  It has long been known that epidemics can travel along communication lines,
such as roads. In the current COVID-19 epidemic, it has been observed that
major roads have enhanced its propagation in Italy. We propose a new simple
model of propagation of epidemics which exhibits this effect and allows for a
quantitative analysis. The model consists of a classical $SIR$ model with
diffusion, to which an additional compartment is added, formed by the infected
individuals travelling on a line of fast diffusion. Exchanges between
individuals on the line and in the rest of the domain are taken into account. A
classical transformation allows us to reduce the proposed model to a system
analogous to one we had previously introduced [5] to describe the enhancement
of biological invasions by lines of fast diffusion. We establish the existence
of a minimal spreading speed and we show that it may be quite large, even when
the basic reproduction number $R_0$ is close to $1$. More subtle qualitative
features of the final state, showing the important influence of the line, are
also proved here.
