Look for my talk on videolectures.net

1. What
Stops
Social
Epidemics?
Greg
Ver
Steeg
Rumi
Ghosh
&
Kris:na
Lerman
USC
Informa:on
Sciences
Ins:tute

2. Informa:on,
viruses,
etc.
spread
from
node
to
node
on
a
network
Infected
Not
Infected
Transmissibility,
λ
=
Probability
to
infect
your
neighbor
2

3. • What
is
an
epidemic?
We
observe
many
cascades
that:
–
Grow
quickly
ini:ally
–
But
remain
too
small
for
standard
(viral)
epidemic
models
• Informa:on
cascades
differ:
– Response
to
repeated
exposure
is
important
on
Digg
(and
TwiVer)
– Dras:cally
alters
predic:ons
about
size
of
epidemics
3

4. What
is
an
epidemic?
On
an
infinite
graph,
an
epidemic
is
any
process
that
spreads
to
a
frac:on
of
all
the
nodes
1
Frac:on
of
nodes
infected
Epidemic
threshold
predicted
for
many
0
cascade
models
Transmissibility,
λ
4

5. Social
news:

6. Distribu:on
of
cascade
size
on
-­‐-­‐-­‐-­‐-­‐-­‐
#nodes
∼300k
Most
cascades
less
than
1%
of
total
network
size!
A
small
frac:on
is
s:ll
a
frac:on,
though,
right?
6

7. Why
are
these
cascades
so
small?
Standard
model
of
epidemic
growth
Most
cascades
fall
in
(Heterogenous
this
range
mean
field
theory,
SIR
model,
same
degree
distribu:on
as
Digg)
λ,
Transmissibility
Transmissibility
of
almost
all
Digg
stories
7
fall
within
width
of
this
line?!

8. Maybe
graph
structure
is
responsible?
←
Mean
field
predic:on
(same
degree
dist.)
←
Simulated
cascades
on
a
random
graph
with
same
degree
dist.
epidemic
threshold
Simulated
cascades
on
the
observed
Digg
graph
transmissibility λ

clustering
reduces
epidemic
threshold
and
cascade
size,
but
not
enough!
8

9. What
about
the
spreading
mechanism?
Infected
Not
Infected
?
Independent
Cascade
Model
implicit
in
many
epidemic
models
9

10. How
important
are
repeat
exposures?
More
than
half
exposed
to
a
story
more
than
once!
10

11. How
do
people
respond
to
repeated
exposure?
Not
much.
We
have
similar
results
for
TwiVer
-­‐-­‐-­‐-­‐-­‐-­‐-­‐
Also
noted
by
Romero,
et
al,
WWW
2011
11

12. Big
consequences
for
epidemic
growth
• Most
people
are
exposed
to
a
story
more
than
once
• Repeated
exposures
have
liVle
effect
• Growth
of
epidemics
is
severely
curtailed
(especially
compared
to
Ind.
Cascade
Model)
12

13. Weak
response
to
repeated
exposure
Take
effect
of
repeat
exposure
into
account:
Actual
Digg
Epidemic
cascades
threshold
unchanged
Result
of
simula:ons
λ*,
Tλ*
ransmissibility
13

14. Also
explains
dynamics
Number
of
new
people
exposed
to
a
story
(who
don’t
vote
on
it)
Number
of
new
people
exposed
to
a
story
(who
do
vote)
14

15. Transmissibility:
the
percentage
of
new
people
exposed
who
end
up
infected/vo:ng
Approximate
:me
of
story
15
promo:on
to
front
page

16. Structure
+
Behavior
=
Accurate
+ model
of
behavior
MrBabyMan TalSiach
kevinrose
xdvx
Independent
+ =
AmyVernon
absolutelytrue
oboy
msaleem
cascade
Bukowsky
skored
badwithcomputer
Burento
model
anderzole
upick
jaybol
louiebaur IvanB
vtbarrera
1KrazyKorean noupsell
MrBabyMan TalSiach
kevinrose
xdvx
+ Accurate
=
AmyVernon
absolutelytrue
oboy
msaleem
model
Bukowsky
skored
badwithcomputer
Burento
of
behavior
anderzole
upick
jaybol
16
louiebaur IvanB
vtbarrera
1KrazyKorean noupsell

17. Summary
• Informa:on
spread
≠
Disease
spread
• Big
consequences
for
epidemics
• Repeat
exposures
are
important
on
Digg
and
TwiVer
• On
Digg,
people
don’t
respond
to
repeat
exposure
– Epidemic
threshold
unchanged
– Dras:cally
reduces
size
of
epidemics
17

18. Decay
of
novelty
18

19. Weak
response
to
repeated
exposure
Standard
model
of
epidemic
growth
(Heterogenous
mean
field
theory,
SIR
model,
same
degree
distribu:on
as
Digg)
λ*
19

20. What
is
an
epidemic
on
a
finite
graph?
Infected
Not
Infected
We
would
call
this
an
epidemic,
right?
And
now?
Epidemics
saturate
the
graph
20

21. What
is
an
epidemic
on
a
finite
graph?
Same
number
of
red
dots
Epidemics
saturate
the
graph
21

22. Sub-­‐epidemic
cascade
size
Reproduc:ve
number,
R0
is
the
average
number
of
new
spreaders
reached
by
each
spreader.
R0
<
1
No
Epidemic
R0 = kλ
Average
number
of
Transmissibility
friends
22

23. 1
Sub-epidemic cascade size = 1 +
1 − R0
200
150
Cascade size 100
50
0
1average degree
Λ, transmissibility
Transmissibility
of
almost
all
Digg
stories
fall
within
width
of
this
line?!
23

24. Satura:on
on
a
real
graph
24

25. 25

26. 26