The viral adoption of Web application

The Viral Adoption of Web Applications: Twitter’s Story

Jameson Toole Marta Gonzalez Tuesday, June 21, 2011

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The Viral Adoption of Web Information Applications: Technologies: Twitter’s Twitter’s Story Story

Outline Background Descriptive Statistics Modeling Simulation


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The Viral Adoption of Information Technologies: Twitter’s Story

Background Epidemic Models

SI, SIR, etc.


Networks

Diffusion of Innovations

Percolation, SI

Threshold, Bass Model

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Questions What roll does geography play in diffusion? What is a more accurate way to incorporate mass media?


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Data


*Meeyoung Cha - KAIST

Number

Time

Place

3.5 million

March 2006 August 2009

City

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Space: Aggregate Dynamics New users, search and news volume per week 1 Adoption News Google Search

Users / Volume

0.8 0.6 0.4 0.2 0

May 06

Nov 06

Jun 07

Dec 07

Jul 08

Jan 09

Aug 09

Cumulative new users, search and news volume 1

Users / Volume

0.8

Adoption News Google Search

0.6 0.4 0.2 0 May 06


Nov 06

Jun 07

Dec 07

6

Jul 08

Jan 09

Aug 09


Time: Media Influence


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Space: Local Dynamics New Users per week 600 Denver, CO Ann Arbor, MI Arlington, VA

500

Users

400 300 200 100 0

May 06

Nov 06

Jun 07

Dec 07

Jul 08

Jan 09

Aug 09

Jul 08

Jan 09

Aug 09

Cumulative users 10000 Denver, CO Ann Arbor, MI Arlington, VA

Users

8000 6000 4000 2000 0


May 06

Nov 06

Jun 07

Dec 07

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Time: Critical Mass


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Time: Types


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dt dM = αI · (1 + cos(ωt)) dt

Modeling Adoption: Analytically dS = −βSI − γM dt dI = +βSI + γM SI-M MODEL dt dM = αI · (1 + cos(ωt)) dt

VII.

DEL

(8)

(9)

dS = −βSI dt dI = +βSI dt

1 1 + e−βt

I(t)(10) =

dS SI Model Bass Model BASS MODEL = −βSI

VIII.

dS = −βSI dt dI = +βSI dt

IX. VIII. CONCLUSION USION

dt dI = +βSI dt

1 I(t) = 1 + e−βt

CONCLUSION

Logistic growth

(10)

(11) (12)

� I(11) (t) = α + βI(t) 1− I(t) (12)

(13)

Seeding External influence

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

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

ciences of the United States of America 102, 11157 (Augustof2005), ISSN 0027Academy of Sciences the United States of America 102, 11157 (August 2005),

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

/dx.doi.org/10.1073/pnas.0501226102.

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

Toole 8424, http://dx.doi.org/10.1073/pnas.0501226102. ndJameson D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN The Viral Adoption Biology of Information232, Technologies: Story Marta Gonzalez 11 [2] P. S. Dodds and D. J. Watts, Journal of Theoretical 587 Twitter’s (February tp://dx.doi.org/10.1016/j.jtbi.2004.09.006. 2]Tuesday, P. S. Dodds June 21, 2011 and D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN

Modeling Adoption: Simulation I

M

NETWORK

S I


I

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Modeling Adoption: Simulation I

Make Network

size, degree, geography, type

S

10%, Poisson, Power-law/pop. Early/Reg I

Dynamics

• • •

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

Analysis

• • •

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


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M I


Modeling Adoption: Results Giant Component Size vs. Homopholy

Giant Component Size

1 0.8 0.6 0.4 0.2 0


Biased Unbiased

0

0.2

0.4 0.6 Homopholy

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0.8

1


Modeling Adoption: Results 4

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real Biased − No Media Unbiased − No Media Biased − Media

12 10 Users

Parameters

Simulation: No Media | Fit to crit. mass

x 10

B = .0035 No/Exog. Media Biased/Unbiased Geography

8 6 4 2 0

0

20

40

60

80

100

120

140

160

180

Critical Mass Achievement Prediction

Time

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

6

x 10

real Biased − No Media Unbiased − No Media Biased − Media

2

Users

150

1.5

Sim. Critical Mass Achievement

2.5

1

140

130

120

0.5 110

0

0

20

40

60

80

100

120

140

160

Time


15

180

100 100

110

120 130 140 Real Critical Mass Achievement

150

160


Modeling Adoption: Results Parameters

Critical Mass Achievement Prediction 160 Biased | !r = .003

B = .0035 No/Exog. Media Biased/Unbiased Geography

Unbiased | ! = .01 r

Sim. Critical Mass Achievement

150

140

130

120

110

100 100


110

120 130 140 Real Critical Mass Achievement

150

16

160


Modeling Adoption: Results

Users

150 140

Adopters Media 0.5

130

0

120

1

110 100 90 100


160

17

0

20

40

60

80

100

120 140 160

Cumulative Adoption

0.5

0 110 120 130 140 150 Real Critical Mass Achievement

B = .0035 a = .15 Poisson, Geography Endog. Media

Media and Adoption per unit time

1

Users

Simulated Critical Mass Achievement

160

Critical Mass Achievement

Parameters

0

20

40

60

80 100 Time

120 140 160


Modeling Adoption: Results 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.


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Selected References [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.


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THANK YOU


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