A Global Village
Issue 4 » Networked

Networking Epidemics

Yun William Yu, Bioengineering, Imperial College London

Although it is online social networking sites like Myspace and Facebook that garner the majority of media attention these days, social networks themselves have always been a part of our lives. From the small hunter-gatherer communities of long ago to our present overlapping family, school, and work groups, humans arguably were and still are defined by their relationships to one another. While the extent to which those connections have evolved over time is debatable, a crucial difference in the modern world is how much quantitative data has been compiled. Even as privacy advocates grow increasingly concerned about data rights, it remains the case that such data could be a veritable gold mine for policy-makers working with phenomenon that spread via network effects.

One such phenomenon that is of considerable interest to public policy is the epidemic spread of disease, for obvious reasons. Traditional models of epidemics compartmentalise the population into broad categories – e.g. those who are susceptible to being infected, those who have already been infected, and those who have been infected and are now immune. However, these models assume that there is random mixing within the population; that is to say, an infected individual is equally likely to infect any member of the susceptible category. This is clearly a somewhat unnatural assumption; in the real world we are far more likely to transmit an infectious disease – for instance, swine flu – to people with whom we come into close contact. Thus, mapping of the network of social interactions could provide insights into both the path and rate of spread of a disease and provide potential tools for halting or interrupting that spread.

Thresholds
Human interaction networks are, however, extraordinarily complex and thus difficult to quantify accurately. Thus, although epidemic modelling historically has roots in the study of human diseases – with seminal work being conducted by Imperial College academics – let us first turn to an analogous but simpler problem: the spread of computer viruses for large networks (such as the Internet).

While different from biological systems in certain key respects, computers can also become infected by viruses (normally much to our dismay and detriment), spread the infection to connected computers, and then recover after a time (whether through anti-virus software or by a hard-disk format). What’s more, the network topology – the structure of the connected computer network – is far better characterized.

Mapping of the network
of social interactions could
provide insights into both
the path and rate of spread
of a disease and provide
potential tools for halting
or interrupting that spread

Scientists at Carnegie Mellon University were able to use a nonlinear dynamical systems model to relate the connectivity of a network to whether or not an epidemic spreads or dies out1. They found that, given the complete network of connections between computer systems, it is possible to derive an epidemic threshold for the virus below which the epidemic dies out exponentially2. In tackling such virus spread, identification of critical nodes, or computers, for ‘immunization’ is key: immunizing a particular computer rewires the network and, if chosen correctly, may stop the spread of infection.

One can compute the change in the epidemic threshold before and after immunization to determine if the node was effectively chosen to stop the spread of the infection. Ideally, if anti-viral resources (‘vaccines’ in the biological disease case) are limited, one wishes to immunize only those computers that result in a rewired network with a minimized epidemic threshold.

Identification of critical
nodes, or computers, for
‘immunization’ is key: 
immunizing a particular
computer rewires the
network and, if chosen
correctly, may stop the
spread of infection

By constructing a similar ‘contact network’ for human disease transmission, it would theoretically be possible to make similar recommendations for vaccination regimes. Often, when a new epidemic is sweeping through a community, vaccine supplies are limited and policy-makers are forced to make unpalatable choices about where efforts should be directed. Network science could one day be used to advise authorities on the optimal allocation of available resources.

Building the Network
Unfortunately, it is somewhat more difficult to generate similar network maps for human diseases. Despite the staggering amount of data available from Facebook, limitations persist3. Scientists must first characterize the types of interactions that contribute to increased transmission rates. In some cases, e.g. for HIV-AIDS, it is well known what sorts of interactions should ‘count’ in constructing the network. However, for many other diseases, it is unclear a priori the types of contact that are linked to transmission rates. Human interactions are also ephemeral in nature such that any network of interactions is constantly evolving.

Over the past few decades researchers have been working on just that: figuring out what sorts of interactions make up a contact network – this is done largely by making copious observations during instances of outbreak of disease. This type of data is almost always imperfect, but statistical inference may permit insight into modes of transmission. For instance, in a study by the Pennsylvania H1N1 working group (composed of researchers from Imperial College and the US Centres for Disease Control and Prevention), researchers examined the rates of swine flu transmission in relation to different features of primary (grade) school life4. While it was impossible to pinpoint directly how particular children were infected, after constructing social networks corresponding to the interaction patterns of the school children, the team could determine accurate probabilities of transmission as correlated with a number of different factors. Unsurprisingly, sex-related mixing patterns played a role – it was hypothesized that because children of the same sex in a class tend to play together, there is an increased likelihood of transmitting disease to one another. However, contrary to what may be popular belief, sitting next to an infected individual in the classroom did not significantly increase the probability of infection.

Although currently of
largely academic interest,
it is only a matter of time
before social networks
become an essential tool
for government strategy in
epidemiology and beyond

Although still a far cry from the extent to which we understand the spread of computer viruses, data of this sort continues to be compiled. As epidemiological modelling continues to advance, it will likely one day be possible to accurately map human disease transmission networks and make policy recommendations such as the one highlighted in the last section.

Brave New World
Of course, while the behaviour of infected computer systems might be in agreement with some models of disease epidemic propagation, such models do not take into account the vagaries of human nature. Unfortunately, while the humanities and social sciences have much of value to say about the human condition, and often advise what people or indeed policy-makers ought to do (whether from a moral, philosophical, or economic perspective), seldom are those fields quantitatively perfectly predictive of actual actions.

One obvious solution would be to ask actual human beings to inhabit the role of agents in an ‘epidemic’ game online. Perhaps an unusual approach, there are plausible advantages to characterizing behaviour in a simulation involving actual people despite that the fact that one’s risk analysis changes considerably when one’s own life – as opposed to one’s game avatar’s life – is at stake! This isn’t a hypothetical; in late 2005, a glitch in the popular online game World of Warcraft resulted in the so-called ‘Corrupted Blood incident’, during which players’ characters could be infected by a deadly ‘disease’. Players invest hundreds of hours, monthly subscription fees, and significant portions of their social lives into the game; the virtual epidemic was able to provoke a wide range of responses from players, from flight to more sparsely populated areas to some characters trying to help others. Several epidemiologists have attempted to draw insight from these events, mapping them onto potential behaviour of people in real life epidemic disease scenarios5.

As our online and offline worlds slowly merge, it is not altogether surprising that we should look from one to the other for insight and prediction. Although currently of largely academic interest, it is only a matter of time before social networks become an essential tool for government strategy in epidemiology and beyond, playing a role not only in dissemination of information, but also in policy and action.

Yun William Yu is a research student in Biomathematics and Theoretical Chemistry at Imperial College London, where he is a British Marshall Scholar.

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[1] Charkrabarti, D. et al. (2008). Epidemic Thresholds in Real Networks. ACM Transactions on Information and System Security.
[2] More precisely, we encode the connectivity of the network into an adjacency matrix A, which specifies which computers are connected to one another for purposes of viral transmission. The epidemic threshold is then the inverse of the dominant eigenvalue of A, easily computable even for extremely large matrices using numerical techniques.
[3] It is possible to get interesting results even in the absence of a known contact network. For example, because of the friendship paradox (‘your friends have more friends than you do’), the named friends of randomly selected people tend to become infected earlier in an epidemic than the randomly selected people themselves, which provides an early-detection mechanism. Christakis, N.A. & Fowler, J.H. (2010). Social Network Sensors for Early Detection of Contagious Outbreaks. PLoS ONE.
[4] Cauchemez, S. et al. (2011). Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza. Proc. Natl. Acad. Sci.
[5] Lofgren, E.T. and Fefferman, N.H. (2007). The untapped potential of virtual game worlds to shed light on real world epidemics. The Lancet Infectious Diseases.