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 S-GEM Suceptible Infected

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, R 0 S-GEM

16. The SIS-model S-GEM

17. The SIS-model S-GEM

18. 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

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

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

21. Clustering/transitivity S-GEM

22. Clustering/transitivity S-GEM

23. Clustering/transitivity Suceptible Infectious S-GEM

24. Variation in number of contacts S-GEM

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

28. Assortative Interaction S-GEM

29. Struktural effects Variation in contacts Clustring assortativity Lower epidemic treshold Smaller outbreaks Slower outbreaks 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 Kansas Massachusetts Pamela Five persons 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

38. 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

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