A unimodal cluster occurs when occupied time cells tend to occur in a sequence, one right after the other, and arise when an initial case is quickly followed by the appearance of daughter cases. This may occur after an ephemeral exposure to an infectious agent or irritant, and with certain behavior-mediated phenomena such as copy-cat suicides.
A simple example clarifies how the center of a unimodal cluster is determined for a single time series. Consider the time series below (refer to line 1). A '0' indicates time intervals with no cases, and a '1' indicates one or more cases. Line 2 is the index of the time interval. Is the sequence of cases from intervals 2 through 8 a unimodal cluster? The total number of time periods, t, is 17. The number of time periods with at least one case, m, is 7. Our first task is to find that time period which is at the center of all the occupied time periods. Line 3 gives the time periods in which at least one case occurred, these are called yi. Where is the center of the yi? For these data r is the least integer greater than or equal to 7/2, and is r=3. Out of all the occupied time periods (the yi), the index of the time period in the middle is given by r+1=4. This corresponds to time period 5, as shown by the underscored, bold type.
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Cases |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
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Indices |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
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yi |
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2 |
3 |
4 |
5 |
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7 |
8 |
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15 |
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