Known conceptual and technical limitations of mainstream environmental health data analysis have directed research to new avenues. The goal is to deal more efficiently with the inherent uncertainty and composite space-time heterogeneity of key attributes, account for multi-sourced knowledge bases (health models, survey data, empirical relationships etc.), and generate more accurate predictions across space-time. Based on a versatile, knowledge synthesis methodological framework, we introduce new space-time covariance functions built by integrating epidemic propagation models and we apply them in the analysis of existing flu datasets. Within the knowledge synthesis framework, the Bayesian maximum entropy theory is our method of choice for the spatiotemporal prediction of the ratio of new infectives (RNI) for a case study of flu in France. The space-time analysis is based on observations during a period of 15 weeks in 1998-1999. We present general features of the proposed covariance functions, and use these functions to explore the composite space-time RNI dependency. We then implement the findings to generate sufficiently detailed and informative maps of the RNI patterns across space and time. The predicted distributions of RNI suggest substantive relationships in accordance with the typical physiographic and climatologic features of the country.