1.
Disease spreading &
control in temporal
networks
Petter Holme, Umeå University & SKKU
in KAIST Dec 14, 2010
with Luis EC Rocha, Sungmin Lee, Fredrik Liljeros

2.
Temporal structures
6,7,9
B
C
1,2,4,5
11
10,15
A
time

3.
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?

4.
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

5.
Avg. max speed vs. 0-
model

6.
SI model, vs ρ = 1

7.
Outbreak diversity

8.
Threshold in
transmissivity

9.
Threshold in duration

10.
Contact seq vs other
models

11.
HIV, two-stage model

12.
A society-wide context

13.
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

14.
Temporal vaccination

15.
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 Prostitution
ΔS(%) Weight
Recent
ΔS(%)
ΔS(%)
ΔS(%)

16.
Relative effic., SIR
Δs(%)
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

17.
Parameter dep. rel. effic.

18.
Explanatory model

19.
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

20.
deadline March 10
March 28 – April 20
nordita.org/network2011