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Lyme disease is one of the most prevalent and fastest growing vector-borne bacterial illnesses in the United States, with over 25,000 new confirmed cases every year. Humans contract the bacterium Borrelia burgdorferi through the bite of the tick Ixodes scapularis. The tick can receive the bacterium from a variety of small mammal and bird species, but the white-footed mouse Peromyscus leucopus is the primary reservoir in the northeastern United States, especially near human settlement. The tick's life cycle and behavior depend greatly on the season, with different stages of tick biting at different times. Reducing the infection in the tick-mouse cycle may greatly lower human Lyme incidence in some areas. However, research on the effects of various mouse-targeted interventions is limited. One particularly promising method involves administering vaccine pellets to white-footed mice through special bait boxes. In this study, we develop and analyze a mathematical model consisting of a system of nonlinear difference equations to understand the complex transmission dynamics and vector demographics in both tick and mice populations. We evaluate to what extent vaccination of white-footed mice can affect Lyme incidence in I. scapularis, and under which conditions this method saves money in preventing Lyme disease. We find that, in areas with high human risk, vaccination can eliminate mouse-tick transmission of B. burgdorferi while saving money.