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We take interest in a reaction-diffusion system which has been recentlyproposed [11] as a model for the effect of a road on propagation phenomenaarising in epidemiology and ecology. This system consists in coupling aclassical Fisher-KPP equation in a half-plane with a line with fast diffusionaccounting for a straight road. The effect of the line on spreading propertiesof solutions (with compactly supported initial data) was investigated in aseries of works starting from [11]. We recover these earlier results in a moregeneral spatially periodic framework by exhibiting a threshold for roaddiffusion above which the propagation is driven by the road and the globalspeed is accelerated. We also discuss further applications of our approach,which will rely on the construction of a suitable generalized principaleigenvalue, and investigate in particular the spreading of solutions withexponentially decaying initial data.

A KPP road-field system with spatially periodic exchange terms