2025-306

Consider the propagation of a virus modeled by the SIS (Susceptible-Infected-Susceptible) system in two distinct networks:

• A Random Network (Erdős-Rényi).
• A Scale-Free Network.

Both networks have the same number of nodes and the same average degree.

Given that the epidemic threshold is defined by the critical spreading rate, below which the virus dies out exponentially, select the correct statement regarding the behavior of this threshold and immunization strategies:

1. Since both networks have the same average degree , the epidemic threshold will be identical for both, as the average connection density determines the initial spreading speed in any topology.
2. The Random Immunization strategy is equally effective in both types of networks, meaning that the same fraction of nodes have to be immunized in both networks to stop the epidemic.
3. In Scale-Free Networks, with degree exponent \(\gamma\) between 2 and 3, the hubs are less relevant, and the network behaves similarly to a random network.
4. In the Scale-Free Network, the epidemic threshold is given by \(\langle k \rangle / \langle k^2 \rangle\).
5. None of the above.

Original idea by: Giancarlo Maldonado Cárdenas