What  Stops  Social  Epidemics?  

Greg  Ver  Steeg  

Rumi  Ghosh  &  Kris:na  Lerman  

USC  Informa:on  Sciences  Ins:tute    

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Informa:on,  viruses,  etc.  spread  from    node  to  node  on  a  network  

Transmissibility,  λ  =  Probability  to  infect  your  neighbor  

Infected  

Not  Infected  

•  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  

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What  is  an  epidemic?  

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Frac:on  of  nodes  infected  

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Transmissibility,  λ  

Epidemic  threshold  predicted  for  many  cascade  models    0  

On  an  infinite  graph,  an  epidemic  is  any  process  that  spreads  to  a  frac:on  of  all  the  nodes  

Social  news:  

Distribu:on  of  cascade  size  on  -­‐-­‐-­‐-­‐-­‐-­‐  

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#nodes  ∼300k  

Most  cascades  less  than  1%  of  total  network  size!  

A  small  frac:on  is  s:ll  a  frac:on,  though,  right?  

Why  are  these  cascades  so  small?  

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Standard  model  of  epidemic  growth  

(Heterogenous  mean  field  theory,  SIR  model,  same  degree  distribu:on  as  Digg)  

Transmissibility  of  almost  all  Digg  stories  fall  within  width  of  this  line?!  

λ,  Transmissibility  

Most  cascades  fall  in  this  range  

Maybe  graph  structure  is  responsible?  

   clustering  reduces  epidemic  threshold  and  cascade  size,              but  not  enough!  

transmissibility λ

epidemic  threshold  

←  Mean  field  predic:on  (same  degree  dist.)  

 ←  Simulated  cascades  on  a  random  graph  with  same  degree  dist.  

   Simulated  cascades  on  the  observed  Digg  graph  

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What  about  the  spreading  mechanism?  

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Independent  Cascade  Model  implicit  in  many  epidemic  models  

Infected  

Not  Infected  

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How  important  are  repeat  exposures?  

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More  than  half  exposed  to  a  story  more  than  once!  

How  do  people  respond  to  repeated  exposure?  

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Not  much.  

We  have  similar  results  for  TwiVer  -­‐-­‐-­‐-­‐-­‐-­‐-­‐  

Also  noted  by  Romero,  et  al,  WWW  2011  

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)  

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Weak  response  to  repeated  exposure  

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Take  effect  of  repeat  exposure  into  account:  

Actual  Digg  cascades  

Result  of  simula:ons  

λ*  

Epidemic  threshold  unchanged  

λ*,  Transmissibility  

Also  explains  dynamics  

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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)  

Transmissibility:  the  percentage  of  new  people  exposed  who  end  up  infected/vo:ng  

15  Approximate  :me  of  story  promo:on  to  front  page  

Structure  +  Behavior  

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Accurate  model    

of  behavior  

Independent  cascade  model  

=+

+ =

+ =

absolutelytrue

msaleem

upickjaybol

noupsell

anderzole

vtbarrera

badwithcomputer

xdvx

Bukowsky

1KrazyKorean

kevinrose

skored

IvanBlouiebaur

AmyVernon

oboy

Burento

MrBabyMan TalSiach

absolutelytrue

msaleem

upickjaybol

noupsell

anderzole

vtbarrera

badwithcomputer

xdvx

Bukowsky

1KrazyKorean

kevinrose

skored

IvanBlouiebaur

AmyVernon

oboy

Burento

MrBabyMan TalSiach

Accurate  model    

of  behavior  

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  

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Decay  of  novelty  

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Weak  response  to  repeated  exposure  

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Standard  model  of  epidemic  growth  

(Heterogenous  mean  field  theory,  SIR  model,  same  degree  distribu:on  as  Digg)  

λ*  

What  is  an  epidemic  on  a  finite  graph?  

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Infected  

Not  Infected  

We  would  call  this  an  epidemic,  right?  

And  now?  

Epidemics  saturate  the  graph  

What  is  an  epidemic  on  a  finite  graph?  

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Same  number  of  red  dots  

Epidemics  saturate  the  graph  

Sub-­‐epidemic  cascade  size  

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Reproduc:ve  number,  R0  is  the  average  number  of  new  spreaders  reached  by  each  spreader.    

R0  <  1    ⇒    No  Epidemic  

R0 = �k�λ

Average  number  of  friends  

Transmissibility  

1�average degree0

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200

Λ, transmissibility

Cascadesize

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Transmissibility  of  almost  all  Digg  stories  fall  within  width  of  this  line?!  

Sub-epidemic cascade size = 1 +1

1−R0

Satura:on  on  a  real  graph  

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