The corresponding ILM consists of an infection rule, where an individual joining the infectious pool is infected by an infectious individual who is uniformly randomly selected, and a removal rule, where a uniformly randomly selected individual leaves the infectious pool. The flow of newly infected individuals is βI(t). Thus, the flow per alreadyinfected individual is β. Since the removed individuals are randomly sampled from the infectious individuals, the average length of the infectious period equals the time expectation of the infectious period, which is 1/β (rather than 1/μ, as calculated from the next-generation method). It follows that R 0 = 1, which is independent of the transmission and death rates from the corresponding ODE. Thus, in this case, R 0 does not signal epidemic growth as anticipated from other methods. Roberts [3] noted three fundamental properties commonly attributed to R 0 : (i) that an endemic infection can persist only if R 0 > 1, (ii) R 0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximise their R 0 value.