Sideward contact tracing and the control of epidemics in large gatherings

Higher-order correlations reveal complex memory in temporal hypergraphs

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. The analysis of human interaction data reveals the existence of coherent and interdependent mesoscopic structures, thus capturing aggregation, fragmentation and nucleation processes in social systems. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the emerging pattern in the data.

Effectiveness of contact tracing on networks with cliques

Contact tracing, the practice of isolating individuals who have been in contact with infected individuals, is an effective and practical way of containing disease spread. Here we show that this strategy is particularly effective in the presence of social groups: Once the disease enters a group, contact tracing not only cuts direct infection paths but can also pre-emptively quarantine group members such that it will cut indirect spreading routes. We show these results by using a deliberately stylized model that allows us to isolate the effect of contact tracing within the clique structure of the network where the contagion is spreading. This will enable us to derive mean-field approximations and epidemic thresholds to demonstrate the efficiency of contact tracing in social networks with small groups. This analysis shows that contact tracing in networks with groups is more efficient the larger the groups are. We show how these results can be understood by approximating the combination of disease spreading and contact tracing with a complex contagion process where every failed infection attempt will lead to a lower infection probability in the following attempts. Our results illustrate how contact tracing in real-world settings can be more efficient than predicted by models that treat the system as fully mixed or the network structure as locally treelike.

Three-layer model for the control of epidemic infection over multiple social networks

Abstract

This paper presents a hierarchical approach for controlling the spread of an epidemic disease. The approach consists of a three-layer architecture where a set of two-layer multiple social networks is governed by a (third) top-layer consisting of an optimal control policy. Each of the two-layer social networks is modeled by a microscopic Markov chain. On top of all the two-layer networks is an optimal control policy that has been developed by using an underlying Markov Decision Process (MDP) model. Mathematical models pertaining to the top-level MDP as well as two-layer microscopic Markov chains have been presented. Practical implementation methodology using the proposed models has also been discussed along with a numerical example. The results in the numerical example illustrate the control of an epidemic using the optimal policy. Directions for further research and characterization of the optimal policy have also been discussed with the help of the same numerical example.

Article Highlights

An optimal approach for controlling the spread of an epidemic infection.The approach is able to model the uncertainties involved in the problem.The approach is able to cater for the underlying social network.

Anomalous finite-size scaling in higher-order processes with absorbing states

Here we study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory [also referred to as the Wentzel-Kramers-Brillouin (WKB) method in some contexts]. We obtain a general expression for the leading and next-to-leading terms of the stationary probability distribution of the fraction of "active" sites as a function of parameters and network size N. We reproduce several results from the literature and, in particular, we derive all the moments of the stationary distribution for the q-susceptible-infected-susceptible (q-SIS) model, i.e., a high-order epidemic model requiring q active ("infected") sites to activate an additional one. We uncover a very rich scenario for the fluctuations of the fraction of active sites, with nontrivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for [1≤q≤3], with a maximal variability at q=2, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability. Moreover, the leading order in a large-deviation approach does not suffice to describe them: next-to-leading terms are essential to capture the intrinsic singularity at the origin of systems with absorbing states. Some possible extensions of this work are also discussed.

Analysing the Effect of Test-and-Trace Strategy in an SIR Epidemic Model

Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and tested independently with some fixed probability. If such a traced individual tests positive it is isolated, and the contact tracing is iterated. This model is analysed using large population approximations, both for the early stage of the epidemic when the "to-be-traced components" of the epidemic behaves like a branching process, and for the main stage of the epidemic where the process of to-be-traced components converges to a deterministic process defined by a system of differential equations. These approximations are used to quantify the effect of testing and of contact tracing on the effective reproduction numbers (for the components as well as for the individuals), the probability of a major outbreak, and the final fraction getting infected. Using numerical illustrations when rates of infection and natural recovery are fixed, it is shown that Test-and-Trace strategy is effective in reducing the reproduction number. Surprisingly, the reproduction number for the branching process of components is not monotonically decreasing in the tracing probability, but the individual reproduction number is conjectured to be monotonic as expected. Further, in the situation where individuals also self-report for testing, the tracing probability is more influential than the screening rate (measured by the fraction infected being screened).