Robustness of networks against propagating attacks under vaccination strategies

We study the effect of vaccination on the robustness of networks against propagating attacks that obey the susceptible-infected-removed model. By extending the generating function formalism developed by Newman (2005Phys.Rev.Lett.95108701), we analytically determine the robustness of networks that depends on the vaccination parameters. We consider the random defense where nodes are vaccinated randomly and the degree-based defense where hubs are preferentially vaccinated. We show that, when vaccines are inefficient, the random graph is more robust against propagating attacks than the scale-free network. When vaccines are relatively efficient, the scale-free network with the degree-based defense is more robust than the random graph with the random defense and the scale-free network with the random defense.