  Motivated by testing for pathogenic diseases we consider a new nonadaptive
group testing problem for which: (1) positives occur within a burst, capturing
the fact that infected test subjects often come in clusters, and (2) that the
test outcomes arise from semiquantitative measurements that provide coarse
information about the number of positives in any tested group. Our model
generalizes prior work on detecting a single burst of positives with classical
group testing[1] as well as work on semiquantitative group testing (SQGT)[2].
Specifically, we study the setting where the burst-length $\ell$ is known and
the semiquantitative tests provide potentially nonuniform estimates on the
number of positives in a test group. The estimates represent the index of a
quantization bin containing the (exact) total number of positives, for
arbitrary thresholds $\eta_1,\dots,\eta_s$. Interestingly, we show that the
minimum number of tests needed for burst identification is essentially only a
function of the largest threshold $\eta_s$. In this context, our main result is
an order-optimal test scheme that can recover any burst of length $\ell$ using
roughly $\frac{\ell}{2\eta_s}+\log_{s+1}(n)$ measurements. This suggests that a
large saturation level $\eta_s$ is more important than finely quantized
information when dealing with bursts. We also provide results for related
modeling assumptions and specialized choices of thresholds.
