Social network and disease spread
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Social network and Social network and disease spread disease spread Laurens Bakker, Philippe Giabbanelli
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Social network and disease spread. Laurens Bakker, Philippe Giabbanelli. Outline. ▪ What is a social network?. ▪ Measures. ▪ Disease spread. ▪ Three case studies. Social networks and disease spread. 1. L Bakker, P Giabbanelli. What is a social network? How does it form?. - PowerPoint PPT Presentation
Transcript of Social network and disease spread
Social network and disease spreadSocial network and disease spread
Laurens Bakker, Philippe Giabbanelli
L Bakker, P Giabbanelli Social networks and disease spread 1
OutlineOutline
▪ What is a social network?
▪ Measures
▪ Disease spread
▪ Three case studies
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What is a social network?How does it form?
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But really, how does it form?
People go places… and meet in the process
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But really, how does it form?
People want things… and use others
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But really, how does it form?
People have things in common… and express their commonalities
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What is a social network?How does it form?
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Fluffy theories
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If we want to do science…
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we need something with teeth!
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Network definition
• Actor => Vertex/Node– Boundary
• Connection => Edge/Link– Interaction
– Dynamic social networks
• Observability– Degree (Dombrowski 2007)
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MeasuresMeasures
Motifs – Clustering – Average distance – Degree distribution
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Local
Global
Motifs
Clustering
Average distance
Degree distribution
(Giabbanellli 2011)
Motifs – Clustering – Average distance – Degree distribution
Given a graph G…
and a set S of random graphs of the same size and average degree,
a motif is a subgraph that appears at a ‘very’ different frequence in
G than in S.
1
2
3
21
0
0
0
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(Milo 2004)
Motifs – Clustering – Average distance – Degree distribution
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Motifs – Clustering – Average distance – Degree distribution
For a given node i , we denote its neighborhood by Ni.
The clustering coefficient Ci of i is the edge density of its neighborhood.
Here, there are two edges between nodes in Ni.
At most, it would be a complete graph with Ni.(Ni-1) edges.
Ci = 2.2/(5.4) = 0.2
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If a graph has high clustering coefficient, then there are communities (i.e., cliques) in this graph.
People tend to form communities so they are common in social networks.
Motifs – Clustering – Average distance – Degree distribution
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The distance is the number of edges to go from one node to another.
The average distance is the average of the distance between all pairs of nodes.
Motifs – Clustering – Average distance – Degree distribution
The average distance l is:
∙ small if l ln(n) ∝
∙ ultrasmall if l ln(ln(n))∝
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(Newman 2003)
(Cohen 2003)
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History (the Hype)
• Milgram (Milgram 1969)
– Small world
• Watts & Strogatz (Watts 1998)
– “Small Worlds” & “6 Degrees”
• Barabasi & Albert (Barabasi 1999)
– Power Law (scale free)
• Newman (Newman 2003)
– Review
Motifs – Clustering – Average distance – Degree distribution
Motifs – Clustering – Average distance – Degree distribution
Many measured phenomena are centered around a particular value.
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(Newman 2005)
Motifs – Clustering – Average distance – Degree distribution
Many measured phenomena are centered around a particular value.
There also exists numerous phenomena with a heavy-tailed distribution.
lets plot it on a log-log scale
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(Newman 2005)
Motifs – Clustering – Average distance – Degree distribution
There also exists numerous phenomena with a heavy-tailed distribution.
The equation of a line is p(x) = -αx + c.
Here we have a line on a log-log scale:
ln p(x) = -α ln x + c
apply exponent e
p(x) = ecxc -α
We say that this distribution follows a power-law, with exponent α.
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(Newman 2005)
Motifs – Clustering – Average distance – Degree distribution
We say that this distribution follows a power-law, with exponent α.
Keep in mind that this is quite common.
people’s incomes
computer files
moon craters visits on web pages
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(Li 2005)
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Disease spreadDisease spread
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Thresholds – Variations – Immunization
A ‘threshold’ is the extent to which a disease must be infectious before you can’t stop it from spreading in the population.
(Wikipédia: modèles compartimentaux en épidémiologie)
Very famous claim: scale-free networks have no thresholds! It will spread!
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Thresholds – Variations – Immunization
Very famous claim: scale-free networks have no thresholds! It will spread!
« in a scale-free network there is no epidemic threshold thus eliminating a sexually transmissible disease is impossible »
(Kretschmar 2007, opening of Networks in Epidemiology)
That’s actually sort of false…
…it needs additional conditions, that may not exist.
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Thresholds – Variations – Immunization
Depending on the diseases, there are several epidemiological classes: infected (I), recovered (R), carriers (C)…
It may be interesting to see how the properties of the network influences the number of individuals in each class over time.
order
randomness
(Kuperman 2001; Crepey 2006)
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Thresholds – Variations – Immunization
There are four broad approaches (Giabbanelli 2011).
Is the disease spreading at the same time?
Yes No
We can immunize anybody
We must follow social links
Global competitive Global preventive
Local preventiveLocal competitive
= network game
NP-hard(Kostka 2008)
= separator problem
NP-complete(Rosenberg 2001)
Agents that fight… …and explore
(Giabbanelli 2009) (Stauffer 2006)
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Case Study #1Case Study #1Measuring what mattersMeasuring what matters
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Example #1: Social networks
Property: average distance
Measure: distance
Example #2: Obesity map
Measure: Centrality
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Example #3: Backbone network
We do not care about clustering or whether the network is scale-free.Measure betweenness and average distance. (Giabbanelli 2010)
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What can we measure in a network?What can we measure in a network?
Network Process Measures
Social network
Disease spread
Factors incluencing obesity
Obesity level
Backbone network Deploying equipment
Average distance
Centrality
Betweenness centrality Average distance
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How do we find out what we should measure?How do we find out what we should measure?
▪ Know the properties of the network you are studying.
▪ Generate many of them using appropriate stochastic models.
▪ Record several measures, and the value of the outcome process.
▪ Analyze which measures are linked to the outcome.
→ Network analysis
→ Network generation
→ Possibly optimization
→ Data mining
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Case Study #2Case Study #2Health & Social Health & Social
NetworksNetworks
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« People are interconnected, and so their health is interconnected. »
« … there has been growing conceptual and empirical attention over the past decade to the impact of social networks on health. »
(Smith 2008)
Christakis&Fowler have used social networks to show that people are correlated in weight status, smoking, and… happiness!
http://www.ted.com/talks/lang/eng/nicholas_christakis_the_hidden_influence_of_social_networks.html
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The basic ideaThe basic idea
A long imbalance between energy intake&output yields obesity.
What spread between people are behaviours impacting intake&output.
Eating Exercising
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How we modelled itHow we modelled it
We used social networks.
Each individual has a level of physical activity
and an energy intake.
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How we modelled itHow we modelled it
We also modelled human metabolism.
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Results from Phase 1Results from Phase 1
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Results from Phase 1Results from Phase 1
Presented at ICO
8.6% acceptance
Positive reactions
Journal on its way
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Case Study #3Case Study #3Homeless in the tri-cities Homeless in the tri-cities
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Homeless in the Tri-Cities (I)
• Hope for Freedom Society
• Vertex definition– Boundary: existence of client file
• Edge definition– Interaction: co-observation
• Time!
– Connection: repeated interaction
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Homeless in the Tri-Cities (II)
• Descriptives:– 2 years– ~250 actors– ~3000 observations
• Statistical Models– Static: PNET = ERGM = logit p* (Hunter 2006)– Dynamic: SIENA (Snijders 2006)
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ReferencesReferences
AL Barabasi, R Albert, Emergence of Scaling in Random Networks, Science, 1999
P Crepey et al, Epidemic variability in complex networks, Phys. Rev. E, 2006.
Drombrowski 2007 K Dombrowski, R Curtis, SR Friedman, Injecting drug user network topologies and infectious disease tranmission: suggestive findings, Working Paper 2007
R Cohen, S Havlin, Scale-free networks are ultrasmall, Physical Review Letters, 2003.
Cohen 2003
Barabasi 1999
Crepey 2006
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Giabbanelli 2010 PJ Giabbanelli, Impact of complex network properties on routing in backbone networks, CCNet 2010 (IEEE Globecom)
Giabbanelli 2011 PJ Giabbanelli, JG Peter, Complex networks and epidemics, TSI, 2011, to appear.
PJ Giabbanelli, Self-improving immunization policies for complex networks, MSc Thesis@SFU, 2009
ReferencesReferences
Giabbanelli 2009
D Hunter, Exponential Random Graph Models for Network Data, Talk, 2006, http://www.stat.psu.edu/~dhunter/talks/ergm.pdf
Hunter 2006
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ReferencesReferencesJ Kostka et al., Word of Mouth : Rumor Dissemination in Social Networks, Lecture Notes in Computer Science, 2008.
M Kretzschmar, J Wallinga, Networks in Epidemiology, Mathematical Population Studies, 2007
Kretzschmar 2007
M Kuperman, G Abramson, Small World Effect in an Epidemiological Model, PhysicalReview Letters, 2001.
Kuperman 2001
Kostka 2008
L Li et al., Towards a Theory of Scale-FreeGraphs : Definition, Properties and Implications, Internet Mathematics, 2005.
Li 2005
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MEJ Newman, Power laws, Pareto distributions and Zipf’s law, Contemporary Physics, 2005.
Newman 2005
J Travers, S Milgram, An Experimental Study of the Small World Problem, Sociometry, 1969
ReferencesReferences
Milgram 1969
MEJ Newman, The structure and function of complex networks, SIAM Review, 2003.
Newman 2003
Milo 2004R Milo, et al., Superfamilies of Evolved and Designed Networks, Science, 2004.
AL Rosenberg, Graph Separators, with Applications, Kluwer Academic, 2001
Rosenberg 2001
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ReferencesReferences
TAB Snijders, Statistical Methods for Network Dynamics, Proceedings of the XLIII Scientific Meeting of the Italian Statistical Society, 2006
DJ Watts, SH Strogatz, Collective dynamics of 'small-world' networks, Nature, 1998
KP Smith, NA Christakis, Social networks and health, Annu Rev Social, 2008
AO Stauffer et al, A dissemination strategy for immunizing scale-free networks, Phys. Rev. E, 2006.
Smith 2008
Snijders 2006
Stauffer 2006
Watts 1998
