In this paper, we will study a two-stage model by complex networks. The dynamic behaviors of the model on a heterogenous scale-free (SF) network are considered, where the absence of the threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained.

In this paper, we will study a two-stage model on complex networks. The dynamic behaviors of the model on a heterogeneous scale-free (SF) network are considered, where the absence of the threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained. Four immunization strategies, proportional immunization, targeted immunization, acquaintance immunization and active immunization are applied in this model. We show that both targeted and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness. For active immunization, the threshold is easier to apply practically.