Optimal response to epidemics and cyber attacks in networks

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.

Mixed-integer nonlinear optimization

“…Applications in communication engineering and computer science include the optimal response to a cyber attack (Goldberg, Leyffer andSafro 2012, Altunay, Leyffer, Linderoth andXie 2011), wireless bandwidth allocation (Bhatia, Segall and Zussman 2006, Sheikh and Ghafoor 2010, Costa-Montenegro, González-Castaño, Rodriguez-Hernández and Burguillo-Rial 2007, selective filtering (Sinha, Yener andYates 2002, Soleimanipour, Zhuang andFreeman 2002), optical network performance optimization (Elwalid, Mitra and Wang 2006), network design with queuing delay constraints (Boorstyn and Frank 1977), and network design topology (Bertsekas andGallager 1987, Chi, Jiang, Horiguchi andGuo 2008), multi-vehicle swarm communication network optimization (Abichandani, Benson and Kam 2008), the design of optimal paths (i.e., minimum time) for robotic arms (Gentilini, Margot and Shimada 2013), the synthesis of periodic waveforms by tripolar pulse codes (Callegari, Bizzarri, Rovatti and Setti 2010), and the solution of MILP under uncertainty of the parameters through robust optimization (Ben-Tal and Nemirovski 1995).…”

Network reliability: Heading out on the highway

“…Indeed, the machinery developed for communications networks can be applied to networks in which links transmit something from nodes to other nodes, such as transportation and distribution networks, spread of an undesirable event such as disease or fire, or signaling pathways in gene expression networks. For example, design for cybersecurity can employ the basic reliability metrics [102], as can methods for probabilistic inference [73]. To avoid writing a book (or encyclopedia), we focus on the basic measures for communications networks through the lens of Networks .…”

Fast response to infection spread and cyber attacks on large-scale networks

“…Introduced as a simplification of the SIR (susceptible-infected-recovered) model in [24], the SIS model has been extensively analyzed in epidemiology and adapted in the cyber security area for analysis of computer viruses propagation [23]. In this paper we follow that general model and the probabilistic version of optimal response model (formulated in [17]) that takes into account the status of all individuals in the network.…”

“…If for some ij ∈ E one of the nodes i or j is solved to be closed, that link does not contribute its w ij to the objective. In general, ( 4) is a nonconvex integer nonlinear program and known to be N P -complete [17].…”