Signatures of non-homogeneous mixing in disease outbreaks

Despite their simplifying assumptions, simple SEIR (susceptible-exposed-infectious-removed)-type models for a homogeneously mixing fully susceptible population continue to provide useful insight and predictive capability. However, non-homogeneous mixing models such as those for outbreaks in social networks are often believed to provide better predictions of the benefits of various mitigation strategies such as isolation or vaccination. In practice, it is rarely known to what extent a SEIR-type model will adequately describe a given population. Therefore, our goal here is to evaluate possible retrospective signatures of non-homogeneous mixing or non-SEIR-type behavior. Each signature evaluated here is a measure of the goodness of fit of a SEIR-type model curve to the actual epidemic curve. For example, the extents of agreement between the final outbreak size and predictions of the final outbreak size based on reproduction number estimates arising from fitting various portions of the epidemic curve are possible signatures. On the basis of simulated outbreaks, we conclude that such signatures can detect non-SEIR-type behavior in some but not all of the social structures considered. The simulation study confirms that these signatures indicate non-SEIR-type behavior in a real 1918 influenza outbreak in Geneva.