Probabilities of eliminating host-seeking larvae from the simulated system decreased from ≈ 1 to ≈ 0 as the percentage of cattle treated decreased from 65 to 45, with elimination probabilities ≈ 1 at higher treatment percentages and ≈ 0 at lower treatment percentages. For treatment percentages between 65% and 45%, a more rapid decline in elimination probabilities was predicted by the version of the model that produced higher densities of host-seeking larvae. Number of weeks after the first acaricide application to elimination of host-seeking larvae was variable among replicate simulations within treatment percentages, with within-treatment variation increasing markedly at treatment percentages ≤ 65. Number of weeks after first application to elimination generally varied between 30 and 40 weeks for those treatment percentages with elimination probabilities ≈ 1.