SARS-CoV-2 Model (K)

Clearing environment

rm(list = ls())

Loading necessary package

require(deSolve)

System of DEs

SARSCOV2Model <- function (t, y, params) {
  
S.h<-y[1] #create local variable S, first element of y
E.h<-y[2] 
I.h<-y[3]
S.l<-y[4]
E.l<-y[5]
I.l<-y[6]
Q<-y[7]
R<-y[8]
V<-y[9]

with(
  as.list(params, y),
  {
dS.h<--q*beta*(I.h+I.l)*S.h/(S.h+E.h+I.h+S.l+E.l+I.l+Q+R)-c*(1-exp((-1/K)*V))*S.h
dE.h<-q*beta*(I.h+I.l)*S.h/(S.h+E.h+I.h+S.l+E.l+I.l+Q+R)+c*(1-exp((-1/K)*V))*S.h-lambda*E.h
dI.h<-lambda*E.h-b*g*I.h-aH*h*(1-g)*I.h-gammah*(1-h)*(1-g)*I.h
dS.l<--(1-p)*q*beta*(I.h+I.l)*S.l/(S.h+E.h+I.h+S.l+E.l+I.l+Q+R)-(1-p)*c*(1-exp((-1/K)*V))*S.l
dE.l<-(1-p)*q*beta*(I.h+I.l)/(S.h+E.h+I.h+S.l+E.l+I.l+Q+R)+(1-p)*c*(1-exp((-1/K)*V))*S.l-lambda*E.l
dI.l<-lambda*E.l-b*I.l
dQ<-b*I.l+g*b*I.h-aQ*h*Q-gammaQ*(1-h)*Q
dR<-gammah*(1-h)*(1-g)*I.h+gammaQ*(1-h)*Q
dV<-omega*I.h+(1-p)*omega*I.l-delta*V
  dy<-c(dS.h,dE.h,dI.h,dS.l,dE.l,dI.l,dQ,dR,dV) #combine results into one vector dy
list(dy)
  }
)
}

Initial Values

times<-seq(0,180,by=1) 
covid.params<-c(q=0.2,beta=13,p=.2,c=0,lambda=1/4.43,b=1/0.77,g=0,gammaQ=0.1,gammah=1/2.7,aQ=1/1.93,aH=1/2.7,h=0.00082,omega=0,delta=1,K=10000)
ystart<-c(S.h=(.2)*100000,E.h=0,I.h=1,S.l=(1-0.2)*100000,E.l=0,I.l=0,Q=0,R=0,V=0)
covid.out <- as.data.frame(lsoda(ystart,times,SARSCOV2Model,covid.params))

Changing K to 1000, 10000, 100000, & 1000000

covid.params.k1 <- c(q=0.5,beta=13,p=.2,c=0,lambda=1/4.43,b=1/0.77,g=0,gammaQ=0.1,gammah=1/2.7,aQ=1/1.93,aH=1/2.7,h=0.00082,omega=0,delta=1,K=1000)
covid.params.k2 <- c(q=0.5,beta=13,p=.2,c=0,lambda=1/4.43,b=1/0.77,g=0,gammaQ=0.1,gammah=1/2.7,aQ=1/1.93,aH=1/2.7,h=0.00082,omega=0,delta=1,K=10000)
covid.params.k3 <- c(q=0.5,beta=13,p=.2,c=0,lambda=1/4.43,b=1/0.77,g=0,gammaQ=0.1,gammah=1/2.7,aQ=1/1.93,aH=1/2.7,h=0.00082,omega=0,delta=1,K=100000)
covid.params.k4 <- c(q=0.5,beta=13,p=.2,c=0,lambda=1/4.43,b=1/0.77,g=0,gammaQ=0.1,gammah=1/2.7,aQ=1/1.93,aH=1/2.7,h=0.00082,omega=0,delta=1,K=1000000)

Creating data frame for each value of k

covid.out.k1 <- as.data.frame(lsoda(ystart,times,SARSCOV2Model,covid.params.k1))
covid.out.k2 <- as.data.frame(lsoda(ystart,times,SARSCOV2Model,covid.params.k2))
covid.out.k3 <- as.data.frame(lsoda(ystart,times,SARSCOV2Model,covid.params.k3))
covid.out.k4 <- as.data.frame(lsoda(ystart,times,SARSCOV2Model,covid.params.k4))

Plotting S.h, S.l, E.h, & E.l

## SUSCEPTIBLES ##
op1 <- par(fig=c(0,0.5,0,1), mar=c(4,4,1,1))
plot(covid.out.k1$S.h~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Susceptible (High)")
lines(covid.out.k2$S.h~covid.out.k2$time, col="red")

lines(covid.out.k3$S.h~covid.out.k3$time, col="purple")
lines(covid.out.k4$S.h~covid.out.k4$time, col="green")

legend(80, 17500,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)

par(fig=c(0.5,1,0,1), mar=c(4,4,1,1), new=T)

plot(covid.out.k1$S.l~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Susceptible (Low)")
lines(covid.out.k2$S.l~covid.out.k2$time, col="red")

lines(covid.out.k3$S.l~covid.out.k3$time, col="purple")
lines(covid.out.k4$S.l~covid.out.k4$time, col="green")

legend(80, 70000,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)
par(op1)

## EXPOSED ##
op2 <- par(fig=c(0,0.5,0,1), mar=c(4,4,1,1))

plot(covid.out.k1$E.h~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Exposed (High)", ylim=c(0,7100))
lines(covid.out.k2$E.h~covid.out.k2$time, col="red")

lines(covid.out.k3$E.h~covid.out.k3$time, col="purple")
lines(covid.out.k4$E.h~covid.out.k4$time, col="green")

legend(80, 6000,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)

par(fig=c(0.5,1,0,1), mar=c(4,4,1,1), new=T)

plot(covid.out.k1$E.l~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Exposed (Low)", ylim=c(0,3))
lines(covid.out.k2$E.l~covid.out.k2$time, col="red")

lines(covid.out.k3$E.l~covid.out.k3$time, col="purple")
lines(covid.out.k4$E.l~covid.out.k4$time, col="green")

legend(80, 2.5,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)
par(op2)

## INFECTED ##
op3 <- par(fig=c(0,0.5,0,1), mar=c(4,4,1,1))

plot(covid.out.k1$I.h~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Infected (High)")
lines(covid.out.k2$I.h~covid.out.k2$time, col="red")

lines(covid.out.k3$I.h~covid.out.k3$time, col="purple")
lines(covid.out.k4$I.h~covid.out.k4$time, col="green")

legend(80, 3000,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)

par(fig=c(0.5,1,0,1), mar=c(4,4,1,1), new=T)

plot(covid.out.k1$I.l~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Infected (Low)")
lines(covid.out.k2$I.l~covid.out.k2$time, col="red")

lines(covid.out.k3$I.l~covid.out.k3$time, col="purple")
lines(covid.out.k4$I.l~covid.out.k4$time, col="green")

legend(80, 0.4,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)
par(op3)

## SELF-ISOLATING ##
op4 <- par(mar=c(6,6,2,2))

plot(covid.out.k1$Q~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Self-Isolating")
lines(covid.out.k2$Q~covid.out.k2$time, col="red")

lines(covid.out.k3$Q~covid.out.k3$time, col="purple")
lines(covid.out.k4$Q~covid.out.k4$time, col="green")

legend(125, 3,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)
par(op4)

## RECOVERED ##
op5 <- par(mar=c(6,6,2,2))

plot(covid.out.k1$R~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Recovered")
lines(covid.out.k2$R~covid.out.k2$time, col="red")

lines(covid.out.k3$R~covid.out.k3$time, col="purple")
lines(covid.out.k4$R~covid.out.k4$time, col="green")

legend(100, 15000,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)
par(op5)

## VIRUS IN ENVIRONMENT ##
op6 <- par(mar=c(6,6,2,2))

plot(covid.out.k1$V~covid.out.k1$time,type="l", col="blue", xlab="Days", ylab = "Virus in Environment")
lines(covid.out.k2$V~covid.out.k2$time, col="red")

lines(covid.out.k3$V~covid.out.k3$time, col="purple")
lines(covid.out.k4$V~covid.out.k4$time, col="green")

legend(100, 15000,legend = c("K = 1,000","K = 10,000","K = 100,000","K = 1,000,000"), col = c("blue", "red", "purple", "green"), lty=1, cex=0.8)
par(op6)

Results of Plots

# first dataframe lists highest values
# second dataframe lists lowest values
# third dataframe lists ending values

results.k1 <- data.frame(
  S.h = c(max(covid.out.k1[ ,2]), max(covid.out.k2[ ,2]), max(covid.out.k3[ ,2]), max(covid.out.k4[ ,2])),
  E.h = c(max(covid.out.k1[ ,3]), max(covid.out.k2[ ,3]), max(covid.out.k3[ ,3]), max(covid.out.k4[ ,3])),
  I.h = c(max(covid.out.k1[ ,4]), max(covid.out.k2[ ,4]), max(covid.out.k3[ ,4]), max(covid.out.k4[ ,4])),
  S.l = c(max(covid.out.k1[ ,5]), max(covid.out.k2[ ,5]), max(covid.out.k3[ ,5]), max(covid.out.k4[ ,5])),
  E.l = c(max(covid.out.k1[ ,6]), max(covid.out.k2[ ,6]), max(covid.out.k3[ ,6]), max(covid.out.k4[ ,6])),
  I.l = c(max(covid.out.k1[ ,7]), max(covid.out.k2[ ,7]), max(covid.out.k3[ ,7]), max(covid.out.k4[ ,7])),
  Q = c(max(covid.out.k1[ ,8]), max(covid.out.k2[ ,8]), max(covid.out.k3[ ,8]), max(covid.out.k4[ ,8])),
  R = c(max(covid.out.k1[ ,9]), max(covid.out.k2[ ,9]), max(covid.out.k3[ ,9]), max(covid.out.k4[ ,9])),
  V = c(max(covid.out.k1[ ,10]), max(covid.out.k2[ ,10]), max(covid.out.k3[ ,10]), max(covid.out.k4[ ,10]))
)

results.k2 <- data.frame(
  S.h = c(min(covid.out.k1[ ,2]), min(covid.out.k2[ ,2]), min(covid.out.k3[ ,2]), min(covid.out.k4[ ,2])),
  E.h = c(min(covid.out.k1[ ,3]), min(covid.out.k2[ ,3]), min(covid.out.k3[ ,3]), min(covid.out.k4[ ,3])),
  I.h = c(min(covid.out.k1[ ,4]), min(covid.out.k2[ ,4]), min(covid.out.k3[ ,4]), min(covid.out.k4[ ,4])),
  S.l = c(min(covid.out.k1[ ,5]), min(covid.out.k2[ ,5]), min(covid.out.k3[ ,5]), min(covid.out.k4[ ,5])),
  E.l = c(min(covid.out.k1[ ,6]), min(covid.out.k2[ ,6]), min(covid.out.k3[ ,6]), min(covid.out.k4[ ,6])),
  I.l = c(min(covid.out.k1[ ,7]), min(covid.out.k2[ ,7]), min(covid.out.k3[ ,7]), min(covid.out.k4[ ,7])),
  Q = c(min(covid.out.k1[ ,8]), min(covid.out.k2[ ,8]), min(covid.out.k3[ ,8]), min(covid.out.k4[ ,8])),
  R = c(min(covid.out.k1[ ,9]), min(covid.out.k2[ ,9]), min(covid.out.k3[ ,9]), min(covid.out.k4[ ,9])),
  V = c(min(covid.out.k1[ ,10]), min(covid.out.k2[ ,10]), min(covid.out.k3[ ,10]), min(covid.out.k4[ ,10]))
)

results.k3 <- data.frame(
  S.h = c(tail(covid.out.k1[ ,2],n=1), tail(covid.out.k2[ ,2],n=1), tail(covid.out.k3[ ,2],n=1), tail(covid.out.k4[ ,2],n=1)), 
  E.h = c(tail(covid.out.k1[ ,3],n=1), tail(covid.out.k2[ ,3],n=1), tail(covid.out.k3[ ,3],n=1), tail(covid.out.k4[ ,3],n=1)),
  I.h = c(tail(covid.out.k1[ ,4],n=1), tail(covid.out.k2[ ,4],n=1), tail(covid.out.k3[ ,4],n=1), tail(covid.out.k4[ ,4],n=1)),
  S.l = c(tail(covid.out.k1[ ,5],n=1), tail(covid.out.k2[ ,5],n=1), tail(covid.out.k3[ ,5],n=1), tail(covid.out.k4[ ,5],n=1)),
  E.l = c(tail(covid.out.k1[ ,6],n=1), tail(covid.out.k2[ ,6],n=1), tail(covid.out.k3[ ,6],n=1), tail(covid.out.k4[ ,6],n=1)), 
  I.l = c(tail(covid.out.k1[ ,7],n=1), tail(covid.out.k2[ ,7],n=1), tail(covid.out.k3[ ,7],n=1), tail(covid.out.k4[ ,7],n=1)),
  Q = c(tail(covid.out.k1[ ,8],n=1), tail(covid.out.k2[ ,8],n=1), tail(covid.out.k3[ ,8],n=1), tail(covid.out.k4[ ,8],n=1)),
  R = c(tail(covid.out.k1[ ,9],n=1), tail(covid.out.k2[ ,9],n=1), tail(covid.out.k3[ ,9],n=1), tail(covid.out.k4[ ,9],n=1)),
  V = c(tail(covid.out.k1[ ,10],n=1), tail(covid.out.k2[ ,10],n=1), tail(covid.out.k3[ ,10],n=1), tail(covid.out.k4[ ,10],n=1))
)

`.rowNamesDF<-`(results.k1,make.names=FALSE,c('K = 1,000','K = 10,000','K = 100,000','K = 1,000,000'))

`.rowNamesDF<-`(results.k2,make.names=FALSE,c('K = 1,000','K = 10,000','K = 100,000','K = 1,000,000'))

`.rowNamesDF<-`(results.k3,make.names=FALSE,c('K = 1,000','K = 10,000','K = 100,000','K = 1,000,000'))

Plotting highest, lowest, and ending values of classes

## HIGHEST ##
op7 <- par(mar=c(6,6,2,2))
plot(results.k1$S.h,type="b", col="blue", xlab="q values", ylab = "Individuals", main="Highest", ylim=c(0,80000))
lines(results.k1$E.h, type = "b", col="red")

lines(results.k1$I.h, type = "b", col="green")
lines(results.k1$S.l, type = "b", col="purple")

lines(results.k1$E.l, type = "b", col="orange")
lines(results.k1$I.l, type = "b", col="forestgreen")

lines(results.k1$Q, type = "b", col="darkturquoise")
lines(results.k1$R, type = "b", col="pink2")

lines(results.k1$V, type = "b", col="yellow")

legend(3, 70000,legend = c("Susceptibles (High)","Exposed (High)","Infected (High)","Susceptibles (Low)","Exposed (Low)","Infected (Low)", "Self-Isolating","Recovered","Virus"), col = c("blue", "red", "green","purple","orange","forestgreen","darkturquoise","pink2","yellow"), lty=1, cex=0.6)

par(op7)

## LOWEST
op8 <- par(mar=c(6,6,2,2))

plot(results.k2$S.h,type="b", col="blue", main="Lowest", xlab="q values", ylab = "Individuals", ylim=c(0,80000))
lines(results.k2$E.h, type = "b", col="red")

lines(results.k2$I.h, type = "b", col="green")
lines(results.k2$S.l, type = "b", col="purple")

lines(results.k2$E.l, type = "b", col="orange")
lines(results.k2$I.l, type = "b", col="forestgreen")

lines(results.k2$Q, type = "b", col="darkturquoise")
lines(results.k2$R, type = "b", col="pink2")

lines(results.k2$V, type = "b", col="yellow")

legend(3, 70000,legend = c("Susceptibles (High)","Exposed (High)","Infected (High)","Susceptibles (Low)","Exposed (Low)","Infected (Low)", "Self-Isolating","Recovered","Virus"), col = c("blue", "red", "green","purple","orange","forestgreen","darkturquoise","pink2","yellow"), lty=1, cex=0.6)

par(op8)

## ENDING ##
op9 <- par(mar=c(6,6,2,2))

plot(results.k3$S.h, type="b", col="blue", main="Ending", xlab="q values", ylab = "Individuals", ylim=c(0,80000))
lines(results.k3$E.h, type = "b", col="red")

lines(results.k3$I.h, type = "b", col="green")
lines(results.k3$S.l, type = "b", col="purple")

lines(results.k3$E.l, type = "b", col="orange")
lines(results.k3$I.l, type = "b", col="forestgreen")

lines(results.k3$Q, type = "b", col="darkturquoise")
lines(results.k3$R, type = "b", col="pink2")

lines(results.k3$V, type = "b", col="yellow")

legend(3, 70000,legend = c("Susceptibles (High)","Exposed (High)","Infected (High)","Susceptibles (Low)","Exposed (Low)","Infected (Low)", "Self-Isolating","Recovered","Virus"), col = c("blue", "red", "green","purple","orange","forestgreen","darkturquoise","pink2","yellow"), lty=1, cex=0.6)

par(op9)