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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

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Stockholm Group for Epidemic Modelling, S-GEM Johan Giesecke SMI/KI Åkes Svensson SMI/SU Fredrik Liljeros SU/KI S-GEM

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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

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Outline Traditional Models Networks Empirical Network Studies S-GEM

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Key Concepts Variation in number of contacts Assortative interaction Clustering/Transitivity Small World Network S-GEM

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Epidemic models Deterministic models Stochastic models Agent-based models (Micro simulation models) S-GEM

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A model should be as simple as possibly (But not to simple) S-GEM

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Deterministic Models S-GEM

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A very simplified example S-GEM Suceptible Infected

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A simple differential equation- model S-GEM

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Global saturation S-GEM

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Our model is to simple capture global saturation S-GEM

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We have to ad the number of susceptible into the model (K-I) S-GEM

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It is possible to study important properties of deterministic models analytically S-GEM

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The Basic reproduction rate, R 0 S-GEM

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The SIS-model S-GEM

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The SIS-model S-GEM

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It is possible to let a deterministic model capture many relevant 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

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What are the implicit network assumptions in deterministic models S-GEM

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Erdös-Rényi network (1960) Pál Erdös Pál Erdös (1913-1996) S-GEM

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Clustering/transitivity S-GEM

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Clustering/transitivity S-GEM

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Clustering/transitivity Suceptible Infectious S-GEM

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Variation in number of contacts S-GEM

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What do variation in number of contacts have on R 0 ? S-GEM

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Assortative Interaction S-GEM

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Struktural effects Variation in contacts Clustring assortativity Lower epidemic treshold Smaller outbreaks Slower outbreaks S-GEM

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Why care about social networks? S-GEM

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What do we know about structural properties of social networks? S-GEM

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Collecting network data S-GEM

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We can not use random samples S-GEM

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Milgrams Study Nebraska Kansas Massachusetts Pamela Five persons S-GEM

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But we know that social networks are clustred Should not the distance between randomly selected individuals be long? S-GEM

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? The Small-world effect S-GEM

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C(p) : clustering coeff. L(p) : average path length (Watts and Strogatz, Nature 393, 440 (1998)) Watts-Strogatz Model (from http://www.aip.org/aip/corporate/2000/watts.htmhttp://www.aip.org/aip/corporate/2000/watts.htm & http://tam.cornell.edu/Strogatz.html)http://tam.cornell.edu/Strogatz.html

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Ongoing Reserch and Verbal preliminary results S-GEM

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Swedish Smallpox Model S-GEM

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Take Home messages Variation in number of contacts Assortative interaction Clustering/Transitivity Small World Network S-GEM

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