The effect of decreasing R 0 pre to R pre is distinct from the effect of isolation and quarantine which reduce c. For tracing to be effective, R q should be smaller than 1, so R pre should be smaller than (12c)/(12cR 0 ), a threshold value determined by c and R 0 [4] [5] [6] . For comparison of contact tracing in different situations, we will choose c = 0 (as in [6] [7] [8] [9] [10] ), because it is easy and as arbitrary as any other value. The value c = 0 is valid for foot-and-mouth disease where traced herds are culled.