Data-driven contact structures: from homogeneous mixing to multilayer networks

Alberto Aleta, Guilherme Ferraz de Arruda, and Yamir Moreno

The modeling of the spreading of communicable diseases has experienced signi cant advances in the last two decades or so. This has been possible due to the proliferation of data and the development of new methods to gather, mine and analyze it. A key role has also been played by the latest advances in new disciplines like network science. Nonetheless, current models still lack a faithful representation of all possible heterogeneities and features that can be extracted from data. Here, we bridge a current gap in the mathematical modeling of infectious diseases and develop a framework that allows to account simultaneously for both the connectivity of individuals and the age-structure of the population. We compare di erent scenarios, namely, i) the homogeneous mixing setting, ii) one in which only the social mixing is taken into account, iii) a setting that considers the connectivity of individuals alone, and nally, iv) a multilayer representation in which both the social mixing and the number of contacts are included in the model. We analytically show that the thresholds obtained for these four scenarios are di erent. In addition, we conduct extensive numerical simulations and conclude that heterogeneities in the contact network are important for a proper determination of the epidemic threshold, whereas the age-structure plays a bigger role beyond the onset of the outbreak. Altogether, when it comes to evaluate interventions such as vaccination, both sources of individual heterogeneity are important and should be concurrently considered. Our results also provide an indication of the errors incurred in situations in which one cannot access all needed information in terms of connectivity and age of the population.

 

Modeling the contact patterns of the population. Panel A: Schematic view of the di erent models considered. If the only information available is the average number of contacts per individual, homogeneous mixing can be assumed (H). If there is information about the average number of contacts between individuals with age a and a´, then a classical group-interaction model can be implemented (M). On the other hand, if the full contact distribution of the population is known, regardless of their age, it is possible to build the contact network of the population (C). Lastly, when both the contact distribution and the interaction patterns between di erent age groups are known, the individual heterogeneity and the global mixing patterns can be combined to create a multilayer network in which each layer represents a di erent age group (C+M). Panel B: Demographic structure of Italy in 2005 [55]. Panel C: Age-contact patterns in Italy obtained in the POLYMOD study. Panel D: Contact distribution in Italy obtained in the POLYMOD study. The distribution is fi tted to a right-censored negative binomial distribution since the maximum number of contacts that could be reported was 45. 

https://arxiv.org/abs/2003.06946

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