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
The Importance of Different Social Networks for Infectious Diseases Fredrik Liljeros Stockholm University Karolinska institutet Supported by the Swedish.
Mar 27, 2015
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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
Johan Giesecke SMI/KI Åkes Svensson SMI/SU Fredrik Liljeros SU/KI
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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?
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Outline
• Traditional Models
• Networks
• Empirical Network Studies
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Key Concepts
• Variation in number of contacts• Assortative interaction• Clustering/Transitivity• Small World Network
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Epidemic models
Deterministic models
Stochastic models
Agent-based models (Micro simulation models)
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A model should be as simple as possibly (But not to simple)
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Deterministic Models
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)(Ifdt
dI
I of functionf(I)
infectedI
A very simplified example
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Suceptible
Infected
A simple differential equation-model
Ikdt
dI
50 100 1500
20
40
6060
0
Infected
Model
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Global saturation
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Our model is to simple capture global saturation
100 200 300 400 5000
50
100100
0
Infected
Model
5001 Time
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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
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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
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The Basic reproduction rate, R0
IKIkdt
dI
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The SIS-model
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The SIS-model
IbIKIkdt
dI
100 200 300 400 5000
50
100100
0
Infected
Model
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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
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What are the implicit ”network” assumptions in deterministic models
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Erdös-Rényi network (1960)
Pál ErdösPál Erdös (1913-1996)
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Clustering/transitivity
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Clustering/transitivity
5 10 15 200
50
100100
0
Infected
Model
201 Time
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Clustering/transitivity
Suceptible
Infectious
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Variation in number of contacts
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What do variation in number of contacts have
on R0?
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Assortative Interaction
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Struktural effects
Variation in contacts
Clustring
assortativity
Lower epidemic treshold
Smaller outbreaks
Slower outbreaks
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Why care about social networks?
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What do we know about structural properties of social
networks?
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Collecting network data
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We can not use random samples
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Milgrams Study
Nebraska
Kansas
Massachusetts
Pamela
Five persons
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But we know that social networks are clustred
Should not the distance between randomly selected
individuals be long?
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?
The Small-world effect
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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
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Swedish Smallpox Model
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Take Home messages
• Variation in number of contacts• Assortative interaction• Clustering/Transitivity• Small World Network
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