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

formulation of our model allows for the possibility of multiple infectious contacts
within a timestep, so for a susceptible individual subject to total hazard rate λj the
probability of infection on a given day is 1−exp(−λj). (Note that the units of β are
day −1 .) We assume density-independent contact rates and random mixing within each
pool, so hazard rates of infection are dependent on the transmission rate for each
infectious class multiplied by the proportion of the population in that class.
Specifically, defining the effective number of individuals in the hospital mixing pool as
Nh=Sh+Eh+Ih+Rh+Im and in the community mixing pool as Nc=Sc+Ec+Ic+Rc+
ρ(Sh+Eh+Ih+Rh), the total hazard rates are λc=[β(Ic+εEc)+ ρβ(Ih+εEh)+γβεEm]/Nc and
λh=ρλc+ηβ(Ih+εEh+κIm)/Nh. In simulations, the number of infection events in each
timestep is determined by random draws from binomial(Sj, 1−exp(−λj)) distributions
(j=c,h). Equations describing the model are given in the appendix.
Figure 2
(A) Sample output from the model, showing cumulative numbers of cases. Five
realizations of the stochastic model are shown for three values of R, to highlight
variability in outcomes and the increased probability of fadeout for lower R. Several
epidemics died out immediately and cannot be resolved: 1 for R=2, and 2 each for
R=1.6 and R=1.2. (B) Probability of epidemic containment (as defined in the text) as a
function of R, for a population of 100,000 with a single initial case. We set ε=0.1, and
β was varied to give the desired R values, with no control measures imposed.
Probabilities were calculated from 100 runs per R value. (C)-(E) Threshold control
policies for containment of the epidemic. Lines show R=1 contours for scenarios where
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