Here we focus on a basic model for a large well-mixed population. To evaluate whether successful invasion of the pathogen is possible we calculate the (basic) reproduction number (denoted by R 0 ), which gives the number of new infections caused by a single infected individual in a population of uninfected individuals in the early stages of an outbreak [15] . If R 0 .1 the pathogen can invade a population in which it is not yet present, while it cannot if R 0 ,1. In the case that the pathogen-induced mortality is such that it hardly affects the infectious period, the reproduction number is given by