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Minimizing Social Cost of Vaccinating Network SIS Epidemics

Reducing the economic costs (losses) as much as possible is one of the main goals of controlling virus spreading and worm propagation on complex networks. Taking into account the interactions and conflicts of interests among egoistic individuals (nodes) in a network, we introduce the zero-determinant (ZD) strategy into our proposed non-cooperative networking vaccination game with the economic incentive mechanism to optimize the social cost against a susceptible-infected-susceptible (SIS) epidemic process. It is critical to select an appropriate node as the administrator to implement the social-cost-based ZD strategy. We study the relationship between the coercive capability of the administrator and its degree in some representative networks, and find that the amount of control that the administrator can implement is negative correlated with its degree. After exploring the topological influence on the performance of the ZD strategy in vaccinating the SIS network epidemics, we find that the minimal social cost of the network increases with its average degree. We propose a coarse graining ZD strategy for a multi-community network with numerical simulations to verify the effectiveness of vaccinating the network epidemics.