A 1D lattice of coupled susceptible/infected/removed (SIR) epidemic centres is considered numerically and analytically. We describe a mechanism for the interaction between nodes in an SIR network, i.e. for the migration process of individuals between epidemic centres with a finite-characteristic time. More specifically, we study a model for a weakly coupled population distributed between the interacting centres with a diffusion-type migration process. A 1D lattice of SIR nodes is studied numerically. Travelling wave-like solutions preserving their shape and speed are found over a wide parameter range. For weak coupling, the main part of the travelling wave is well approximated by the limiting SIR solution. Explicit formulae are found for the speed of the travelling waves and compared with the results of numerical simulation.