Individual-based perspectives on R(0).

Without doubt the basic reproductive ratio, R(0), is the most widely used quantity in epidemic theory. Standard compartmental models show how R(0)is related to the average age of infection, vaccination thresholds for eradication and equilibrium solutions. However, many of the basic formulae for R(0)break down when we consider transmission of infection to be a stochastic process involving discrete individuals. This paper clarifies why and when these differences arise and predicts when individual-based considerations are likely to be important in modelling infection dynamics.