Flash talk at SINM 2019 (http://danlarremore.com/sinm2019/)
See also: "Interacting simple contagions are complex contagions," by Laurent Hébert-Dufresne: https://speakerdeck.com/laurenthebert/interacting-simple-contagions-are-complex-contagions
Contagions never occur in a vacuum. Instead, diseases and ideas interact with each other and with externalities such as host connectivity, behaviour, and mobility. Several recent studies have shown that many of these non-linear mechanism lead to rich dynamics that can exhibit, for example, a non-monotonous relation between the expected epidemic size and their average transmission rate and discontinuous phase transitions. Surprisingly, many of these features arise from minor alterations to the mechanistic rules of the models. In other words, innocuous looking modeling choices can produce drastically different outcomes that would lead to very different conclusions about intervention strategies or risk. Understanding how to properly generalize contagion models is, as a result, perhaps one of the most pressing challenge of network epidemiology.
Recent work shows that so-called “complex contagions models” can induce many of the defining features of the new wave of non-linear mechanistic models. Complex contagion models achieve this by modifying the transmission rate β(I), as to let it depend on the density of infected individuals in the neighbourhood of the susceptible individuals. In this work, we show that some complex contagion models are in fact indistinguishable from a number of non-linear mechanistic models at the population level. This motivates us to think of complex contagion (on Erdős-Rényi graphs) as a useful effective model of contagion on networks. The complex contagion function β(I) that appears in this model captures arbitrary non-linear effects, allowing us to the contagions without making any mechanistic assumptions. By understanding how mechanistic models map unto this complex contagion model, we can interpret the function β(I) and draw tentative inference about the population under scrutiny.
We develop a fully Bayesian method to fit our effective contagion model to population-level data. This allows us to infer posterior distributions of: Potential epidemiological trajectory, complex contagion functions β(I), and noise components. We avoid overfitting—a problem that arises in related approaches—by parameterizing the complex contagion functions as low degree polynomials. The net results is a flexible, efficient, yet expressive model that can be easily fitted to real and synthetic data alike.