This paper is devoted to the mathematical analysis of a reaction and diffusion model for
Lyme disease. In the case of a bounded spatial habitat, we obtain the global stability of either
disease-free or endemic steady state in terms of the basic reproduction number R?. In the case of an unbounded spatial habitat, we establish the existence of the spreading speed of the
disease and its coincidence with the minimal wave speed for traveling fronts. Our analytic results show that R? is a threshold value for the global dynamics and that the spreading speed is linearly determinate.