Decentralized Protection Strategies against SIS Epidemics in Networks

Defining an optimal protection strategy against viruses, spam propagation or any other kind of contamination process is an important feature for designing new networks and architectures. In this work, we consider decentralized optimal protection strategies when a virus is propagating over a network through a SIS epidemic process. We assume that each node in the network can fully protect itself from infection at a constant cost, or the node can use recovery software, once it is infected. We model our system using a game theoretic framework and find pure, mixed equilibria, and the Price of Anarchy (PoA) in several network topologies. Further, we propose both a decentralized algorithm and an iterative procedure to compute a pure equilibrium in the general case of a multiple communities network. Finally, we evaluate the algorithms and give numerical illustrations of all our results.Comment: accepted for publication in IEEE Transactions on Control of Network System

What Makes a Good Plan? An Efficient Planning Approach to Control Diffusion Processes in Networks

In this paper, we analyze the quality of a large class of simple dynamic resource allocation (DRA) strategies which we name priority planning. Their aim is to control an undesired diffusion process by distributing resources to the contagious nodes of the network according to a predefined priority-order. In our analysis, we reduce the DRA problem to the linear arrangement of the nodes of the network. Under this perspective, we shed light on the role of a fundamental characteristic of this arrangement, the maximum cutwidth, for assessing the quality of any priority planning strategy. Our theoretical analysis validates the role of the maximum cutwidth by deriving bounds for the extinction time of the diffusion process. Finally, using the results of our analysis, we propose a novel and efficient DRA strategy, called Maximum Cutwidth Minimization, that outperforms other competing strategies in our simulations.Comment: 18 pages, 3 figure

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network

INDEMICS: An Interactive High-Performance Computing Framework for Data Intensive Epidemic Modeling

We describe the design and prototype implementation of Indemics (_Interactive; Epi_demic; _Simulation;)—a modeling environment utilizing high-performance computing technologies for supporting complex epidemic simulations. Indemics can support policy analysts and epidemiologists interested in planning and control of pandemics. Indemics goes beyond traditional epidemic simulations by providing a simple and powerful way to represent and analyze policy-based as well as individual-based adaptive interventions. Users can also stop the simulation at any point, assess the state of the simulated system, and add additional interventions. Indemics is available to end-users via a web-based interface. Detailed performance analysis shows that Indemics greatly enhances the capability and productivity of simulating complex intervention strategies with a marginal decrease in performance. We also demonstrate how Indemics was applied in some real case studies where complex interventions were implemented

Epidemic mitigation by statistical inference from contact tracing data

Contact-tracing is an essential tool in order to mitigate the impact of pandemic such as the COVID-19. In order to achieve efficient and scalable contact-tracing in real time, digital devices can play an important role. While a lot of attention has been paid to analyzing the privacy and ethical risks of the associated mobile applications, so far much less research has been devoted to optimizing their performance and assessing their impact on the mitigation of the epidemic. We develop Bayesian inference methods to estimate the risk that an individual is infected. This inference is based on the list of his recent contacts and their own risk levels, as well as personal information such as results of tests or presence of syndromes. We propose to use probabilistic risk estimation in order to optimize testing and quarantining strategies for the control of an epidemic. Our results show that in some range of epidemic spreading (typically when the manual tracing of all contacts of infected people becomes practically impossible, but before the fraction of infected people reaches the scale where a lock-down becomes unavoidable), this inference of individuals at risk could be an efficient way to mitigate the epidemic. Our approaches translate into fully distributed algorithms that only require communication between individuals who have recently been in contact. Such communication may be encrypted and anonymized and thus compatible with privacy preserving standards. We conclude that probabilistic risk estimation is capable to enhance performance of digital contact tracing and should be considered in the currently developed mobile applications.Comment: 21 pages, 7 figure

Protection against Contagion in Complex Networks

In real-world complex networks, harmful spreads, commonly known as contagions, are common and can potentially lead to catastrophic events if uncontrolled. Some examples include pandemics, network attacks on crucial infrastructure systems, and the propagation of misinformation or radical ideas. Thus, it is critical to study the protective measures that inhibit or eliminate contagion in these networks. This is known as the network protection problem. The network protection problem investigates the most efficient graph manipulations (e.g., node and/or edge removal or addition) to protect a certain set of nodes known as critical nodes. There are two types of critical nodes: (1) predefined, based on their importance to the functionality of the network; (2) unknown, whose importance depends on their location in the network structure. For both of these groups and with no assumption on the contagion dynamics, I address three major shortcomings in the current network protection research: namely, scalability, imprecise evaluation metric, and assumption on global graph knowledge. First, to address the scalability issue, I show that local community information affects contagion paths through characteristic path length. The relationship between the two suggests that, instead of global network manipulations, we can disrupt the contagion paths by manipulating the local community of critical nodes. Next, I study network protection of predefined critical nodes against targeted contagion attacks with access to partial network information only. I propose the CoVerD protection algorithm that is fast and successfully increases the attacker’s effort for reaching the target nodes by 3 to 10 times compared to the next best-performing benchmark. Finally, I study the more sophisticated problem of protecting unknown critical nodes in the context of biological contagions, with partial and no knowledge of network structure. In the presence of partial network information, I show that strategies based on immediate neighborhood information give the best trade-off between performance and cost. In the presence of no network information, I propose a dynamic algorithm, ComMit, that works within a limited budget and enforces bursts of short-term restriction on small communities instead of long-term isolation of unaffected individuals. In comparison to baselines, ComMit reduces the peak of infection by 73% and shortens the duration of infection by 90%, even for persistent spreads

Optimal deployment of resources for maximizing impact in spreading processes

The effective use of limited resources for controlling spreading processes on networks is of prime significance in diverse contexts, ranging from the identification of "influential spreaders" for maximizing information dissemination and targeted interventions in regulatory networks, to the development of mitigation policies for infectious diseases and financial contagion in economic systems. Solutions for these optimization tasks that are based purely on topological arguments are not fully satisfactory; in realistic settings the problem is often characterized by heterogeneous interactions and requires interventions over a finite time window via a restricted set of controllable nodes. The optimal distribution of available resources hence results from an interplay between network topology and spreading dynamics. We show how these problems can be addressed as particular instances of a universal analytical framework based on a scalable dynamic message-passing approach and demonstrate the efficacy of the method on a variety of real-world examples