Brazilian Spotted Fever (BSF), caused by the bacterium Rickettsia rickettsii, is the tick-borne disease that generates the largest number of human deaths in the world. In Brazil, the current increase of BSF human cases has been associated with the presence and expansion of capybaras Hydrochoerus hydrochaeris, which act as primary hosts for the tick Amblyomma sculptum, vector of the R. rickettsii in this area. We proposed a semi-discrete-time stochastic model to evaluate the role of capybaras in the transmission dynamics of R. rickettsii. Through a sensitivity analysis, we identified the parameters with significant influence on the R. rickettsii establishment. Afterward, we implemented the Gillespie's algorithm to simulate the impact of potential public health interventions to prevent BSF human cases. The introduction of a single infected capybara with at least one infected attached tick is enough to trigger the disease in a non-endemic area. We found that to avoid the formation of new BSF-endemic areas, it is crucial to impede the emigration of capybaras from endemic areas by reducing their birth rate by more than 58%. Model results were corroborated by ex-situ data generated from field studies, and this supports our proposal to prevent BSF human cases by implementing control strategies focused on capybaras. The proposed stochastic model illustrates how strategies for the control and prevention of vector-borne infectious diseases can be focused on amplifier hosts management practices. This work provides a basis for future prevention strategies for other neglected vector-borne diseases.