Optimal Containment of Epidemics in Temporal and Adaptive Networks
In this chapter, we focus on the problem of containing the spread of diseases taking place on both temporal and adaptive networks (i.e., networks whose structure changes as a result of the epidemic). We specifically focus on the problem of finding the opt
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Optimal Containment of Epidemics in Temporal and Adaptive Networks Masaki Ogura and Victor M. Preciado
Abstract In this chapter, we focus on the problem of containing the spread of diseases taking place on both temporal and adaptive networks (i.e., networks whose structure changes as a result of the epidemic). We specifically focus on the problem of finding the optimal allocation of containment resources (e.g., vaccines, medical personnel, traffic control resources, etc.) to eradicate epidemic outbreaks over the following three models of temporal and adaptive networks: (i) Markovian temporal networks, (ii) aggregated-Markovian temporal networks, and (iii) stochastically adaptive network models. For each model, we present a rigorous and tractable mathematical framework to efficiently find the optimal distribution of control resources to eliminate the disease. In contrast with other existing results, our results are not based on heuristic control strategies, but on a disciplined analysis using tools from dynamical systems and convex optimization.
11.1 Introduction The containment of spreading processes taking place on complex networks is a major research area with applications in social, biological, and technological systems [3, 31, 71]. The spread of information in on-line social networks, the evolution of epidemic outbreaks in human contact networks, and the dynamics of cascading failures in the electrical grid are relevant examples of these processes. While major advances have been made in this field (see, for example, [34, 42] and references therein), most current results are specifically tailored to study spreading processes taking place on static networks. Cohen et al. [13] proposed a heuristic
M. Ogura () Nara Institute of Science and Technology, 8916-5 Takayama, 630-0192, Ikoma, Nara, Japan e-mail: [email protected] V.M. Preciado University of Pennsylvania, 3330 Walnut Street, 19104, Philadelphia, PA, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 N. Masuda, P. Holme (eds.), Temporal Network Epidemiology, Theoretical Biology, DOI 10.1007/978-981-10-5287-3_11
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vaccination strategy called acquaintance immunization policy and proved it to be much more efficient than random vaccine allocation. In [5], Borgs et al. studied theoretical limits in the control of spreading processes in undirected network with a non-homogeneous distribution of antidotes. Chung et al. [11] studied a heuristic immunization strategy based on the PageRank vector of the contact graph. Preciado et al. [44, 47] studied the problem of determining the optimal allocation of control resources over static networks to efficiently eradicate epidemics described by the networked SIS (Susceptible-Infected-Susceptible) model. This work was later extended in [10, 32, 35, 38, 45, 46, 69, 70] by considering more general epidemic models. Wan et al. developed in [67] a control theoretic framework for disease spreading, which has been recently extended to the case of sparse control str
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