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Epidemiological Modeling of News and
Rumors on Twitter
Fang Jin, Edward Dougherty, Parang Saraf, Peng Mi,
Yang Cao, Naren Ramakrishnan
Virginia Tech
Aug 11, 2013
2
Outline
o Motivation
o Approach
o Implementation
o Results and Analysis
o Conclusions & Limitation
3
Motivation
Ø  Can twitter data (news and rumor) be represented by epidemic
models?
Ø  Can we gain insight into the acceptance, comprehension, and spread
of information?
v  How effectively does information spread via twitter?
v  What is the rate of information propagation?
Ø  Can we observe any differences between news spreading and rumor
spreading?
4
Twitter VS disease
o Idea spreading is an intentional act
o It is advantageous to acquire new ideas
o Idea spreading on twitter has no
(intrinsic) spatial concept
o Idea: no immune system, no “R”
Ideas spread model: SIS and SEIZ
o Both infectious
o May take time to accept
o Have transmission route
。。。
5
Epidemic Model
Susceptible
Infected
Exposed
Skeptics
Twitter accounts
Believe news / rumor, (I) post a tweet
Be exposed but not yet believe
Skeptics, do not tweet
S
E
I
Z
Disease Twitter
6
S I S
Model Description
Disease Applications:
–  Influenza
–  Common Cold
Twitter Application Reasoning:
–  An individual either believes a rumor (I),
–  or is susceptible to believing the rumor (S)
h"p://www.me.ucsb.edu/~moehlis/APC514/tutorials/tutorial_seasonal/node2.html
7
SEIZ Model Description
p
b
β
l
(1-l)
(1-p)
ρ
S E
I
Z
S-I contact rate
S-Z contact rate
Probability of (S → I)
given contact with adopters
E-I contact rate
Probability of (S → Z)
given contact with skeptics
Probability of (S → E)
given contact with skeptics
Probability of (S →E)
given contact with adopters
Total:175M
Active: 39M
Following none: 56M
No followers: 90M
Fake:0.5M
Challenges
–  Time Zone Differences
–  Users “unplugging”, they may offline
-  We have very little information: no rate, no initial compartments
-  Population == Number of Twitter Accounts
h"p://techcrunch.com/2012/07/30/analyst-­‐twi"er-­‐passed-­‐500m-­‐users-­‐in-­‐june-­‐2012-­‐140m-­‐of-­‐them-­‐in-­‐us-­‐jakarta-­‐biggest-­‐tweeHng-­‐city/	
  
9
Approach
Assumptions:
–  No vital dynamics
–  N, S(t0), E(t0), I(t0), Z(t0) are unknown
Implementation:
–  Nonlinear least squares fit, using lsqnonlin function
–  Selecting a set of parameter values, solve ordinary differential equation(ODE) system
–  Minimize the error of |I(t) – tweets(t)|
Rumor Identification
bl: effective rate of S → Z
βp: effective rate of S → I
b(1-l): effective rate of S → E via contact with Z
β(1-p): effective rate of S → E via contact with I
Є: E-I Incubation rate
ρ: E-I contact rate
RSI, a kind of flux ratio, the ratio of effects entering E to those leaving E.
By SEIZ model parameters
p
b
β
l
(1-l)
(1-p)
ρ
S E
I
Z
Є
11
¢  Obama injured. 04-23-2013
¢  Doomsday rumor. 12-21-2012
¢  Fidel Castro’s coming death. 10-15-2012
¢  Riots and shooting in Mexico. 09-05-2012
¢  Boston Marathon Explosion. 04-15-2013
¢  Pope Resignation. 02-11-2013
¢  Venezuela's refinery explosion. 08-25-2012
¢  Michelle Obama at the 2013 Oscars. 02-24-2013
Datasets
12
Boston Marathon Bombing
SIS Model SEIZ Model
SEIZ models Twitter data more accurately than SIS model, specially at the initial points.
Error = norm( I – tweets ) / norm( tweets )
13
Pope Resignation
SIS Model SEIZ Model
SEIZ models Twitter data more accurately than SIS model, specially at the initial points.
14
Doomsday
SIS Model SEIZ Model
15
SIS VS SEIZ
What can we deduce?
Ø  SEIZ models Twitter data more accurately than SIS model
Ø  SEIZ models Twitter data (via I(t) function) well
Fitting error of SIS and SEIZ models:
Boston	
   Pope	
   Amuay	
   Michelle	
   Obama	
   Doomsday	
   Castro	
   Riot	
   Average	
  
SIS	
   0.058	
   0.041	
   0.058	
   0.088	
   0.102	
   0.028	
   0.082	
   0.088	
   0.0680	
  
SEIZ	
   0.010	
   0.004	
   0.027	
   0.061	
   0.101	
   0.029	
   0.073	
   0.093	
   0.0499	
  
Rumor detection via SEIZ model
SEIZ model parameter result
28.31	
  
24.66	
  
3.58	
  
0.34	
   0.25	
   0.2	
   0.18	
   0.02	
  
0	
  
5	
  
10	
  
15	
  
20	
  
25	
  
30	
  
Boston Pope Amuay Michelle Obama Doomsday Castro Riot
RSI value for eight stories
17
Conclusion
v Twitter stories can be modeled by epidemiological models.
- SEIZ models Twitter data (via I(t) function) well
- SEIZ models Twitter data more accurately than SIS model, especially at initial points
v Generate a wealth of valuable parameters from SEIZ
v These parameters can be incorporated into a strategy to support the
identification of Twitter topics as rumor vs news.
18
Limitations
v Tweets could be suppressing rumor or news
–  A tweet could contain skeptical information
v Our study does not incorporate follower information
v May be possible to incorporate some level of population information
v More accurate models, based on more reasonable assumptions.
19

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Slides: Epidemiological Modeling of News and Rumors on Twitter

  • 1. Epidemiological Modeling of News and Rumors on Twitter Fang Jin, Edward Dougherty, Parang Saraf, Peng Mi, Yang Cao, Naren Ramakrishnan Virginia Tech Aug 11, 2013
  • 3. 3 Motivation Ø  Can twitter data (news and rumor) be represented by epidemic models? Ø  Can we gain insight into the acceptance, comprehension, and spread of information? v  How effectively does information spread via twitter? v  What is the rate of information propagation? Ø  Can we observe any differences between news spreading and rumor spreading?
  • 4. 4 Twitter VS disease o Idea spreading is an intentional act o It is advantageous to acquire new ideas o Idea spreading on twitter has no (intrinsic) spatial concept o Idea: no immune system, no “R” Ideas spread model: SIS and SEIZ o Both infectious o May take time to accept o Have transmission route 。。。
  • 5. 5 Epidemic Model Susceptible Infected Exposed Skeptics Twitter accounts Believe news / rumor, (I) post a tweet Be exposed but not yet believe Skeptics, do not tweet S E I Z Disease Twitter
  • 6. 6 S I S Model Description Disease Applications: –  Influenza –  Common Cold Twitter Application Reasoning: –  An individual either believes a rumor (I), –  or is susceptible to believing the rumor (S) h"p://www.me.ucsb.edu/~moehlis/APC514/tutorials/tutorial_seasonal/node2.html
  • 7. 7 SEIZ Model Description p b β l (1-l) (1-p) ρ S E I Z S-I contact rate S-Z contact rate Probability of (S → I) given contact with adopters E-I contact rate Probability of (S → Z) given contact with skeptics Probability of (S → E) given contact with skeptics Probability of (S →E) given contact with adopters
  • 8. Total:175M Active: 39M Following none: 56M No followers: 90M Fake:0.5M Challenges –  Time Zone Differences –  Users “unplugging”, they may offline -  We have very little information: no rate, no initial compartments -  Population == Number of Twitter Accounts h"p://techcrunch.com/2012/07/30/analyst-­‐twi"er-­‐passed-­‐500m-­‐users-­‐in-­‐june-­‐2012-­‐140m-­‐of-­‐them-­‐in-­‐us-­‐jakarta-­‐biggest-­‐tweeHng-­‐city/  
  • 9. 9 Approach Assumptions: –  No vital dynamics –  N, S(t0), E(t0), I(t0), Z(t0) are unknown Implementation: –  Nonlinear least squares fit, using lsqnonlin function –  Selecting a set of parameter values, solve ordinary differential equation(ODE) system –  Minimize the error of |I(t) – tweets(t)|
  • 10. Rumor Identification bl: effective rate of S → Z βp: effective rate of S → I b(1-l): effective rate of S → E via contact with Z β(1-p): effective rate of S → E via contact with I Є: E-I Incubation rate ρ: E-I contact rate RSI, a kind of flux ratio, the ratio of effects entering E to those leaving E. By SEIZ model parameters p b β l (1-l) (1-p) ρ S E I Z Є
  • 11. 11 ¢  Obama injured. 04-23-2013 ¢  Doomsday rumor. 12-21-2012 ¢  Fidel Castro’s coming death. 10-15-2012 ¢  Riots and shooting in Mexico. 09-05-2012 ¢  Boston Marathon Explosion. 04-15-2013 ¢  Pope Resignation. 02-11-2013 ¢  Venezuela's refinery explosion. 08-25-2012 ¢  Michelle Obama at the 2013 Oscars. 02-24-2013 Datasets
  • 12. 12 Boston Marathon Bombing SIS Model SEIZ Model SEIZ models Twitter data more accurately than SIS model, specially at the initial points. Error = norm( I – tweets ) / norm( tweets )
  • 13. 13 Pope Resignation SIS Model SEIZ Model SEIZ models Twitter data more accurately than SIS model, specially at the initial points.
  • 15. 15 SIS VS SEIZ What can we deduce? Ø  SEIZ models Twitter data more accurately than SIS model Ø  SEIZ models Twitter data (via I(t) function) well Fitting error of SIS and SEIZ models: Boston   Pope   Amuay   Michelle   Obama   Doomsday   Castro   Riot   Average   SIS   0.058   0.041   0.058   0.088   0.102   0.028   0.082   0.088   0.0680   SEIZ   0.010   0.004   0.027   0.061   0.101   0.029   0.073   0.093   0.0499  
  • 16. Rumor detection via SEIZ model SEIZ model parameter result 28.31   24.66   3.58   0.34   0.25   0.2   0.18   0.02   0   5   10   15   20   25   30   Boston Pope Amuay Michelle Obama Doomsday Castro Riot RSI value for eight stories
  • 17. 17 Conclusion v Twitter stories can be modeled by epidemiological models. - SEIZ models Twitter data (via I(t) function) well - SEIZ models Twitter data more accurately than SIS model, especially at initial points v Generate a wealth of valuable parameters from SEIZ v These parameters can be incorporated into a strategy to support the identification of Twitter topics as rumor vs news.
  • 18. 18 Limitations v Tweets could be suppressing rumor or news –  A tweet could contain skeptical information v Our study does not incorporate follower information v May be possible to incorporate some level of population information v More accurate models, based on more reasonable assumptions.
  • 19. 19