There are a huge number of pathogens with multi-component transmission cycles, involving amplifier hosts, vectors or complex pathogen life cycles. These complex systems present challenges in terms of modeling and policy development. A lethal tick-borne infectious disease, the Brazilian Spotted Fever (BSF), is a relevant example of that. The current increase of human cases of BSF has been associated with the presence and expansion of the capybara Hydrochoerus hydrochaeris, amplifier host for the agent Rickettsia rickettsii and primary host for the tick vector Amblyomma sculptum. We introduce a stochastic dynamical model that captures the spatial distribution of capybaras and ticks to gain a better understanding of the spatial spread of the R. rickettsii and potentially predict future epidemic outcomes. We implemented a reaction-diffusion process in which individuals were divided into classes denoting their state with respect to the disease. The model considered bidirectional movements between base and destination locations limited by the carrying capacity of the environment. We performed systematic stochastic simulations and numerical analysis of the model and investigate the impact of potential interventions to mitigate the spatial spread of the disease. The mobility of capybaras and their attached ticks was significantly influenced by the birth rate of capybaras and therefore, disease propagation velocity was higher in places with higher carrying capacity. Some geographical barriers, generated for example by riparian reforesting, can impede the spatial spread of BSF. The results of this work will allow the formulation of public actions focused on the prevention of BSF human cases.