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

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

)(Ifdt

dI

I of functionf(I)

infectedI

A very simplified example

S-GEM

Suceptible

Infected

A simple differential equation-model

Ikdt

dI

50 100 1500

20

40

6060

0

Infected

Model

1701 TimeS-GEM

Global saturation

S-GEM

Our model is to simple capture global saturation

100 200 300 400 5000

50

100100

0

Infected

Model

5001 Time

S-GEM

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

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

The Basic reproduction rate, R0

IKIkdt

dI

S-GEM

The SIS-model

S-GEM

The SIS-model

IbIKIkdt

dI

100 200 300 400 5000

50

100100

0

Infected

Model

5001 TimeS-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 ErdösPál Erdös (1913-1996)

S-GEM

Clustering/transitivity

S-GEM

Clustering/transitivity

5 10 15 200

50

100100

0

Infected

Model

201 Time

S-GEM

Clustering/transitivity

Suceptible

Infectious

S-GEM

Variation in number of contacts

S-GEM

What do variation in number of contacts have

on R0?

S-GEM

S-GEM

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

S-GEM

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.htm & http://tam.cornell.edu/Strogatz.html)

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