Minimizing the social cost of an epidemic
In this paper we quantify the total cost of an epidemic spreading through a social network, accounting for both the immunization and disease costs. Previous research has typically focused on determining the optimal strategy to limit the lifetime of a disease, without considering the cost of such strategies. In the large graph limit, we calculate the exact expected disease cost for a general random graph, and we illustrate it for the specific example of an Erdös-Rényi network. We also give an upper bound on the expected disease cost for finite-size graphs, and show through simulation that the upper bound is tight for Erdös-Rényi networks and graphs with exponential degree distributions. Finally, we study how to optimally perform a one-shot immunization to minimize the social cost of a disease, including both the cost of the disease and the cost of immunization.
© 2012 Springer. The authors would like to thank Professor K. Mani Chandy for his useful comments and suggestions for this paper. This work was supported in part by the National Science Foundation under grants NSF CNS-0846025, CCF-0729203, CNS-0932428 and CCF-1018927, by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech's Lee Center for Advanced Networking.
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