Efforts to eradicate invasive alien species commonly use simulations to calculate the cost-effectiveness of surveys. Although eradication of Solenopsis invicta in the early stages of an invasion is important, few simulations are available to calculate the cost-effectiveness of surveys when a single colony has been detected. In the case of S. invicta, it is difficult to determine from the status of the detected colony whether new queens have dispersed, so it is necessary to consider dispersal as a probabilistic event and calculate its probability. We therefore first constructed a mathematical model in which we used Bayesian statistics to estimate the probability of dispersal as a function of the results of the survey. This mathematical model revealed that the efficacy of the survey and the associated cost differed greatly between cases depending on whether dispersal was or was not confirmed. Next, we developed a simulation that incorporated this mathematical model to inform the determination of the survey area when a single colony had been detected. The simulation showed how ecological parameters and geographical information could be used to identify an efficacious survey area, even in heterogeneous landscapes such as international ports where invasions occur sporadically. Finally, we used this simulation to assess the efficacy of a survey in the case of an S. invicta outbreak at the Port of Tokyo, Japan. The results suggested that the survey covered a sufficiently wide area but that it could have been designed in a more efficacious manner.