At the beginning of the semester we were given a sheet depicting numerous real life models of a variety of social networks. Most of edges concerned interaction between nodes, such as the spread of informational e-mails, friendships within organizations and clubs, or the outbreak of a disease. This blog focuses on a more theoretical application of both game theory and network dynamics.

Experts connected to the Brookings Institute have developed a theoretical “simulation” centered on the dynamics of the spread of fear and disease in a paper entitled, “Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations,” by Joshua M. Epstein, Jon Parker, Derek Cummings, and Ross A. Hammond

(http://www.brookings.edu/~/media/Files/rc/papers/2007/10dynamics_epstein/10dynamics_epstein.pdf).

The first part of the paper describes a model in which (1) a disease is spread throughout a population in concert with (2) the fear of contracting that disease. Traditional mathematical epidemiology models assume perfect mixing within the population. In contrast, these authors model a population in which people, when confronted with the fear of contracting a disease, may change their social patterns or “contact patterns”. Both fear and the disease itself are similarly contagious in their model and both can spread independently. Disease is spread through contact with the disease-infected, while fear is spread through contact with disease-infected, fear-infected, or disease-and-fear-infected people. People within the network fall into seven categories (Susceptible to pathogen and fear, Infected with fear only, Infected with pathogen only, Infected with pathogen and fear, Removed from circulation due to fear, Removed from circulation due to fear and infected with pathogen, Recovered from pathogen and immune to fear).

A key conclusion from the model is that fear spreads faster than disease. While disease can spread through people infected with the pathogen or infected with the pathogen and fear, fear can spread in three ways: people the have contracted the infection, contracted fear, or contracted fear and the infection. A second conclusion emerges when the authors consider flight due to fear of disease: flight amplifies the spread of diseases. That is, the barrier between the infected and those susceptible to infection is broken with the flight of fearful individuals. The authors reference several cases in support of their elegant model.

Several interesting expansions of this model come immediately to mind. Consider, for example, overlaying this model with the additional variable of level and sophistication of communication. With limited communication, i.e., in the pre-information boom era with the internet and television, the original model would have held. An example that comes to mind is spread of disease brought by Europeans to the Americas in the 15th and 16th centuries. As more people fled the disease, this would have had a predictably amplified effect on the population. But now consider a similar situation in the presence of nearly perfect information transfer and exchange. While one may see a similar change in social patterns, would the same “flight” instinct hold in an informed population? Take for instance the spread of meningtis throughout a population. A highly contagious disease, a case of meningitis has the potential to spread rapidly, and amplified as people fled the disease. In a hypothetical population lacking near perfect information, one may see a similar pattern of flight as a result of fear from the disease. Today though an outbreak of menigitis means nothing more than shots for the networks of infected individuals, individuals infected with fear, and those infected with both fear and the disease. Moreover though it may be the instant spread of information between well informed individuals that dampens the “flight” tendency? Something for thought.