K - College of Natural Resources - University of California, Berkeley

In all cases (Figure 2C, 2D), we identify a sharp threshold in the interaction
between κ and hc. For example, in an outbreak with R0=2.5 and η=0.5 (Figure 2D, red
lines), making improvements in isolation practices (decreasing κ) has little effect on R if
current control measures place the system at point A, but show dramatic benefits if the
system is at point B. Conversely, increasing hc significantly boosts control from point
A but has negligible effects from point B. This threshold arises because even if all
cases are isolated immediately (hc=1) the epidemic will not be contained unless κ is
sufficiently low. Conversely, even if isolation stops transmission entirely (κ=0), the
outbreak will not be contained unless a sufficient proportion of cases are isolated soon
enough. The sharpness of this threshold arises in part because the proportion of
individuals not isolated by the n th day is (1-hc) n , where values of n~10-20 are pertinent
because individuals with SARS often remain symptomatic for an extended period. The
threshold softens as R0 increases, since when transmission rates are higher the critical
values of n are smaller (i.e. individuals must be isolated sooner, on average, in order to
keep R