Modelling and simulation have been heavily used in epidemiology, for instance to study the transmission of infectious diseases, their pathogenicity and their propagation. A major hindrance to modelling in epidemiology is the mixing of concerns that ought to be separated. The most obvious one is the computer implementation that should not be mixed with domain aspects. But several domain concerns should also be separated from the core epidemiological ones. These include the distribution of the studied populations into spatial regions, age intervals, sexes, species, viral strains... We propose an approach that relies on a mathematical model of the dynamics of a compartment-based population. The separation of domain concerns is provided by expressing each one as a stochastic automaton and combining them with a tensor sum. A DSL, Kendrick, and a tool, support this approach that has been validated on several case studies.