the importance of different social networks for infectious diseases fredrik liljeros stockholm...

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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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Page 1: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

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

Page 2: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Stockholm Group for Epidemic Modelling, S-GEM

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

S-GEM

Page 3: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

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

Page 4: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Outline

• Traditional Models

• Networks

• Empirical Network Studies

S-GEM

Page 5: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Key Concepts

• Variation in number of contacts• Assortative interaction• Clustering/Transitivity• Small World Network

S-GEM

Page 6: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Epidemic models

Deterministic models

Stochastic models

Agent-based models (Micro simulation models)

S-GEM

Page 7: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

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

S-GEM

Page 8: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Deterministic Models

S-GEM

)(Ifdt

dI

I of functionf(I)

infectedI

Page 9: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

A very simplified example

S-GEM

Suceptible

Infected

Page 10: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

A simple differential equation-model

Ikdt

dI

50 100 1500

20

40

6060

0

Infected

Model

1701 TimeS-GEM

Page 11: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Global saturation

S-GEM

Page 12: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Our model is to simple capture global saturation

100 200 300 400 5000

50

100100

0

Infected

Model

5001 Time

S-GEM

Page 13: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

100 200 300 400 5000

50

100100

0

Infected

Model

5001 Time

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

IKIkdt

dI

constantk

Infected I

population the of SizeK

S-GEM

Page 14: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

It is possible to study important properties of deterministic models

analytically

IKIk 0

100 200 300 400 5000

50

100100

0

Infected

Model

5001 Time

S-GEM

Page 15: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

The Basic reproduction rate, R0

IKIkdt

dI

S-GEM

Page 16: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

The SIS-model

S-GEM

Page 17: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

The SIS-model

IbIKIkdt

dI

100 200 300 400 5000

50

100100

0

Infected

Model

5001 TimeS-GEM

Page 18: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

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

Page 19: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

What are the implicit ”network” assumptions in deterministic models

S-GEM

Page 20: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Erdös-Rényi network (1960)

Pál ErdösPál Erdös (1913-1996)

S-GEM

Page 21: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Clustering/transitivity

S-GEM

Page 22: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Clustering/transitivity

5 10 15 200

50

100100

0

Infected

Model

201 Time

S-GEM

Page 23: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Clustering/transitivity

Suceptible

Infectious

S-GEM

Page 24: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Variation in number of contacts

S-GEM

Page 25: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

What do variation in number of contacts have

on R0?

S-GEM

Page 26: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

S-GEM

Page 27: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

S-GEM

Page 28: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Assortative Interaction

S-GEM

Page 29: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Struktural effects

Variation in contacts

Clustring

assortativity

Lower epidemic treshold

Smaller outbreaks

Slower outbreaks

S-GEM

Page 30: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Why care about social networks?

S-GEM

Page 31: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

What do we know about structural properties of social

networks?

S-GEM

Page 32: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Collecting network data

S-GEM

Page 33: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

We can not use random samples

S-GEM

Page 34: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Milgrams Study

Nebraska

Kansas

Massachusetts

Pamela

Five persons

S-GEM

Page 35: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

But we know that social networks are clustred

Should not the distance between randomly selected

individuals be long?

S-GEM

Page 36: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

?

The Small-world effect

S-GEM

Page 37: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

S-GEM

Page 39: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Ongoing Reserch and Verbal preliminary results

S-GEM

Page 40: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Swedish Smallpox Model

S-GEM

Page 41: The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish

Take Home messages

• Variation in number of contacts• Assortative interaction• Clustering/Transitivity• Small World Network

S-GEM