P1: qVa Trim: 6.125in×9.25in Top: 0.5in Gutter: 0.75in
CUUS2079-07 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:17
7.7 Exercises 213
Information Cascades
- Briefly describe the independent cascade model (ICM).
- What is the objective of cascade maximization? What are the usual
constraints? - Follow the ICM procedure until it converges for the following graph.
Assume that nodeiactivates nodejwheni−j≡1(mod3) and
node 5 is activated at time 0.
4
32
5
6 1
Epidemics
- Discuss the mathematical relationship between the SIR and the SIS
models. - Based on our assumptions in the SIR model, the probability that an
individual remains infected follows a standard exponential distribu-
tion. Describe why this happens. - In the SIR model, what is the most likely time to recover based on
the value ofγ? - In the SIRS model, compute the length of time that an infected
individual is likely to remain infected before he or she recovers. - After the model saturates, how many are infected in the SIS model?