Function to estimate Ro and critical vaccine of Ex25 by Prof Tom Britton; SISMID2014
ex25 <- function(z,n,r){
tau = z/n
Ro <- -log(1-tau)/tau
vc <- 1 - 1/Ro
t1 <- 1 + r^2*(1-tau)*Ro^2
t2 <- tau*(1-tau)
t <- t1/t2
t <- t/n
seR <- sqrt(t)
u.Ro <- seR + 1.96
l.Ro <- seR - 1.96
CI.Ro <- c(l.Ro,u.Ro)
t3 <- Ro^4*tau*(1-tau)
t4 <- t1/t3
t4 <- t4/n
seVc <- sqrt(t4)
u.Vc <- seVc + 1.96
l.Vc <- seVc -1.96
CI.Vc <- c(l.Vc,u.Vc)
return(as.list(c(tau=tau,Ro=Ro,CI.Ro=CI.Ro,vc=vc,CI.Vc=CI.Vc,seR=seR,seVc=seVc)))
}