Global dynamics of a reaction and diffusion model for Lyme disease.

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 R₀. 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 R₀ is a threshold value for the global dynamics and that the spreading speed is linearly determinate.