Caterina M. Scoglio

An individual-based approach to SIR epidemics in contact networks.

Many approaches have recently been proposed to model the spread of epidemics on networks. For instance, the Susceptible/Infected/Recovered (SIR) compartmental model has successfully been applied to different types of diseases that spread out among humans and animals. When this model is applied on a contact network, the centrality characteristics of the network plays an important role in the spreading process. However, current approaches only consider an aggregate representation of the network structure, which can result in inaccurate analysis. In this paper, we propose a new individual-based SIR approach, which considers the whole description of the network structure. The individual-based approach is built on a continuous time Markov chain, and it is capable of evaluating the state probability for every individual in the network. Through mathematical analysis, we rigorously confirm the existence of an epidemic threshold below which an epidemic does not propagate in the network. We also show that the epidemic threshold is inversely proportional to the maximum eigenvalue of the network. Additionally, we study the role of the whole spectrum of the network, and determine the relationship between the maximum number of infected individuals and the set of eigenvalues and eigenvectors. To validate our approach, we analytically study the deviation with respect to the continuous time Markov chain model, and we show that the new approach is accurate for a large range of infection strength. Furthermore, we compare the new approach with the well-known heterogeneous mean field approach in the literature. Ultimately, we support our theoretical results through extensive numerical evaluations and Monte Carlo simulations.

Topological analysis of the power grid and mitigation strategies against cascading failures

This paper presents a complex systems overview of a power grid network. In recent years, concerns about the robustness of the power grid have grown because of several cascading outages in different parts of the world. In this paper, cascading effect has been simulated on three different networks, the IEEE 300 bus test system, the IEEE 118 bus test system, and the WSCC 179 bus equivalent model. Power Degradation has been discussed as a measure to estimate the damage to the network, in terms of load loss and node loss. A network generator has been developed to generate graphs with characteristics similar to the IEEE standard networks and the generated graphs are then compared with the standard networks to show the effect of topology in determining the robustness of a power grid. Three mitigation strategies, Homogeneous Load Reduction, Targeted Range-Based Load Reduction, and Use of Distributed Renewable Sources in combination with Islanding, have been suggested. The Homogeneous Load Reduction is the simplest to implement but the Targeted Range-Based Load Reduction is the most effective strategy.

Epidemic spreading on weighted contact networks

The study of epidemics is a crucial issue to several areas. An epidemic can have devastating economic and social consequences. A single crop disease in Kansas could destroy the yearly income of many farmers. Previous work using graph theory has determined a universal epidemic threshold found in the graph topology for a binary contact network in the compartmental susceptible-infected (SI) analysis. We expand this threshold to a more realistic measure. A binary uniform level of contact within a society is too idealistic and an improved threshold is found in allowing a spectrum of contact within a contact network. The expanded contact network also allows for asymmetric contact such as a mother caring for her child. Further study in this area should lead to improved simulators, disease modeling, policies and control of infectious diseases and viruses.

Efficient mitigation strategies for epidemics in rural regions.

Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and results of general studies cannot be directly applied since population densities and human mobility factors are very different in rural regions from those in cities. We create a network model of a rural community in Kansas, USA, by collecting data on the contact patterns and computing rates of contact among a sampled population. We model the impact of different mitigation strategies detecting closely connected groups of people and frequently visited locations. Within those groups and locations, we compare the effectiveness of random and targeted vaccinations using a Susceptible-Exposed-Infected-Recovered compartmental model on the contact network. Our simulations show that the targeted vaccinations of only 10% of the sampled population reduced the size of the epidemic by 34.5%. Additionally, if 10% of the population visiting one of the most popular locations is randomly vaccinated, the epidemic size is reduced by 19%. Our results suggest a new implementation of a highly effective strategy for targeted vaccinations through the use of popular locations in rural communities.

Elasticity: topological characterization of robustness in complex networks

Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines a networks survivability in the advent of classical component failures and at the onset of cryptic malicious attacks. To date, robustness metrics are deficient and unfortunately the following dilemmas exist: accurate models necessitate complex analysis while conversely, simple models lack applicability to our definition of robustness. In this paper, we define robustness and present a novel metric, elasticity- a bridge between accuracy and complexity-a link in the chain of network robustness. Additionally, we test-drive the performance of elasticity on Internet topologies and online social networks, and articulate results.

Multicast algorithms in service overlay networks

Overlay routing enhances the reliability and performance of IP networks since it can bypass network congestion and transient outages by forwarding traffic through one or more intermediate overlay nodes. In this paper, two algorithms for multicast applications in service overlay networks are presented. The first algorithm is tailored for source-specific applications such as live video, software and file distribution, replicated database, web site replication, and periodic data delivery; it builds a virtual source-rooted multicast tree to allow one member in the multicast group to send data to the other members. The second algorithm is tailored for group-shared applications such as videoconference, distributed games, file sharing, collaborative groupware, and replicated database; it constructs a virtual shared tree among group members. The objective of both algorithms is to achieve traffic balancing on the overlay network so as to avoid traffic congestion and fluctuation on the underlay network, which cause low performance. To address these problems, the algorithms actively probe the underlay network and compute virtual multicast trees by dynamically selecting the least loaded available paths on the overlay network. This way, network resources are optimally distributed and the number of multicast trees that can be setup is maximized. Both algorithms can offer service differentiation, i.e., provide QoS at application-layer without IP-layer support. The low computational complexity of the proposed algorithms leads to time and resource saving, as shown through extensive simulation experiments.

Optimal topology design for overlay networks

Overlay topology design has been one of the most challenging research areas over the past few years. In this paper, we consider the problem of finding the overlay topology that minimizes a cost function which takes into account the overlay link creation cost and the routing cost. First, we formulate the problem as an Integer Linear Programming (ILP) given a traffic matrix in case of cooperative and non cooperative node behavior. Then, we propose some heuristics to find near-optimal overlay topologies with a reduced complexity. The solutions of the ILP problem in average-size networks have been analyzed, showing that the traffic demands between the nodes affects the decision of creating new overlay links. The heuristics are also compared through extensive numerical evaluation, and guidelines for the selection of the best heuristic as a function of the cost parameters are also provided.

A network-based approach for resistance transmission in bacterial populations

Horizontal transfer of mobile genetic elements (conjugation) is an important mechanism whereby resistance is spread through bacterial populations. The aim of our work is to develop a mathematical model that quantitatively describes this process, and to use this model to optimize antimicrobial dosage regimens to minimize resistance development. The bacterial population is conceptualized as a compartmental mathematical model to describe changes in susceptible, resistant, and transconjugant bacteria over time. This model is combined with a compartmental pharmacokinetic model to explore the effect of different plasma drug concentration profiles. An agent-based simulation tool is used to account for resistance transfer occurring when two bacteria are adjacent or in close proximity. In addition, a non-linear programming optimal control problem is introduced to minimize bacterial populations as well as the drug dose. Simulation and optimization results suggest that the rapid death of susceptible individuals in the population is pivotal in minimizing the number of transconjugants in a population. This supports the use of potent antimicrobials that rapidly kill susceptible individuals and development of dosage regimens that maintain effective antimicrobial drug concentrations for as long as needed to kill off the susceptible population. Suggestions are made for experiments to test the hypotheses generated by these simulations.

A New Metric for Robustness with Respect to Virus Spread

The robustness of a network is depending on the type of attack we are considering. In this paper we focus on the spread of viruses on networks. It is common practice to use the epidemic threshold as a measure for robustness. Because the epidemic threshold is inversely proportional to the largest eigenvalue of the adjacency matrix, it seems easy to compare the robustness of two networks. We will show in this paper that the comparison of the robustness with respect to virus spread for two networks actually depends on the value of the effective spreading rate *** . For this reason we propose a new metric, the viral conductance, which takes into account the complete range of values *** can obtain. In this paper we determine the viral conductance of regular graphs, complete bi-partite graphs and a number of realistic networks.

Modeling and Forecasting Secondary User Activity in Cognitive Radio Networks

Prior research efforts on cognitive radio networks have mainly focused on effective sensing of primary users to determine the availability of a spectrum band for opportunistic use. However, when multiple secondary users compete for a limited amount of spectrum, quality of service (QoS) for these users could degrade due to interference. In this paper, we present an integrated modeling and forecasting framework characterizing spectrum use by secondary users in a cognitive radio network (CRN). In our proposed method, each secondary user in a CRN, first enters a learning and modeling phase where it attempts to estimate the traffic parameters of other secondary users. Following this phase, the secondary user actively participates in opportunistic spectrum use. Assuming a continuous time Markov chain model for secondary user activity, we develop a Kalman filter based approach for estimating the number of secondary users. This estimate is in turn used to predict the number of secondary users in a future time instant. Experimental results show that our proposed forecasting technique provides a good upper bound prediction for the number of secondary users.