Studying the spread of a pathogen at regional scale in a managed metapopulation such as cattle herds in a region often requires to take into account the within-herd transmission dynamics, as well as the between-herd dynamics. Management induces an heterogeneous contact structure which needs to be taken into account for moderately diffusive pathogens. This can lead to high-dimensional metapopulation systems resulting from the coupling of several within-herd transmission models. To tackle this problem, we aim here at reducing the dimension of a tractable but realistic dynamical system reproducing the within-herd spread. The context chosen to illustrate our purpose is the BVDV transmission in a cattle herd structured in two age classes and several epidemiological states, including two infectious states (transiently and permanently infected). Different time scales, corresponding to the epidemiological and demographic processes, are identified and allow to build a reduced model. Singular perturbation technique is used to prove that, under some non-restrictive conditions on parameter values, the behaviour of the initial system is quite accurately approximated by that of the reduced system. Simulations are also performed to corroborate the approximation quality. Our study illustrates the methodological interest of using singular perturbations to reduce model complexity. It also rigorously proves the biologically intuitive assumption that transiently infected individuals can be neglected when capturing the global dynamics of BVDV spread.