Cross et al. [26] showed that when R 0 is based on data collected from simulated epidemics mimicking epidemiological contact-tracing data, R 0 can be substantially greater than one and yet not cause a pandemic. In populations with social or spatial structure, a chronic disease is more likely to invade than an acute disease with the same R 0 , because it persists longer within each group and allows for more host movement between groups.