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

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.

Limited efficacy of forward contact tracing in epidemics

Infectious diseases that spread silently through asymptomatic or pre-symptomatic infections represent a challenge for policy makers. A traditional way of achieving isolation of silent infectors from the community is through forward contact tracing, aimed at identifying individuals that might have been infected by a known infected person. In this work we investigate how efficient this measure is in preventing a disease from becoming endemic. We introduce an SIS-based compartmental model where symptomatic individuals may self-isolate and trigger a contact tracing process aimed at quarantining asymptomatic infected individuals. Imperfect adherence and delays affect both measures. We derive the epidemic threshold analytically and find that contact tracing alone can only lead to a very limited increase of the threshold. We quantify the effect of imperfect adherence and the impact of incentivizing asymptomatic and symptomatic populations to adhere to isolation. Our analytical results are confirmed by simulations on complex networks and by the numerical analysis of a much more complex model incorporating more realistic in-host disease progression.

Spreading dynamics in networks under context-dependent behavior

In some systems, the behavior of the constituent units can create a "context" that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading. In our model, agents actively impede (favor) or not diffusion during an interaction, depending on the behavior they observe among all the peers in the group within which that interaction occurs. We divide the population into two behavioral types and provide a mean-field theory to parametrize mixing patterns of arbitrary type-assortativity within groups of any size. As an application, we examine an epidemic-spreading model with context-dependent adoption of prophylactic tools such as face masks. By analyzing the distributions of groups' size and type-composition, we uncover a rich phenomenology for the basic reproduction number and the endemic state. We analytically show how changing the group organization of contacts can either facilitate or hinder epidemic spreading, eventually moving the system from the subcritical to the supercritical phase and vice versa, depending mainly on sociological factors, such as whether the prophylactic behavior is hardly or easily induced. More generally, our work provides a theoretical foundation to model higher-order contexts and analyze their dynamical implications, envisioning a broad theory of context-dependent interactions that would allow for a new systematic investigation of a variety of complex systems.

Epidemic control in networks with cliques

Social units, such as households and schools, can play an important role in controlling epidemic outbreaks. In this work, we study an epidemic model with a prompt quarantine measure on networks with cliques (a clique is a fully connected subgraph representing a social unit). According to this strategy, newly infected individuals are detected and quarantined (along with their close contacts) with probability f. Numerical simulations reveal that epidemic outbreaks in networks with cliques are abruptly suppressed at a transition point f_{c}. However, small outbreaks show features of a second-order phase transition around f_{c}. Therefore, our model can exhibit properties of both discontinuous and continuous phase transitions. Next, we show analytically that the probability of small outbreaks goes continuously to 1 at f_{c} in the thermodynamic limit. Finally, we find that our model exhibits a backward bifurcation phenomenon.

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.