The combination of targeted vaccination and ring vaccination.

Complex networks have become an important tool for investigating epidemic dynamics. A widely concerned research field for epidemics is to develop and study mitigation strategies or control measures. In this paper, we devote our attention to ring vaccination and targeted vaccination and consider the combination of them. Based on the different roles ring vaccination plays in the mixed strategy, the whole parameter space can be roughly divided into two regimes. In one regime, the mixed strategy performs poorly compared with targeted vaccination alone, while in the other regime, the addition of ring vaccination can improve the performance of targeted vaccination. This result gives us the more general and overall comparison between targeted and ring vaccination. In addition, we construct a susceptible-infected-recovered epidemic model coupled with the immunization dynamics on random networks. The comparison between stochastic simulations and numerical simulations confirms the validity of the model we propose.