cu*Rncu3v1*(rho_v2)
dRpar3v2 = pi*(1-phi_av2)*gamma_I*Iar3v2 + pi*gamma_A*Aar3v2 + pi*(1-mu_a)*gamma_H*Har3v2 -kappa3*Rpar3v2 - omega2_pa*Rpar3v2 - delta3_ar*Rpar3v2 + delta2_ar*Rpar3v1+ delta2_ar*Rnar3v1*(rho_v2)
dRpau3v2 = pi*(1-phi_av2)*gamma_I*Iau3v2 + pi*gamma_A*Aau3v2 + pi*(1-mu_a)*gamma_H*Hau3v2 -kappa3*Rpau3v2 - omega2_pa*Rpau3v2 - delta3_au*Rpau3v2 + delta2_au*Rpau3v1+ delta2_au*Rnau3v1*(rho_v2)
dRper3v2 = pi*(1-phi_ev2)*gamma_I*Ier3v2 + pi*gamma_A*Aer3v2 + pi*(1-mu_e)*gamma_H*Her3v2 -kappa3*Rper3v2 - omega2_pe*Rper3v2 - delta3_er*Rper3v2 + delta2_er*Rper3v1+ delta2_er*Rner3v1*(rho_v2)
dRpeu3v2 = pi*(1-phi_ev2)*gamma_I*Ieu3v2 + pi*gamma_A*Aeu3v2 + pi*(1-mu_e)*gamma_H*Heu3v2 -kappa3*Rpeu3v2 - omega2_pe*Rpeu3v2 - delta3_eu*Rpeu3v2 + delta2_eu*Rpeu3v1+ delta2_eu*Rneu3v1*(rho_v2)
#Recovered and not seropositive
dRncr3v2 = (1-pi)*(1-phi_cv2)*gamma_I*Icr3v2 + (1-pi)*gamma_A*Acr3v2 + (1-pi)*(1-mu_c)*gamma_H*Hcr3v2 + kappa3*Rpcr3v2 - omega2_nc*Rncr3v2 - delta3_cr*Rncr3v2 + delta2_cr*Rncr3v1*(1-rho_v2)
dRncu3v2 = (1-pi)*(1-phi_cv2)*gamma_I*Icu3v2 + (1-pi)*gamma_A*Acu3v2 + (1-pi)*(1-mu_c)*gamma_H*Hcu3v2 + kappa3*Rpcu3v2 - omega2_nc*Rncu3v2 - delta3_cu*Rncu3v2 + delta2_cu*Rncu3v1*(1-rho_v2)
dRnar3v2 = (1-pi)*(1-phi_av2)*gamma_I*Iar3v2 + (1-pi)*gamma_A*Aar3v2 + (1-pi)*(1-mu_a)*gamma_H*Har3v2 + kappa3*Rpar3v2 - omega2_na*Rnar3v2 - delta3_ar*Rnar3v2 + delta2_ar*Rnar3v1*(1-rho_v2)
dRnau3v2 = (1-pi)*(1-phi_av2)*gamma_I*Iau3v2 + (1-pi)*gamma_A*Aau3v2 + (1-pi)*(1-mu_a)*gamma_H*Hau3v2 + kappa3*Rpau3v2 - omega2_na*Rnau3v2 - delta3_au*Rnau3v2 + delta2_au*Rnau3v1*(1-rho_v2)
dRner3v2 = (1-pi)*(1-phi_ev2)*gamma_I*Ier3v2 + (1-pi)*gamma_A*Aer3v2 + (1-pi)*(1-mu_e)*gamma_H*Her3v2 + kappa3*Rper3v2 - omega2_ne*Rner3v2 - delta3_er*Rner3v2 + delta2_er*Rner3v1*(1-rho_v2)
dRneu3v2 = (1-pi)*(1-phi_ev2)*gamma_I*Ieu3v2 + (1-pi)*gamma_A*Aeu3v2 + (1-pi)*(1-mu_e)*gamma_H*Heu3v2 + kappa3*Rpeu3v2 - omega2_ne*Rneu3v2 - delta3_eu*Rneu3v2 + delta2_eu*Rneu3v1*(1-rho_v2)
#Deaths
dDcr3v2 = mu_c*gamma_H*Hcr3v2
dDcu3v2 = mu_c*gamma_H*Hcu3v2
dDar3v2 = mu_a*gamma_H*Har3v2
dDau3v2 = mu_a*gamma_H*Hau3v2
dDer3v2 = mu_e*gamma_H*Her3v2
dDeu3v2 = mu_e*gamma_H*Heu3v2
################################
##Vaccinated three dose and unexposed####
################################
#Susceptible seropositive
dSpcr0v3 = omegav_pc*Vpcr0v3 -Spcr0v3 * sd * foi_cr_0v3 - kappa3*Spcr0v3 - omega3_pc*Spcr0v3 +delta3_cr*Sncr0v3*rho_v3
dSpcu0v3 = omegav_pc*Vpcu0v3 -Spcu0v3 * sd * foi_cu_0v3 - kappa3*Spcu0v3 - omega3_pc*Spcu0v3 +delta3_cu*Sncu0v3*rho_v3
dSpar0v3 = omegav_pa*Vpar0v3 -Spar0v3 * sd * foi_ar_0v3 - kappa3*Spar0v3 - omega3_pa*Spar0v3 +delta3_ar*Snar0v3*rho_v3