the viral adoption of web applications: twitter’s story · the viral adoption of information...

The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez

The Viral Adoption of Web Applications: Twitter’s Story

1Jameson TooleMarta Gonzalez The Viral Adoption of Web Applications: Twitter’s Story

Tuesday, June 21, 2011


Outline

The Viral Adoption of Information Technologies: Twitter’s Story

Background

Descriptive Statistics

Modeling Simulation

2



BackgroundEpidemic Models

Networks Diffusion of Innovations

SI, SIR, etc. Percolation, SI Threshold, Bass Model

The Viral Adoption of Information Technologies: Twitter’s Story3



Questions

The Viral Adoption of Information Technologies: Twitter’s Story4

What roll does geography play in diffusion?

What is a more accurate way to incorporate mass media?



DataNumber Time Place

3.5 million March 2006 - August 2009

City

5

*Meeyoung Cha - KAIST


The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez 6

Space: Aggregate Dynamics

May 06 Nov 06 Jun 07 Dec 07 Jul 08 Jan 09 Aug 090

0.2

0.4

0.6

0.8

1U

sers

/ Vo

lum

eNew users, search and news volume per week

AdoptionNewsGoogle Search


0.2

0.4

0.6

0.8

1

Use

rs /

Volu

me

Cumulative new users, search and news volume

AdoptionNewsGoogle Search



Time: Media Influence

7



Space: Local Dynamics

8


100

200

300

400

500

600

User

s

New Users per week


2000

4000

6000

8000

10000

User

s

Cumulative users

Denver, COAnn Arbor, MIArlington, VA

Denver, COAnn Arbor, MIArlington, VA



Time: Critical Mass


The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez 10Jameson TooleMarta Gonzalez The Viral Adoption of Information Technologies: Twitter’s Story

Time: Types



Modeling Adoption: Analytically

11Jameson TooleMarta Gonzalez The Viral Adoption of Information Technologies: Twitter’s Story

SI Model Bass Model

Logistic growthSeeding

External influence

VI. SI-M MODEL

dS

dt= −βSI − γM (8)

dI

dt= +βSI + γM (9)

dM

dt= αI · (1 + cos(ωt)) (10)

VII. SI-M MODEL

dS

dt= −βSI (11)

dI

dt= +βSI (12)

VIII. CONCLUSION

[1] D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds, Proceedings of the National

Academy of Sciences of the United States of America 102, 11157 (August 2005), ISSN 0027-

8424, http://dx.doi.org/10.1073/pnas.0501226102.

[2] P. S. Dodds and D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN

00225193, http://dx.doi.org/10.1016/j.jtbi.2004.09.006.

[3] C. Moore and M. E. J. Newman, Physical Review E 61, 5678 (May 2000), http://dx.doi.

org/10.1103/PhysRevE.61.5678.

[4] M. E. J. Newman, I. Jensen, and R. M. Ziff, Physical Review E 65, 021904+ (Jan 2002),

http://dx.doi.org/10.1103/PhysRevE.65.021904.

[5] B. Karrer and M. E. J. Newman, Physical Review E 82, 016101+ (Jul 2010), http://dx.

doi.org/10.1103/PhysRevE.82.016101.

[6] The online version of Richard Dawkins’ terminology describing ideas and beliefs that spread

from person to person.

25

VI. SI-M MODEL

dS


dI

dt= +βSI + γM (9)

dM

dt= αI · (1 + cos(ωt)) (10)

VII. SI-M MODEL

dS

dt= −βSI (11)

dI

dt= +βSI (12)

I(t) =1

1 + e−βt(13)

VIII. CONCLUSION







org/10.1103/PhysRevE.61.5678.

[4] M. E. J. Newman, I. Jensen, and R. M. Ziff, Physical Review E 65, 021904+ (Jan 2002),

http://dx.doi.org/10.1103/PhysRevE.65.021904.

[5] B. Karrer and M. E. J. Newman, Physical Review E 82, 016101+ (Jul 2010), http://dx.

doi.org/10.1103/PhysRevE.82.016101.

25

VI. SI-M MODEL

dS


dI

dt= +βSI + γM (9)

dM

dt= αI · (1 + cos(ωt)) (10)

VII. SI-M MODEL

dS

dt= −βSI (11)

dI

dt= +βSI (12)

I(t) =1

1 + e−βt(13)

VIII. BASS MODEL

I �(t)

1− I(t)= α + βI(t) (14)

IX. CONCLUSION







org/10.1103/PhysRevE.61.5678.

25


The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez 12Jameson TooleMarta Gonzalez The Viral Adoption of Information Technologies: Twitter’s Story

S

II

IM

Modeling Adoption: Simulation

NETWORK


The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta GonzalezJameson TooleMarta Gonzalez

S

II

IM

Modeling Adoption: Simulation

Make Network

size, degree, geography, type10%, Poisson, Power-law/pop. Early/Reg

Dynamics• Seed infection• Inf. nodes try to inf. nbr.• Media infects

Analysis• Probabilistic - Many runs• Fit parameters to data.• What parameters matter?

13Jameson TooleMarta Gonzalez The Viral Adoption of Information Technologies: Twitter’s Story



Modeling Adoption: Results

14

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Homopholy

Gia

nt C

ompo

nent

Siz

e

Giant Component Size vs. Homopholy

BiasedUnbiased




15

Parameters

B = .0035No/Exog. Media

Biased/Unbiased Geography

0 20 40 60 80 100 120 140 160 1800

2

4

6

8

10

12

14x 104

Time

Use

rs

Simulation: No Media | Fit to crit. mass

realBiased − No MediaUnbiased − No MediaBiased − Media

0 20 40 60 80 100 120 140 160 1800

0.5

1

1.5

2

2.5x 106

Time

Use

rs

realBiased − No MediaUnbiased − No MediaBiased − Media

100 110 120 130 140 150 160100

110

120

130

140

150

160

Real Critical Mass Achievement

Sim

. Crit

ical

Mas

s Ac

hiev

emen

t

Critical Mass Achievement Prediction

Biased | !r = .003Unbiased | !r = .01




16

Parameters

B = .0035No/Exog. Media

Biased/Unbiased Geography

100 110 120 130 140 150 160100

110

120

130

140

150

160


Sim

. Crit

ical

Mas

s Ac

hiev

emen

t

Critical Mass Achievement Prediction

Biased | !r = .003Unbiased | !r = .01




17

Parameters

B = .0035a = .15

Poisson, GeographyEndog. Media

0 20 40 60 80 100 120 140 1600

0.5

1

Use

rs

Media and Adoption per unit time

0 20 40 60 80 100 120 140 1600

0.5

1

Time

Use

rs

Cumulative Adoption

100 110 120 130 140 150 16090

100

110

120

130

140

150

160


Sim

ulat

ed C

ritic

al M

ass

Achi

evem

ent

Critical Mass Achievement

AdoptersMedia




18

Parameters Insights

Social • Preferences correlated with demographics.• Homopholy plays a large roll in local spread.

Geography • Geographically biased friendships matter.• Different areas respond to influences differently.

Media• Not all news is the same. Hyper-influencials vs. mass media.• Media affects are very strong, on par with word-of mouth.• Endog. media responds to adoption rates.



[Bass, 1969]Bass, F. M. (1969, January). A new product growth for model consumer durables. MANAGEMENT SCIENCE 15(5), 215–227.

[Watts et al., 2005]Watts, D. J., R. Muhamad, D. C. Medina, and P. S. Dodds (2005, August). Multiscale, resurgent epidemics in a hierarchical metapopulation model. Proceedings of the National Academy of Sciences of the United States of America 102(32), 11157–11162

[Valente, 1995]Valente, T. W. (1995, January). Network Models of the Diffusion of Innovations (Quantitative Methods in Communication Subseries). Hampton Press (NJ).

[Leskovec et al., 2007]Leskovec, J., L. A. Adamic, and B. A. Huberman (2007, May). The dynamics of viral marketing. ACM Trans. Web 1.

[Liben-Nowell et al., 2005]Liben-Nowell, D., J. Novak, R. Kumar, P. Raghavan, and A. Tomkins (2005, August). Geographic routing in social networks. Proceedings of the National Academy of Sciences of the United States of America 102(33), 11623–11628.

Selected References



THANK YOU

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