The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish.

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Presentation transcript:

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 S-GEM Suceptible Infected

A simple differential equation- model S-GEM

Global saturation S-GEM

Our model is to simple capture 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 Basic reproduction rate, R 0 S-GEM

The SIS-model S-GEM

The SIS-model S-GEM

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

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

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

Clustering/transitivity S-GEM

Clustering/transitivity S-GEM

Clustering/transitivity Suceptible Infectious S-GEM

Variation in number of contacts S-GEM

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

Assortative Interaction S-GEM

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

Why care about social networks? S-GEM

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

Collecting network data S-GEM

We can not use random samples S-GEM

Milgrams Study Nebraska Kansas Massachusetts Pamela Five persons 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

C(p) : clustering coeff. L(p) : average path length (Watts and Strogatz, Nature 393, 440 (1998)) Watts-Strogatz Model (from &

Ongoing Reserch and Verbal preliminary results S-GEM

Swedish Smallpox Model S-GEM

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