Infection patterns in simple and complex contagion processes on networks

Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the network structure on spreading process has been widely investigated, but not the reverse question: do different processes unfolding on a given network lead to different infection patterns? How do the infection patterns depend on a model’s parameters or on the nature of the contagion processes? Here we address this issue by investigating the infection patterns for a variety of models. In simple contagion processes, where contagion events involve one connection at a time, we find that the infection patterns are extremely robust across models and parameters. In complex contagion models instead, in which multiple interactions are needed for a contagion event, non-trivial dependencies on models parameters emerge, as the infection pattern depends on the interplay between pairwise and group contagions. In models involving threshold mechanisms moreover, slight parameter changes can significantly impact the spreading paths. Our results show that it is possible to study crucial features of a spread from schematized models, and inform us on the variations between spreading patterns in processes of different nature.Author summary: Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. We here observe how the network is explored by the contagion process, i.e. which links are used for contagions and how frequently. The resulting infection pattern depends on the chosen infection model but surprisingly not all the parameters and models features play a role in the infection pattern. We discover for instance that in simple contagion processes, where contagion events involve one connection at a time, the infection patterns are extremely robust across models and parameters. This has consequences in the role of models in decision-making, as it implies that numerical simulations of simple contagion processes using simplified settings can bring important insights even in the case of a new emerging disease whose properties are not yet well known. In complex contagion models instead, in which multiple interactions are needed for a contagion event, non-trivial dependencies on model parameters emerge and infection patterns cannot be confused with those observed for simple contagion.