Barabási: Ch. 10 — Spreading Phenomena

In the homogeneous-mixing SI model, which statement correctly describes the analytical solution for the time required to reach a fraction $i(t) = 0.5$?

a) It depends only on the total population size and not on the infection rate $𝛽$

b) It always occurs at the same time, regardless of the initial condition

c) It is inversely proportional to the contact density but not to $𝛽$

d) It increases linearly with the initial number of infected individuals

e) None of the above. 

Original idea by: Gabriel Sato

Barabási: Ch. 8 — Network Robustness

Consider an Erdos-Rényi network with $N=1000$ nodes and an average degree $\langle k \rangle = 8$. The network undergoes a targeted attack (removal of the highest-degree nodes). Approximately what fraction $f_A$ of nodes needs to be removed to fragment the network? Now, consider a scale-free network with same $N=1000$, $\langle k \rangle = 8$, and $\gamma=2.5$. If the fraction calculated for the Erdos-Rényi network is removed from the scale-free network in a targeted attack, what is expected to happen?

a) $f_A \approx 87.5\%$. The scale free network will also require $f_A \approx 87.5\%$ removal, as the $\langle k \rangle$ is the same.

b) $f_A \approx 12.5\%$. The scale free network will be completely fragmented long before the removal of $f_A$.

c) $f_A \approx 87.5\%$. The scale free network will be completely fragmented long before the removal of $f_A$.

d) $f_A \approx 12.5\%$. The scale free network will also require $f_A \approx 12.5\%$ removal, because the attack is targeted.

e) None of the above

Original idea by: Gabriel Sato