Infestation by the red imported fire ant, Solenopsis invicta Buren, has destructive effects on native biodiversity, agriculture, and public health. This ant's aggressive foraging behavior and high reproductive capability have enabled its establishment of wild populations in most regions into which it has been imported. The key to eradication is thorough nest monitoring and destruction during early invasion to prevent range expansion. However, how intense must monitoring be on a spatio-temporal scale to eradicate the fire ant is not known. Assuming that the ant was introduced into a region and that monitoring was conducted immediately after nest detection in an effort to detect all other potentially established nests, we developed a mathematical model to investigate detection rates. Setting the monitoring limit to 3 years, the detection rate was maximized when monitoring was conducted shifting bait trap locations and setting them at intervals of 30 m for each monitoring. Monitoring should be conducted in a radius of at least 4 km around the source nest, or wider---depending on how late a nest is found. For ease of application, we also derived equations for finding the minimum bait interval required in an arbitrary ant species for thorough monitoring.