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.

Herd immunity and epidemic size in networks with vaccination homophily.

We study how the herd immunity threshold and the expected epidemic size depend on homophily with respect to vaccine adoption. We find that the presence of homophily considerably increases the critical vaccine coverage needed for herd immunity and that strong homophily can push the threshold entirely out of reach. The epidemic size monotonically increases as a function of homophily strength for a perfect vaccine, while it is maximized at a nontrivial level of homophily when the vaccine efficacy is limited. Our results highlight the importance of vaccination homophily in epidemic modeling.

Directed percolation in random temporal network models with heterogeneities.

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similarly to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and, otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low-dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks.

Epidemic spreading and digital contact tracing: Effects of heterogeneous mixing and quarantine failures.

Contact tracing via digital tracking applications installed on mobile phones is an important tool for controlling epidemic spreading. Its effectivity can be quantified by modifying the standard methodology for analyzing percolation and connectivity of contact networks. We apply this framework to networks with varying degree distributions, numbers of application users, and probabilities of quarantine failures. Further, we study structured populations with homophily and heterophily and the possibility of degree-targeted application distribution. Our results are based on a combination of explicit simulations and mean-field analysis. They indicate that there can be major differences in the epidemic size and epidemic probabilities which are equivalent in the normal susceptible-infectious-recovered (SIR) processes. Further, degree heterogeneity is seen to be especially important for the epidemic threshold but not as much for the epidemic size. The probability that tracing leads to quarantines is not as important as the application adoption rate. Finally, both strong homophily and especially heterophily with regard to application adoption can be detrimental. Overall, epidemic dynamics are very sensitive to all of the parameter values we tested out, which makes the problem of estimating the effect of digital contact tracing an inherently multidimensional problem.

Topological analysis of interaction patterns in cancer-specific gene regulatory network: persistent homology approach.

In this study, we investigated cancer cellular networks in the context of gene interactions and their associated patterns in order to recognize the structural features underlying this disease. We aim to propose that the quest of understanding cancer takes us beyond pairwise interactions between genes to a higher-order construction. We characterize the most prominent network deviations in the gene interaction patterns between cancer and normal samples that contribute to the complexity of this disease. What we hope is that through understanding these interaction patterns we will notice a deeper structure in the cancer network. This study uncovers the significant deviations that topological features in cancerous cells show from the healthy one, where the last stage of filtration confirms the importance of one-dimensional holes (topological loops) in cancerous cells and two-dimensional holes (topological voids) in healthy cells. In the small threshold region, the drop in the number of connected components of the cancer network, along with the rise in the number of loops and voids, all occurring at some smaller weight values compared to the normal case, reveals the cancerous network tendency to certain pathways.