such that the system is reactive when E 0 > 1 and nonreactive when E 0 < 1. E 0 describes the transitory behaviour of disease following a temporary perturbation in prevalence. If the threshold for epidemicity is surpassed, then disease prevalence can increase further even when the disease is not endemic. This suggests that epidemics can occur even in areas where long-term transmission cannot be maintained. Reluga et al. [47] defined the discounted reproductive number R d . The discounted reproductive number is a measure of reproductive success that is an individual's expected lifetime offspring production discounted by the background population growth rate. It is calculated as