## Abstract

This article introduces novel formulations for optimally responding to epidemics and cyber attacks in networks. In our models, at a given time period, network nodes (e.g., users or computing resources) are associated with probabilities of being infected, and each network edge is associated with some probability of propagating the infection. A decision maker would like to maximize the network's utility; keeping as many nodes open as possible, while satisfying given bounds on the probabilities of nodes being infected in the next time period. The model's relation to previous deterministic optimization models and to both probabilistic and deterministic asymptotic models is explored. Initially, maintaining the stochastic independence assumption of previous work, we formulate a nonlinear integer program with high-order multilinear terms. We then propose a quadratic formulation that provides a lower bound and feasible solution to the original problem. Further motivation for the quadratic model is given by showing that it alleviates the assumption of stochastic independence. The quadratic formulation is then linearized in order to be solved by standard integer programming solvers. We develop valid inequalities for the resulting formulations.

Original language | English |
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Pages (from-to) | 145-158 |

Number of pages | 14 |

Journal | Networks |

Volume | 66 |

Issue number | 2 |

DOIs | |

State | Published - 1 Sep 2015 |

### Bibliographical note

Publisher Copyright:© 2015 Wiley Periodicals, Inc.NETWORKS, Vol. 66(2), 145-158 2015 © 2015 Wiley Periodicals, Inc.

## Keywords

- cutting planes
- cybersecurity
- epidemiology
- network optimization
- nonlinear integer programming
- probability bounds