Modeling the SIS immunization epidemic on finite size of BA network

An immunization strategy is often defined as the choice of a set of individuals who cannot catch nor transmit the disease. The choice is mainly based on the attributes of nodes in the network topology. In BA networks, the spread threshold value of virus is very small, and decreases with the increase of network scale. If the scale of BA network is infinite, the spread threshold value of virus is zero. In the past decade, the studies about interactions between two pathogens spread show that the interactions can change propagation threshold value of each other, which provides a new thinking of immune method that one kind of spread eradication or inhibition. The immunization agent is put on a few of individual, and spreads out from these individuals on network in SIS propagation method just like a virus. The immunization agent, with certain immune success rate, prevents virus infecting their nodes. On a finite scale of BA network, the analysis and simulation of evolution equation of the model show that immune propagation have a significant impact on the threshold of infectious virus spread and its steady-state density.