A well-known framework with strong potential for epidemic prediction and the ability to incorporate realistic contact structures is edge-based compartmental modeling (EBCM). However, models built from this framework lead to a multiplication of ordinary differential equations and many parameters to be estimated, which make the models complex and difficult to extend or to reuse. The Kendrick approach has shown promising results in generalizing compartmental models to take into account aspects of contact networks while preserving the separation of concerns, thus allowing to define modular, extensible and reusable models. But this generalization of compartmental models to contact network aspects is still limited to a few contact networks. In this paper, we present an attempt to extend Kendrick's approach from an approximation of EBCM models to further support aspects of contact networks, thereby improving the predictive quality of models with significant heterogeneity in contact structure, while maintaining the simplicity of compartmental models. This extension consists of an integration of the basic reproductive number R 0 into the compartmental SIR framework. This attempted is validated using Miller's mass action and the approximation of EBCM configuration model.