Mathematical and computational models have become widely used and demanded tools for examining mechanisms of transmission, exploring characteristics of epidemics, predicting future courses of an outbreak and evaluating strategies to find a best control-program. One of the problems of modelling is bridging the gap between conceptual models (i.e compartmental models of epidemiology) and their computer simulation (through deterministic, stochastic or agent-based implementation). Domain Specific Languages (DSLs) are often used to address such difficulties by separating two concerns of modelling, specification (conceptual model) and implementation (computational model). In this perspective, we develop a DSL called KENDRICK targeted to the epidemiological modelling and coupled with a simulation platform that allows the study of such models. The other important issue needs to be addressed in the context of epidemiological modelling is the heterogeneities introduced by separate concerns. In order to facilitate the specification of models and their evolution, it is crucial to be able to define concerns with as few dependencies with each other as possible and to combine them as freely as possible. We address such challenges by proposing a common mathematical meta-model that supports both concerns and models and enabling their compositions by some operators. We then implement our proposal language KENDRICK based on this meta-model. The language simplifies the construction of complex epidemiological models by decomposing them into modular concerns, by which common concerns can be reused across models and can be easily changed.