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

individuals and a hospital of 3,000 individuals (c.f. Dwost et al 2003). In the appendix
we assess sensitivity of our results to absolute population size, and also to the relative
size of the two pools.
3. Results and Discussion
Stochastic epidemics and the reproductive number
Epidemics with reproductive number R less than 1 tend to fade out, because on
average each infection does not replace itself. When R is greater than 1, the epidemic is
expected to grow, although if the number of cases is small then random events can lead
to fadeout of the disease, particularly if R is close to 1. (Note that these statements
apply equally to the basic reproductive number, R0, and the effective reproductive
number under a control strategy, R). Sample simulations of our model exhibit this basic
trend (Figure 2A), as we see fadeout for four of five simulations corresponding to
R=1.2, two of five for R=1.6 and one of five for R=2. Also note the variability in
epidemic timing and rate of growth between realizations of our stochastic model.
Because fadeout is an imprecise concept, we frame our results in terms of
“epidemic containment”, which we define as eradication of the disease within 200 days
of the first case, subject to the additional criterion that fewer than 1% of the population
ever become infected. (This criterion is needed because a highly virulent disease can
pass through a population within 200 days and still infect a large proportion of
individuals before extinguishing itself.) The probability of containment in our model
decreases with increasing R (Figure 2B), but is still significantly larger than zero for
R~5. (This relationship can be defined precisely for stochastic models simpler than
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