Macroscopic patterns of interacting contagions are indistinguishable from social reinforcement


From ‘fake news’ to innovative technologies, many contagions spread as complex contagions via a process of social reinforcement, where multiple exposures are distinct from prolonged exposure to a single source1. Contrarily, biological agents such as Ebola or measles are typically thought to spread as simple contagions2. Here, we demonstrate that these different spreading mechanisms can have indistinguishable population-level dynamics once multiple contagions interact. In the social context, our results highlight the challenge of identifying and quantifying spreading mechanisms, such as social reinforcement3, in a world where an innumerable number of ideas, memes and behaviours interact. In the biological context, this parallel allows the use of complex contagions to effectively quantify the non-trivial interactions of infectious diseases.

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Fig. 1: Analytical solutions of both susceptible–infectious–susceptible (SIS) ordinary differential equation systems from Box 1 for both interacting simple contagions and complex contagions.
Fig. 2: Statistics of SIS simulations of simple, interacting and complex contagions.
Fig. 3: Signatures of non-interacting and interacting SIR epidemics.
Fig. 4: Complexity of real social and epidemiological contagions.

Data availability

The data represented in Figs. 14 are available as Source Data. Raw data and processing scripts are available online (;

Code availability

The inference software is available online (


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L.H.-D. acknowledges support from the National Science Foundation grant DMS-1829826 and the National Institutes of Health 1P20 GM125498-01 Centers of Biomedical Research Excellence Award. S.V.S. acknowledges support from start-up funds provided by Northeastern University. J.-G.Y. is supported by a James S. McDonnell Postdoctoral Fellowship. We also thank A. Allard, B. M. Althouse, M. Newman, G. Cantwell and A. Kirkley for insightful discussions as well as J. Burkardt for sharing his Bernstein polynomial implementation.

Author information

L.H.-D. conceived the study and conducted the simulations. J.-G.Y. designed and implemented the inference procedure. L.H.-D. and J.-G.Y. performed the calculations. S.V.S. compiled the empirical data. All authors interpreted the results and wrote the manuscript.

Correspondence to Laurent Hébert-Dufresne.

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Peer review information Nature Physics thanks Nicholas Christakis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–9, details and benchmarks for the inference procedure and numerical simulations, and additional computational tests of the results.

Source data

Source Data Fig. 1

Computational Source Data.

Source Data Fig. 2

Statistical Source Data.

Source Data Fig. 3

Statistical and computational Source Data.

Source Data Fig. 4

Statistical Source Data.

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Hébert-Dufresne, L., Scarpino, S.V. & Young, J. Macroscopic patterns of interacting contagions are indistinguishable from social reinforcement. Nat. Phys. (2020).

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