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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 l.jpg

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 l.jpg
Stockholm Group for Epidemic Modelling Diseases, S-GEM

Johan Giesecke SMI/KI Åkes Svensson SMI/SU Fredrik Liljeros SU/KI

S-GEM


Why model epidemics l.jpg
Why model epidemics? Diseases

  • 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 l.jpg
Outline Diseases

  • Traditional Models

  • Networks

  • Empirical Network Studies

S-GEM


Key concepts l.jpg
Key Concepts Diseases

  • Variation in number of contacts

  • Assortative interaction

  • Clustering/Transitivity

  • Small World Network

S-GEM


Epidemic models l.jpg
Epidemic models Diseases

Deterministic models

Stochastic models

Agent-based models (Micro simulation models)

S-GEM



Deterministic models l.jpg
Deterministic Models Diseases

S-GEM


A very simplified example l.jpg
A very simplified example Diseases

Suceptible

Infected

S-GEM



Global saturation l.jpg
Global saturation Diseases

S-GEM



Slide13 l.jpg

We have to ad the number of s Diseasesusceptible into the model (K-I)

S-GEM


It is possible to study important properties of deterministic models analytically l.jpg
It is possible to study important properties of deterministic models analytically

S-GEM


The basic reproduction rate r 0 l.jpg
The Basic reproduction rate, deterministic models analyticallyR0

S-GEM


The sis model l.jpg
The SIS-model deterministic models analytically

S-GEM


The sis model17 l.jpg
The SIS-model deterministic models analytically

S-GEM


It is possible to let a deterministic model capture ma n y relevant properties l.jpg
It is possible to let a deterministic model capture ma deterministic models analyticallynyrelevant 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



Erd s r nyi network 1960 l.jpg
Erdös-Rényi deterministic modelsnetwork (1960)

Pál Erdös(1913-1996)

S-GEM


Clustering transitivity l.jpg
Clustering/transitivity deterministic models

S-GEM


Clustering transitivity22 l.jpg
Clustering/transitivity deterministic models

S-GEM


Clustering transitivity23 l.jpg

Suceptible deterministic models

Infectious

Clustering/transitivity

S-GEM


Variation in number of contacts l.jpg
Variation in number of contacts deterministic models

S-GEM



Slide26 l.jpg

S-GEM deterministic models


Slide27 l.jpg

S-GEM deterministic models


Assortative interaction l.jpg
Assortative Interaction deterministic models

S-GEM


Struktural effects l.jpg
Struktural effects deterministic models

Variation in contacts

Lower epidemic treshold

Smaller outbreaks

assortativity

Slower outbreaks

Clustring

S-GEM


Why care about social networks l.jpg
Why care about social networks? deterministic models

S-GEM



Collecting network data l.jpg
Collecting network data networks?

S-GEM



Milgrams study l.jpg
Milgrams Study networks?

Nebraska

Pamela

Five persons

Massachusetts

Kansas

S-GEM


But we know that social networks are clustred l.jpg
But we know that social networks are clustred networks?

Should not the distance between randomly selected individuals be long?

S-GEM


The small world effect l.jpg
The Small-world effect networks?

?

S-GEM


Slide37 l.jpg

S-GEM networks?


Watts strogatz model l.jpg

(from networks?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 l.jpg
Swedish Smallpox Model networks?

S-GEM


Take home messages l.jpg
Take Home messages networks?

  • Variation in number of contacts

  • Assortative interaction

  • Clustering/Transitivity

  • Small World Network

S-GEM