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The Importance of Different Social Networks for Infectious Diseases. Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish Institute for Public Health and The Swedish Emergency Management Agency. S-GEM. Stockholm Group for Epidemic Modelling , S-GEM.
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The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish Institute for Public Health and The Swedish Emergency Management Agency S-GEM
Stockholm Group for Epidemic Modelling, S-GEM Johan Giesecke SMI/KI Åkes Svensson SMI/SU Fredrik Liljeros SU/KI S-GEM
Why model epidemics? • Will there be an outbreak? • How many will be infected? • The speed of the outbreak? • How can we best limit the effects of an outbreak • How many must be vaccinated? • Who should be vaccinated? S-GEM
Outline • Traditional Models • Networks • Empirical Network Studies S-GEM
Key Concepts • Variation in number of contacts • Assortative interaction • Clustering/Transitivity • Small World Network S-GEM
Epidemic models Deterministic models Stochastic models Agent-based models (Micro simulation models) S-GEM
A model should be as simple as possibly (But not to simple) S-GEM
Deterministic Models S-GEM
A very simplified example Suceptible Infected S-GEM
Global saturation S-GEM
We have to ad the number of susceptible into the model (K-I) S-GEM
It is possible to study important properties of deterministic models analytically S-GEM
The SIS-model S-GEM
The SIS-model S-GEM
It is possible to let a deterministic model capture manyrelevant properties • Individuals may become immune • Individuals may die • New individuals may be borned • Individuals may belong to different groups with different type of behavior S-GEM
What are the implicit ”network” assumptions in deterministic models S-GEM
Erdös-Rényi network (1960) Pál Erdös(1913-1996) S-GEM
Clustering/transitivity S-GEM
Clustering/transitivity S-GEM
Suceptible Infectious Clustering/transitivity S-GEM
Assortative Interaction S-GEM
Struktural effects Variation in contacts Lower epidemic treshold Smaller outbreaks assortativity Slower outbreaks Clustring S-GEM
What do we know about structural properties of social networks? S-GEM
Collecting network data S-GEM
Milgrams Study Nebraska Pamela Five persons Massachusetts Kansas S-GEM
But we know that social networks are clustred Should not the distance between randomly selected individuals be long? S-GEM
The Small-world effect ? S-GEM
(from http://www.aip.org/aip/corporate/2000/watts.htm & http://tam.cornell.edu/Strogatz.html) Watts-Strogatz Model C(p) : clustering coeff. L(p) : average path length (Watts and Strogatz, Nature 393, 440 (1998))
Swedish Smallpox Model S-GEM
Take Home messages • Variation in number of contacts • Assortative interaction • Clustering/Transitivity • Small World Network S-GEM