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The Importance of Different Social Networks for Infectious Diseases

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

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  1. 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

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

  3. 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

  4. Outline • Traditional Models • Networks • Empirical Network Studies S-GEM

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

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

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

  8. Deterministic Models S-GEM

  9. A very simplified example Suceptible Infected S-GEM

  10. A simple differential equation-model S-GEM

  11. Global saturation S-GEM

  12. Our model is to simple capture global saturation S-GEM

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

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

  15. The Basic reproduction rate, R0 S-GEM

  16. The SIS-model S-GEM

  17. The SIS-model S-GEM

  18. 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

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

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

  21. Clustering/transitivity S-GEM

  22. Clustering/transitivity S-GEM

  23. Suceptible Infectious Clustering/transitivity S-GEM

  24. Variation in number of contacts S-GEM

  25. What do variation in number of contacts have on R0? S-GEM

  26. S-GEM

  27. S-GEM

  28. Assortative Interaction S-GEM

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

  30. Why care about social networks? S-GEM

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

  32. Collecting network data S-GEM

  33. We can not use random samples S-GEM

  34. Milgrams Study Nebraska Pamela Five persons Massachusetts Kansas S-GEM

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

  36. The Small-world effect ? S-GEM

  37. S-GEM

  38. (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))

  39. Ongoing Reserch and Verbal preliminary results S-GEM

  40. Swedish Smallpox Model S-GEM

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

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