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Cattle-fever tick (Boophilus microplus and B. annulatus) populations that develop acaricide resistance become more difficult to control or eradicate. We used a simulation model to assess the direct and indirect effects of interactions among season, habitat type, grazing strategy, and acaricide resistance on the ability to eradicate Boophilus infestations in semi-arid thornshrublands of Texas, USA. Season of infestation appeared to have the strongest effect, with infestations begun on 27 September (autumn) tending to die out sooner than those begun on 1 March (spring) and to remain undetected. Habitat type had the next strongest effect, with infestations surviving much longer as canopy cover increased from uncanopied buffelgrass (Cenchrus ciliaris) habitats to mesquite (Prosopis glandulosa)-canopied grass habitats. Acaricide resistance had a moderate effect; as expected, highly resistant tick populations survived longer than those with no acaricide resistance. The importance of grazing strategy varied with changes in habitat type: as canopy cover increased, infestation duration increased faster under continuous grazing than under rotational grazing strategies. Importance of grazing strategy also varied with acaricide resistance: detected tick populations with no and slight acaricide resistance subjected to acaricide treatments tended to survive longer under rotational grazing than continuous grazing, due to reduced contact with a treated host. Populations with moderate and high resistance behaved more like untreated populations, tending to survive longer under continuous, rather than rotational, grazing, because they experienced less mortality on a treated host. Assuming acaricide treatments at 2-week intervals and maintenance of cattle in infested pastures, results indicate that, for each habitat type, infesting ticks have a threshold of acaricide resistance below which one can eradicate them faster with continuous grazing than with rotational grazing. As canopy cover increases, this threshold appears to shift from high resistance (in grass) to slight resistance (in mesquite).