How to Untangle Cascade Effects in Complex Systems

Jairo Mejía and Pablo Fleurquin

d&a blog

The application of statistical physics and graph theory to social phenomena is helping scientists to discover surprising patterns of behavior that will eventually help companies, such as BBVA, to react more effectively to destabilizing events in complex networks. Greater computing processing capacity and the availability of better data allows us to anticipate events that can affect the system in its entirety, for example, in a population exposed to a disease, or companies struggling to response to an economic crisis.


Prediction of epidemics in the city of Cali (Colombia) from empirical mobility flows.


By making use of relational data, we can put into context events that would otherwise ignore patterns of behavior and human interaction that are especially relevant when a system faces a destabilization event.

This is what led researchers from the University of Zaragoza Jesús Gómez and David Soriano and Alex Arenas, from the Universitat Rovira i Virgili, to analyze in a paper published in January’s issue of the journal Nature Physics how mobility affects the way a disease spreads in an urban environment.

The paper titled, “Critical regimes driven by recurrent mobility patterns of reaction–diffusion processes in networks”, took into account the daily routines of displacement between neighborhoods in the Colombian city of Cali. In one of the three scenarios analyzed the researchers found a surprising and counterintuitive conclusion: although we tend to believe that staying indoors will slow an outbreak, the use of graph theory to this problem showed that the daily shift of population among city districts or metapopulations, with different population densities, can diminish the ability of the disease to grow. “Interestingly, we reveal a regime of the reaction–diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks,” the research states.

Arenas, as well as José Ramasco ( Spain’s CSIC researcher), collaborate with BBVA Data & Analytics in new models to simulate how delinquency spreads among economic agents, particularly in customer-supplier networks.

Currently, the research team -which includes BBVA Data & Analytics data scientists Pablo Fleurquin, Elena Tomás and Jordi Nin- seeks to adapt epidemic-type models to understand the spread of financial stress among companies. Through this new modelling, they are able to understand how diffusion is different among economic sectors and within them, measuring the sectoral sensitivity and capacity to transmit debt and eventually delinquency. Another line of research of the team examines the use of models originally applied to ecological systems of the predator-prey type (Generalized Lotka-Volterra models) to understand the dynamic balance of the liquidity of companies and how sudden cash flow changes due to financial stress can generate a cascade effect through a network of businesses.

“The goal is not so much to predict whether a company is going to fall behind, but to model the emerging behavior by detecting the weakest nodes in the system, and design firewalls that can halt defaults when a systemic crisis like the one experienced in 2008 occurs”, Fleurquin explains.


To learn more about this topic, we recommend you the following links:

Los viajes cotidianos pueden reducir la incidencia de una epidemia [Spanish]

Critical HexSIRSize: A contagion process near its critical point