Sequences of counts of potentially harmful organisms in foods usually exhibit an irregular fluctuating pattern. The counts are determined by the interplay of numerous random factors that tend to promote or inhibit the organisms' growth. The counts can be recorded as zero, indicating that either the organism is not present or is below a minimum detectable level, or they can fluctuate randomly within characteristic bounds. An outburst is said to occur when the population surpasses a specified threshold determined by safety or quality considerations. The growth pattern in this ‘explosive’ mode is also governed by a combination of random mechanisms that determine the growth rate and eventual decline of the population. This paper presents a probabilistic model for such scenarios. The model parameters represent the underlying distribution of the fluctuations, the detection and explosion thresholds and the probability of continued growth after an outburst has begun. A simplified version of the model was used to simulate examples of microbial histories that resemble those of sensitive foods. It is also used to elucidate how the frequency, intensity and duration of outbursts are affected by the parameters of the model. In addition, we demonstrate how to estimate the model's parameters from actual records and illustrate the efficacy of the estimation method with simulated data. The utility of such models for risk assessment will depend on the availability of long records of microbial counts that include outbursts in order to test their predictive ability. Because the presence of a harmful agent is not always sufficient to cause food poisoning, models of this kind can only estimate the expected frequency of outbursts but not the frequency of actual food-poisoning outbreaks.