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CUUS2079-07 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:17
206 Information Diffusion in Social Media10080604020(^00102030)
t
Population
40 50
S(t)
I(t)
R(t)
Figure 7.13. SIR Model Simulated withS 0 =99, I 0 =1,R 0 =0,β= 0 .01, and
γ= 0 .1.
However, there is no closed-form solution to this integration, and only
numerical approximation is possible. Figure7.13depicts the behavior of
the SIR model for a set of initial parameters.
The two models in the next two subsections are generalized versions
of the two models discussed thus far: SI and SIR. These models allow
individuals to have temporary immunity and to get reinfected.
7.4.4 SIS Model
The SIS model is the same as the SI model, with the addition of infected
nodes recovering and becoming susceptible again (see Figure 7.14). The
differential equations describing the model are
dS
dt
=γI−βIS, (7.42)
dI
dt
=βIS−γI. (7.43)
SI
β1
γ
Figure 7.14. SIS Model.