Disease spreading & control in temporal

networks

Petter Holme, Umeå University & SKKUin KAIST Dec 14, 2010

with Luis EC Rocha, Sungmin Lee, Fredrik Liljeros

Temporal structures

6,7,9

BC

1,2,4,511

10,15

Atime

What we are interested in

• How does temporal structures in empirical networks affect disease spreading?

• Can we exploit these structures to slow down disease spreading?

Our datasets

• E-mail: 3,188 nodes, 309,125 contacts over 83 days

• Internet dating: 29,341 nodes, 536,276 contacts over 512 d

• Hospital: 295,107 nodes, 64,625,283 contacts over 8,521 d

• Prostitution: 16,730 nodes, 50,632 contacts

Avg. max speed vs. 0-model

SI model, vs ρ = 1

Outbreak diversity

Threshold in transmissivity

Threshold in duration

Contact seq vs other models

HIV, two-stage model

A society-wide context

Summary

• Temporal correlations speed up the outbreaks on a short time scale & slows it down on a longer time scale

• Temporal effects create distinct and comparatively high epidemic thresholds

• HIV can not spread in the prostitution data alone and probably does not serve as a reservoir of HIV in a society-wide

Temporal vaccination

Relative effic., worst case

f (%)

f (%) f (%)

20

10

0

–10

–20

2

0

–2

–4

0 20 40 60 80 0 20 40 60 80

1

0

–1

–2

2

–3

20

10

0

–10

–20

0 20 40 60 80 0 20 40 60 80

f (%)

D E-mailC Hospital

B Internet datingA ProstitutionΔS

(%

)Weight

Recent

ΔS (

%)

ΔS (

%)

ΔS (

%)

Relative effic., SIRΔs

(%

)

0.2

0.1

0

–0.1

–0.2

–0.3

Δs (

%)

10

5

0

–5

–10

–15

f (%)

0 20 40 60 80 0 20 40 60 80

f (%)

f (%)

0 20 40 60 80 0 20 40 60 80

f (%)

40

20

0

–20

10

5

0

–5

–10

–15

Δs (

%)

Δs (

%)

B Internet dating

C Hospital D E-mail

A Prostitution Weight

Recent

Parameter dep. rel. effic.

Explanatory model

Summary

• Temporal correlations do affect disease spreading and can be exploited in targeted vaccination

• The best vaccination strategy depends on the type of temporal structure

• Until more structural information is available, we recommend the strategy Recent

deadline March 10March 28 – April 20

nordita.org/network2011