The southern cattle fever tick (SCFT), Rhipicephalus (Boophilus) microplus, remains endemic in Puerto Rico. Systematic treatment programmes greatly reduced and even eradicated temporarily this tick from the island. However, a systemic treatment programme that includes integrated management practices for livestock against SCFT remains to be established in the island. We describe a spatially-explicit, individual-based model that simulates climate–livestock–SCFT–landscape interactions. This model was developed as an investigative tool to aid in a research project on integrated management of the SCFT that took place in Puerto Rico between 2014 and 2017. We used the model to assess the efficacy of tick suppression and probability of tick elimination when applying safer acaricides at 3-week intervals to different proportions of a herd of non-lactating dairy cattle.