In our analyses tracing effectiveness will be expressed as the critical tracing probability p c *, defined as the proportion of contacts that need to be traced to achieve R pre = 1. If at least that many contacts are traced, epidemics will certainly die out if transmission during isolation or quarantine is prevented or limited to a small number of health-care workers that do not re-introduce the infection into the general community (see also [5] ). If such reintroductions cannot be excluded, a lower R pre may be aimed for. Because of this threshold of 1, the R 0 pre values (without tracing) were assumed to have some value larger than 1 (otherwise tracing would not be needed at all) and less than published R 0 values for the specific cases (Table 2) . First we study p c * as a function of R 0 pre and t lat (with tracing delay d = 0), and second as a function of t lat and d (with R 0 pre = 1.5).