Centrality-based epidemic control in complex social networks

Power law of path multiplicity in complex networks

Complex networks describe a wide range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a vital role in network science. Rather than focusing on the path length or path centrality, here we draw attention to the path multiplicity related to decision-making efficiency, which is defined as the number of shortest paths between node pairs and thus characterizes the routing choice diversity. Notably, through extensive empirical investigations from this new perspective, we surprisingly observe a "hesitant-world" feature along with the "small-world" feature and find a universal power-law of the path multiplicity, meaning that a small number of node pairs possess high path multiplicity. We demonstrate that the power-law of path multiplicity is much stronger than the power-law of node degree, which is known as the scale-free property. Then, we show that these phenomena cannot be captured by existing classical network models. Furthermore, we explore the relationship between the path multiplicity and existing typical network metrics, such as average shortest path length, clustering coefficient, assortativity coefficient, and node centralities. We demonstrate that the path multiplicity is a distinctive network metric. These results expand our knowledge of network structure and provide a novel viewpoint for network design and optimization with significant potential applications in biological, social, and man-made networks.

Network-based control of epidemic via flattening the infection curve: high-clustered vs. low-clustered social networks

Recent studies in network science and control have shown a meaningful relationship between the epidemic processes (e.g., COVID-19 spread) and some network properties. This paper studies how such network properties, namely clustering coefficient and centrality measures (or node influence metrics), affect the spread of viruses and the growth of epidemics over scale-free networks. The results can be used to target individuals (the nodes in the network) to flatten the infection curve. This so-called flattening of the infection curve is to reduce the health service costs and burden to the authorities/governments. Our Monte-Carlo simulation results show that clustered networks are, in general, easier to flatten the infection curve, i.e., with the same connectivity and the same number of isolated individuals they result in more flattened curves. Moreover, distance-based centrality measures, which target the nodes based on their average network distance to other nodes (and not the node degrees), are better choices for targeting individuals for isolation/vaccination.

Discriminating Power of Centrality Measures in Complex Networks

Centrality metrics are one of the most fundamental tools in social network analysis and network science, and various measures for evaluating node importance metrics have been devised. However, the crucial issue of testing the discriminating power of different centrality measures is still open. In this article, we propose to assess the discriminating power of node centrality measures by using the notion of automorphism and orbit: nodes in the same orbit have identical metric scores, while nodes in different orbits should have different centrality values. Under this assumption, we present a benchmark for the discriminating power of node centrality measures. Moreover, we propose an efficient approach to evaluate centrality measures in terms of the discriminating power, which is devoid of finding orbits. Extensive experiments on real and model networks are executed to compare seven commonly used node centrality metrics.

Disease extinction for susceptible-infected-susceptible models on dynamic graphs and hypergraphs

We consider stochastic, individual-level susceptible-infected-susceptible models for the spread of disease, opinion, or information on dynamic graphs and hypergraphs. We set up "snapshot" models where the interactions at any time are independently and identically sampled from an underlying distribution that represents a typical scenario. In the hypergraph case, this corresponds to a new Gilbert-style random hypergraph model. After justifying this modeling regime, we present useful mean field approximations. With an emphasis on the derivation of spectral conditions that determine long-time extinction, we give computational simulations and accompanying theoretical analysis for the exact models and their mean field approximations.

Smart testing and selective quarantine for the control of epidemics

This paper is based on the observation that, during Covid-19 epidemic, the choice of which individuals should be tested has an important impact on the effectiveness of selective confinement measures. This decision problem is closely related to the problem of optimal sensor selection, which is a very active research subject in control engineering. The goal of this paper is to propose a policy to smartly select the individuals to be tested. The main idea is to model the epidemics as a stochastic dynamic system and to select the individual to be tested accordingly to some optimality criteria, e.g. to minimize the probability of undetected asymptomatic cases. Every day, the probability of infection of the different individuals is updated making use of the stochastic model of the phenomenon and of the information collected in the previous days. Simulations for a closed community of 10'000 individuals show that the proposed technique, coupled with a selective confinement policy, can reduce the spread of the disease while limiting the number of individuals confined if compared to the simple contact tracing of positive and to an off-line test selection strategy based on the number of contacts.