Biology Reference
In-Depth Information
Algorithm 1
Create log-normal outbreak
Input:
{
μ
, σ,
numCases
}
samples = Generate
numCases
samples from a log-normal distribution with mean =
μ
and sd = σ
outbreak = histogram(sample)
trim
t
% last cases from outbreak
2.5.2.1 Single-Day Spike
Generating a single-day spike outbreak requires either specifying
noutbreak
directly for each series, or it can be set as a multiple of the standard deviation
of the initial series:
n
outbreak
=
const
×
std
We anticipate that some users will be more comfortable with specifying
the total count increase directly, while others will prefer to determine the
increase in terms of standard deviations (as is customary in statistical pro-
cess control). In general, we consider small-to-medium spike sizes, because
biosurveillance systems are designed to detect early and more subtle indica-
tions of a disease outbreak.
2.5.2.2 Lognormal Outbreak Signature
A lognormal progression is a reasonable epicurve model, because as
Burkom (2003a) describes, the incubation period distribution of many
infectious diseases tends to be lognormal, with distribution parameters
dependent on the disease agent and route of infection. Generating a log-
normal signature such as the spike requires specifying the size of the out-
break
n
outbreak
. The main difference is that this quantity now spans over
more than a single day such that
n
outbreak
is in fact the area under the log-
normal curve. Similar to the spike,
n
outbreak
can either be set directly or as a
multiple of the standard deviation of the series (excluding DOW, seasonal,
and holiday effects).
In addition to the signature size, the user must specify its shape, deter-
mined by the lognormal distribution parameters
μ
and σ. The peak of the
outbreak signature (which corresponds to the mode of a lognormal distribu-
tion) is approximately on day exp
μ
- σ
2
. We then trim the latest
t%
of the
cases to avoid long tails. This process is summarized by algorithm 1, and an
example of a simulated lognormal outbreak is given in Figure 2.4.
2.5.2.3 Adding Effects to Initial Outbreak Signatures
To this “initial” outbreak, effects such as DOW, seasonal patterns, and holi-
days can be added in the same way that they are added to the initial simu-
lated data (see Section 2.3).
