Social Media Mining: An Introduction

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CUUS2079-07 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:17

7.3 Diffusion of Innovations 199

500 1000 1500

t

A(t)

0 2000 2500 3000

0

50

100

150

200

Figure 7.8. Internal-Influence Model forA 0 =30,β= 10 −^5 ,andP=200.

By solving the differential equation, we arrive at

A(t)=

P−αα(P+−βAA^00 )e−(α+βP)(t−t^0 )

1 +βα(+Pβ−AA 00 )e−(α+βP)(t−t^0 )

, (7.26)

whereA(t=t 0 )=A 0. TheA(t) function for the mixed-influence model is

depicted in Figure7.9.

500 1000 1500

t

A(t)

0 2000 2500 3000

0

50

100

150

200

Figure 7.9. Mixed-Influence Model forP=200,β= 10 −^5 ,A 0 =30, andα= 10 −^3.