Published bi- and tri-trophic physiologically based demographic system models having similar sub components are used to assess prospectively the geographic distributions and relative abundance (a measure of invasiveness) of six invasive herbivorous insect species across the United States and Mexico. The plant hosts and insect species included in the study are: 1) cotton/pink bollworm, 2) a fruit tree host/Mediterranean fruit fly, 3) olive/olive fly, 4) a perennial host/light brown apple moth, 5) grapevine/glassy-winged sharpshooter and its two egg parasitoids, and 6) grapevine/European grapevine moth. All of these species are currently or have been targets for eradication. The goal of the analyses is to predict and explain prospectively the disparate distributions of the six species as a basis for examining eradication or containment efforts against them. The eradication of the new world screwworm is also reviewed in the discussion section because of its pivotal role in the development of the eradication paradigm. The models used are mechanistic descriptions of the weather driven biology of the species. Observed daily weather data (i.e., max‐min temperatures, solar radiation) from 1,221 locations across the United States and Mexico for the period 1983‐2003 were used to drive the models. Soil moisture and nutrition were assumed nonlimiting. The simulation results were mapped using GRASS GIS. The mathematical underpinnings of the modeling approach are reviewed in the appendix and in the supplemental materials.