Invasive species are non-native plants and animals that can significantly harm societal and natural values such as agriculture, social amenity, the environment and native ecosystems and species. Efficient preparation for their incursion requires understanding their potential impact, influenced by factors such as introduction pathways, host material availability, climate suitability, and the value of affected agriculture. A crucial factor that is specific to the incursion and therefore unpredictable beforehand is the size of the outbreak at the time of detection, which can curtail the range of management options: if the invading population is small then eradication may be affordable, whereas if it is large then eradication may be impossible. We propose a statistical model for this random variable to aid decision-support systems. We analyze the relationship between surveillance and organism detection using survival analysis, treating detection as analogous to a failure event. This approach links the distribution of infestation size at detection with the probability of detecting an incursion—specifically, the hazard function describing the instantaneous detection rate. Under this survival model, we connect the probability density function of infestation size at detection to the hazard function. Moreover, we introduce an approximation using the Weibull distribution to model the population size before pest detection. This approximation holds when dealing with a small fixed number of traps or a low probability of detection per trap. By assuming a relationship between the invasive population size and the time it remains undetected, we estimate the probability density function for the population’s duration of occupancy. We develop a computer program to perform the analysis, using the Mediterranean fruit fly as a case study to demonstrate its application. We believe that representing the invasive population size at detection provides valuable insights into control and eradication strategies, potentially applicable to broader invasive species management efforts.