## Using derivation for final size from Nishiura, 2012
finalsize.Nishiura <- function(y,R0,k){
	if(y==1){
		fs <- 1/(1+R0/k)^k
	}
	else if(y>1){
		xx <- 0
		for(j in 0:(y-2)){	
			xx <- xx + log(j/k+y)
		}
		
		ll <- xx - lfactorial(y) + log(((k/(R0+k))^(k*y))*((R0*k/(R0+k))^(y-1)))
		fs <- exp(ll)
	}
	fs
}