and transport networks (see [@TRH] and the references therein).

In [@BRR1], the authors established the existence of an asymptotic speed of propagation (see Definition \[deasp\]) of the solution of , starting from a continuous, nonnegative, compactly supported initial datum $(u_0, v_0)\neq(0, 0)$, towards the unique steady state of the problem, as well as some qualitative properties of it. Denoting such speed by $c^*_{\infty}$, they showed that, if $D\leq 2d$, then $c^*_{\infty}={c_{\operatorname{KPP}}}$, where $$\label{13}
{c_{\operatorname{KPP}}}=2\sqrt{df'(0)}$$ is the asymptotic speed of propagation of the classical Fisher-KPP equation $$v_t(x,y,t)-d\D v(x,y,t)=f(v(x,y,t))$$ in the half-plane (see [@KPP; @AW]), while, if $D> 2d$, then $c^*_{\infty}>{c_{\operatorname{KPP}}}$. This means that a large diffusion on the road speeds up the propagation of the population in the field. Moreover the authors showed that the spreading velocity increases to infinity as the diffusivity on the line grows to infinity. In [@BRR2] they also studied the influence that a drift term and a Fisher-KPP reaction also on the road have on the asymptotic speed of propagation.

In this work we investigate the effect of the road on the propagation in a field which is no longer a half-plane but a strip $\O={{\mathbb{R}}}\times(0,L)$. On the other part of the boundary of the field 